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<strong>GroMo</strong> | 18,566 followers on LinkedIn. Increasing accessibility of financial products in India. Enabling lakhs of microentrepreneurs to sell financial products | <strong>GroMo</strong> is on the mission to increase the accessibility of financial products across all corners of the Real “Bharat”. The penetration ...

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Authors:
(1) Renan F. F. da Silva, Institute of Computing, University of Campinas;
(2) Yulle G. F. Borges, Institute of Computing, University of Campinas;
(3) Rafael C. S. Schouery, Institute of Computing, University of Campinas. 9 Conclusion Our approaches were quite effective, enabling us to find solutions very close to the optimal solution, even in instances with many items. These results are partly due to the excellent quality of the solutions given by Two-by-Two, which efficiently handles color constraints. Another positive factors are our neighborhoods, which are efficient in quality and time complexity. Lastly, Gilmore and Gomory Formulation has a strong relaxation for the BPP, and this property may extend to CBPP. For a strong relaxation, the values for the optimal fractional and integer solutions are very close, so the patterns used by relaxation probably belong to integer solutions of high quality. Therefore, this is an excellent method to find a good set of patterns for the initial build of GRASP. Acknowledgements This project was supported by the S˜ao Paulo Research Foundation (FAPESP) grants #2015/11937-9 and #2020/06511-0; and the Brazilian National Council For Scientific and Technological Development (CNPq) grants #144257/2019-0, #311039/2020-0 and #425340/2016 3. Declarations Conflict of interest All authors declare that they have no conflicts of interest. References [1] Alsarhan H, Chia D, Christman A, et al (2016) A two-pass algorithm for unordered colored bin packing. Proceedings of the 9th International Conference on Discrete Optimization and Operations Research and Scientific School pp 1–10 [2] Balogh J, B´ek´esi J, Dosa G, et al (2013) Black and white bin packing. In: Erlebach T, Persiano G (eds) Approximation and Online Algorithms. Springer Berlin Heidelberg, Berlin, Heidelberg, pp 131–144, https://doi.org/10.1007/978-3-642-38016-7_12 [3] Balogh J, B´ek´esi J, D´osa G, et al (2015) Offline black and white bin packing. Theoretical Computer Science 596:92–101. https://doi.org/10.1016/j.tcs.2015.06.045 [4] Belov G, Scheithauer G (2006) A branch-and-cut-and-price algorithm for one-dimensional stock cutting and two-dimensional two-stage cutting. European Journal of Operational Research 171(1):85–106. https://doi.org/10.1016/j.ejor.2004.08.036 [5] B¨ohm M, Sgall J, Vesel´y P (2015) Online colored bin packing. In: Bampis E, Svensson O (eds) Approximation and Online Algorithms. Springer International Publishing, Cham, pp 35–46, https://doi.org/10.1007/978-3-319-18263-6_4 [6] B¨ohm M, D´osa G, Epstein L, et al (2018) Colored bin packing: Online algorithms and lower bounds. Algorithmica 80(1):155–184. https://doi.org/10.1007/s00453-016-0248-2 [7] Borges Y, Schouery R (2020) Modelos pseudo polinomiais para o problema do empacotamento colorido. In: Anais do V Encontro de Teoria da Computa¸c˜ao, pp 37–40, https://doi.org/ 10.5753/etc.2020.11084, (In Portuguese) [8] Borges YGF, Schouery RCS, Miyazawa FK (2023) Mathematical models and exact algorithms for the colored bin packing problem. 2305.15291 [9] Brand˜ao F, Pedroso JP (2016) Bin packing and related problems: General arc-flow formulation with graph compression. Computers & Operations Research 69:56–67. https://doi.org/10. 1016/j.cor.2015.11.009 [10] Buljubaˇsi´c M, Vasquez M (2016) Consistent neighborhood search for one-dimensional bin packing and two-dimensional vector packing. Computers & Operations Research 76:12–21. https://doi.org/10.1016/j.cor.2016.06.009 [11] Carvalho JMVd (1999) Exact solution of bin-packing problems using column generation and branch-and-bound. Annals of Operations Research 86(0):629–659. https://doi.org/10. 1023/A:1018952112615 [12] Castelli M, Vanneschi L (2014) A hybrid harmony search algorithm with variable neighbourhood search for the bin-packing problem. 2014 Sixth World Congress on Nature and Biologically Inspired Computing (NaBIC 2014) pp 1–6. https://doi.org/10.1109/NaBIC.2014. 6921849 [13] Chen J, Han X, Bein W, et al (2015) Black and white bin packing revisited. In: Lu Z, Kim D, Wu W, et al (eds) Combinatorial Optimization and Applications. Springer International Publishing, Cham, pp 45–59, https://doi.org/10.1007/978-3-319-26626-8_4 [14] Delorme M, Iori M (2020) Enhanced pseudo-polynomial formulations for bin packing and cutting stock problems. INFORMS Journal on Computing 32(1):101–119. https://doi.org/ 10.1287/ijoc.2018.0880 [15] Delorme M, Iori M, Martello S (2018) Bpplib: a library for bin packing and cutting stock problems. Optimization Letters 12(2):235–250. https://doi.org/10.1007/s11590-017-1192-z [16] Demˇsar J (2006) Statistical comparisons of classifiers over multiple data sets. The Journal of Machine learning research 7:1–30 [17] D´osa G, Epstein L (2014) Colorful bin packing. In: Ravi R, Gørtz IL (eds) Algorithm Theory – SWAT 2014. Springer International Publishing, Cham, pp 170–181, https://doi.org/10. 1007/978-3-319-08404-6_15 [18] Feo TA, Resende MG (1989) A probabilistic heuristic for a computationally difficult set covering problem. Operations Research Letters 8(2):67–71. https://doi.org/https://doi.org/ 10.1016/0167-6377(89)90002-3 [19] Fleszar K, Hindi KS (2002) New heuristics for one-dimensional bin-packing. Computers & Operations Research 29(7):821–839. https://doi.org/10.1016/S0305-0548(00)00082-4 [20] Friedman M (1937) The use of ranks to avoid the assumption of normality implicit in the analysis of variance. Journal of the American Statistical Association 32(200):675–701. https: //doi.org/10.1080/01621459.1937.10503522 [21] Gilmore PC, Gomory RE (1961) A linear programming approach to the cutting-stock problem. Operations Research 9(6):849–859. https://doi.org/10.1287/opre.29.6.1092 [22] Gonz´alez-San-Mart´ın J, Cruz-Reyes L, G´omez-Santill´an C, et al (2023) Comparative Study of Heuristics for the One-Dimensional Bin Packing Problem, Springer Nature Switzerland, Cham, pp 293–305. https://doi.org/10.1007/978-3-031-28999-6_19 [23] Gupta JND, Ho JC (1999) A new heuristic algorithm for the one-dimensional binpacking problem. Production Planning & Control 10(6):598–603. https://doi.org/10.1080/ 095372899232894 [24] Iman RL, Davenport JM (1980) Approximations of the critical region of the fbietkan statistic. Communications in Statistics - Theory and Methods 9(6):571–595. https://doi.org/10. 1080/03610928008827904 [25] Karp RM (1972) Reducibility among Combinatorial Problems, Springer US, Boston, MA, pp 85–103. https://doi.org/10.1007/978-1-4684-2001-2_9 [26] de Lima VL, Iori M, Miyazawa FK (2022) Exact solution of network flow models with strong relaxations. Mathematical Programming pp 1–34. https://doi.org/10.1007/ s10107-022-01785-9 [27] Loh KH, Golden B, Wasil E (2008) Solving the one-dimensional bin packing problem with a weight annealing heuristic. Computers & Operations Research 35(7):2283–2291. https:// doi.org/10.1016/j.cor.2006.10.021 [28] Mladenovi´c N, Hansen P (1997) Variable neighborhood search. Computers & Operations Research 24(11):1097–1100. https://doi.org/10.1016/S0305-0548(97)00031-2 [29] Nemenyi PB (1963) Distribution-free multiple comparisons. PhD thesis, Princeton University [30] Pessoa A, Sadykov R, Uchoa E, et al (2020) A generic exact solver for vehicle routing and related problems. Mathematical Programming 183(1):483–523. https://doi.org/10.1007/ s10107-020-01523-z [31] Vance PH (1998) Branch-and-price algorithms for the one-dimensional cutting stock problem. Computational Optimization and Applications 9(3):211–228. https://doi.org/10.1023/A: 1018346107246 [32] Wei L, Luo Z, Baldacci R, et al (2020) A new branch-and-price-and-cut algorithm for onedimensional bin-packing problems. INFORMS Journal on Computing 32(2):428–443. https://doi.org/10.1287/ijoc.2018.0867 This paper is available on arxiv under CC 4.0 license. Authors: (1) Renan F. F. da Silva, Institute of Computing, University of Campinas; (2) Yulle G. F. Borges, Institute of Computing, University of Campinas; (3) Rafael C. S. Schouery, Institute of Computing, University of Campinas. Authors: (1) Renan F. F. da Silva, Institute of Computing, University of Campinas; (2) Yulle G. F. Borges, Institute of Computing, University of Campinas; (3) Rafael C. S. Schouery, Institute of Computing, University of Campinas. 9 Conclusion Our approaches were quite effective, enabling us to find solutions very close to the optimal solution, even in instances with many items. These results are partly due to the excellent quality of the solutions given by Two-by-Two, which efficiently handles color constraints. Another positive factors are our neighborhoods, which are efficient in quality and time complexity. Lastly, Gilmore and Gomory Formulation has a strong relaxation for the BPP, and this property may extend to CBPP. For a strong relaxation, the values for the optimal fractional and integer solutions are very close, so the patterns used by relaxation probably belong to integer solutions of high quality. Therefore, this is an excellent method to find a good set of patterns for the initial build of GRASP. Acknowledgements This project was supported by the S˜ao Paulo Research Foundation (FAPESP) grants #2015/11937-9 and #2020/06511-0; and the Brazilian National Council For Scientific and Technological Development (CNPq) grants #144257/2019-0, #311039/2020-0 and #425340/2016 3. Acknowledgements Declarations Conflict of interest All authors declare that they have no conflicts of interest. Conflict of interest References [1] Alsarhan H, Chia D, Christman A, et al (2016) A two-pass algorithm for unordered colored bin packing. Proceedings of the 9th International Conference on Discrete Optimization and Operations Research and Scientific School pp 1–10 [2] Balogh J, B´ek´esi J, Dosa G, et al (2013) Black and white bin packing. In: Erlebach T, Persiano G (eds) Approximation and Online Algorithms. Springer Berlin Heidelberg, Berlin, Heidelberg, pp 131–144, https://doi.org/10.1007/978-3-642-38016-7_12 [3] Balogh J, B´ek´esi J, D´osa G, et al (2015) Offline black and white bin packing. Theoretical Computer Science 596:92–101. https://doi.org/10.1016/j.tcs.2015.06.045 [4] Belov G, Scheithauer G (2006) A branch-and-cut-and-price algorithm for one-dimensional stock cutting and two-dimensional two-stage cutting. European Journal of Operational Research 171(1):85–106. https://doi.org/10.1016/j.ejor.2004.08.036 [5] B¨ohm M, Sgall J, Vesel´y P (2015) Online colored bin packing. In: Bampis E, Svensson O (eds) Approximation and Online Algorithms. Springer International Publishing, Cham, pp 35–46, https://doi.org/10.1007/978-3-319-18263-6_4 [6] B¨ohm M, D´osa G, Epstein L, et al (2018) Colored bin packing: Online algorithms and lower bounds. Algorithmica 80(1):155–184. https://doi.org/10.1007/s00453-016-0248-2 [7] Borges Y, Schouery R (2020) Modelos pseudo polinomiais para o problema do empacotamento colorido. In: Anais do V Encontro de Teoria da Computa¸c˜ao, pp 37–40, https://doi.org/ 10.5753/etc.2020.11084, (In Portuguese) [8] Borges YGF, Schouery RCS, Miyazawa FK (2023) Mathematical models and exact algorithms for the colored bin packing problem. 2305.15291 [9] Brand˜ao F, Pedroso JP (2016) Bin packing and related problems: General arc-flow formulation with graph compression. Computers & Operations Research 69:56–67. https://doi.org/10. 1016/j.cor.2015.11.009 [10] Buljubaˇsi´c M, Vasquez M (2016) Consistent neighborhood search for one-dimensional bin packing and two-dimensional vector packing. Computers & Operations Research 76:12–21. https://doi.org/10.1016/j.cor.2016.06.009 [11] Carvalho JMVd (1999) Exact solution of bin-packing problems using column generation and branch-and-bound. Annals of Operations Research 86(0):629–659. https://doi.org/10. 1023/A:1018952112615 [12] Castelli M, Vanneschi L (2014) A hybrid harmony search algorithm with variable neighbourhood search for the bin-packing problem. 2014 Sixth World Congress on Nature and Biologically Inspired Computing (NaBIC 2014) pp 1–6. https://doi.org/10.1109/NaBIC.2014. 6921849 [13] Chen J, Han X, Bein W, et al (2015) Black and white bin packing revisited. In: Lu Z, Kim D, Wu W, et al (eds) Combinatorial Optimization and Applications. Springer International Publishing, Cham, pp 45–59, https://doi.org/10.1007/978-3-319-26626-8_4 [14] Delorme M, Iori M (2020) Enhanced pseudo-polynomial formulations for bin packing and cutting stock problems. INFORMS Journal on Computing 32(1):101–119. https://doi.org/ 10.1287/ijoc.2018.0880 [15] Delorme M, Iori M, Martello S (2018) Bpplib: a library for bin packing and cutting stock problems. Optimization Letters 12(2):235–250. https://doi.org/10.1007/s11590-017-1192-z [16] Demˇsar J (2006) Statistical comparisons of classifiers over multiple data sets. The Journal of Machine learning research 7:1–30 [17] D´osa G, Epstein L (2014) Colorful bin packing. In: Ravi R, Gørtz IL (eds) Algorithm Theory – SWAT 2014. Springer International Publishing, Cham, pp 170–181, https://doi.org/10. 1007/978-3-319-08404-6_15 [18] Feo TA, Resende MG (1989) A probabilistic heuristic for a computationally difficult set covering problem. Operations Research Letters 8(2):67–71. https://doi.org/https://doi.org/ 10.1016/0167-6377(89)90002-3 [19] Fleszar K, Hindi KS (2002) New heuristics for one-dimensional bin-packing. Computers & Operations Research 29(7):821–839. https://doi.org/10.1016/S0305-0548(00)00082-4 [20] Friedman M (1937) The use of ranks to avoid the assumption of normality implicit in the analysis of variance. Journal of the American Statistical Association 32(200):675–701. https: //doi.org/10.1080/01621459.1937.10503522 [21] Gilmore PC, Gomory RE (1961) A linear programming approach to the cutting-stock problem. Operations Research 9(6):849–859. https://doi.org/10.1287/opre.29.6.1092 [22] Gonz´alez-San-Mart´ın J, Cruz-Reyes L, G´omez-Santill´an C, et al (2023) Comparative Study of Heuristics for the One-Dimensional Bin Packing Problem, Springer Nature Switzerland, Cham, pp 293–305. https://doi.org/10.1007/978-3-031-28999-6_19 [23] Gupta JND, Ho JC (1999) A new heuristic algorithm for the one-dimensional binpacking problem. Production Planning & Control 10(6):598–603. https://doi.org/10.1080/ 095372899232894 [24] Iman RL, Davenport JM (1980) Approximations of the critical region of the fbietkan statistic. Communications in Statistics - Theory and Methods 9(6):571–595. https://doi.org/10. 1080/03610928008827904 [25] Karp RM (1972) Reducibility among Combinatorial Problems, Springer US, Boston, MA, pp 85–103. https://doi.org/10.1007/978-1-4684-2001-2_9 [26] de Lima VL, Iori M, Miyazawa FK (2022) Exact solution of network flow models with strong relaxations. Mathematical Programming pp 1–34. https://doi.org/10.1007/ s10107-022-01785-9 [27] Loh KH, Golden B, Wasil E (2008) Solving the one-dimensional bin packing problem with a weight annealing heuristic. Computers & Operations Research 35(7):2283–2291. https:// doi.org/10.1016/j.cor.2006.10.021 [28] Mladenovi´c N, Hansen P (1997) Variable neighborhood search. Computers & Operations Research 24(11):1097–1100. https://doi.org/10.1016/S0305-0548(97)00031-2 [29] Nemenyi PB (1963) Distribution-free multiple comparisons. PhD thesis, Princeton University [30] Pessoa A, Sadykov R, Uchoa E, et al (2020) A generic exact solver for vehicle routing and related problems. Mathematical Programming 183(1):483–523. https://doi.org/10.1007/ s10107-020-01523-z [31] Vance PH (1998) Branch-and-price algorithms for the one-dimensional cutting stock problem. Computational Optimization and Applications 9(3):211–228. https://doi.org/10.1023/A: 1018346107246 [32] Wei L, Luo Z, Baldacci R, et al (2020) A new branch-and-price-and-cut algorithm for onedimensional bin-packing problems. INFORMS Journal on Computing 32(2):428–443. https://doi.org/10.1287/ijoc.2018.0867 This paper is available on arxiv under CC 4.0 license. This paper is available on arxiv under CC 4.0 license. available on arxiv

Fast Neighborhood Search Heuristics for the Colorful Bin Packing Problem: Conclusion and References

Authors:
(1) Renan F. F. da Silva, Institute of Computing, University of Campinas;
(2) Yulle G. F. Borges, Institute of Computing, University of Campinas;
(3) Rafael C. S. Schouery, Institute of Computing, University of Campinas. Abstract The Colorful Bin Packing Problem (CBPP) is a generalization of the Bin Packing Problem (BPP). The CBPP consists of packing a set of items, each with a weight and a color, in bins of limited capacity, minimizing the number of used bins and satisfying the constraint that two items of the same color cannot be packed side by side in the same bin. In this article, we proposed an adaptation of BPP heuristics and new heuristics for the CBPP. Moreover, we propose a set of fast neighborhood search algorithms for CBPP. These neighborhoods are applied in a meta-heuristic approach based on the Variable Neighborhood Search (VNS) and a matheuristic approach that mixes linear programming with the meta-heuristics VNS and Greedy Randomized Adaptive Search (GRASP). The results indicate that our matheuristic is superior to VNS and that both approaches can find near-optimal solutions for a large number instances, even for instances with many items. Keywords: Cutting; Packing; Meta-heuristic; Matheuristic; Neighborhood Search 1 Introduction In the Bin Packing Problem (BPP), there is a set of items and an unlimited set of bins of equal capacity. The objective is to allocate the items in bins, respecting their capacities and minimizing the number of used bins. A generalization of BPP is the Colorful Bin Packing Problem (CBPP), where each item also has a color, and there is an additional constraint that two items of the same color cannot be packed side by side in the same bin. The CBPP was proposed independently by B¨ohm et al [5] and D´osa and Epstein [17], being studied in these articles only from the point of view of online algorithms and approximation algorithms. In particular, B¨ohm et al. show that the adaptations of the BPP classic algorithms First Fit, Best Fit, and Worst Fit for the CBPP have unbounded approximation ratios. Moreover, the authors prove that any online algorithm has an asymptotic competitive ratio of at least 2.5 and show an (absolute) 3.5-competitive algorithm. Also, some years before these works, Balogh et al [2] introduced the Black and White Bin Packing Problem (BWBPP), a particular case of CBPP with only two colors. Just like Balogh et al [2], the following works Chen et al [13], Balogh et al [3], and B¨ohm et al [6] studied approximation algorithms for online and offline versions of BWBPP and CBPP. An exact and linear algorithm for CBPP was proposed by Alsarhan et al [1] for the particular case where all items have zero weight. Later, Borges and Schouery [7], Borges et al [8] proposed four exact algorithms for the CBPP. The first two are pseudo-polynomial formulations based on Arc Flow Formulation for the BPP proposed by Carvalho [11]. On the other hand, the last two are set-partition formulations solved by the VRPSolver framework proposed by Pessoa et al [30]. Balogh et al [2] presents two applications for CBPP. The first one is in packing problems of twodimensional objects of similar widths that must be packed alternately. For example, consider the contents of information and advertisement on video-content sharing portals (like YouTube) and Social Media, which should fit under each other due to the tiny display of smartphones. Thus, the maximum content that fits in one screen is the bin capacity, the content height is the item size, the information contents have the color white, and advertisement contents have the color black. The second application is commercial breaks on radio or TV, where commercials of different lengths and genres must be scheduled for commercial blocks. In this case, the length of the commercial blocks represents the bin capacity, and the commercial duration is the item size. Two commercials of the same genre have the same color to prohibit them from being transmitted in sequence. The CBPP is an NP-hard problem since it is a generalization of BPP (Karp [25]). For dealing with NP-hard problems, in addition to the exact algorithm approach, another interesting approach is heuristic algorithms, in particular, the meta-heuristic approach, which commonly finds high-quality solutions in reasonable computational time. In this article, we study CBPP using meta-heuristic and matheuristic approaches, and, as far as we know, it is the first study in the literature to use this approach. Next, we present a literature review of heuristic approaches to BPP and present our contribution to CBPP. 1.1 Literature Review Many authors have studied BPP and its variants in the literature, using much as exact algorithms as meta-heuristic algorithms. Next, we present a review of the best-known algorithms for BPP and its generalization called the Cutting Stock Problem (CSP). Also, we introduce the main studies that utilize the VNS in the BPP. The BPP exact algorithms are based on two main formulation types: the formulation of Gilmore and Gomory [21] and the Arc Flow Formulation of Carvalho [11]. Other works that use Gilmore and Gomory Formulation are Vance [31], Belov and Scheithauer [4], and Wei et al [32]. On the other hand, for the arc flow, there are the following works Brand˜ao and Pedroso [9], Delorme and Iori [14], and de Lima et al [26]. Conversely, in the heuristic algorithm approach, Fleszar and Hindi [19] study the Variable Neighborhood Search (VNS) meta-heuristic applied to BPP. In this work, the authors use a variation of the heuristic called Minimum Bin Slack, proposed by Gupta and Ho [23] as an initial solution for VNS. This combination proved to be quite powerful and is able to find the optimal solution in 1329 of the 1370 instances evaluated. Sequentially, Loh et al [27] use the Weight Annealing meta-heuristic in the BPP, which finds optimal solutions in all instances used by Fleszar and Hindi. Castelli and Vanneschi [12] propose a BPP heuristic called BPHS, which is used as the initial solution of the VNS. Despite promising results, this combination has shown a lower performance than two previous studies. Finally, Gonz´alez-San-Mart´ın et al [22] presents a comparative study among nineteen heuristic algorithms proposed in the last two decades. The best algorithm in the study was the Consistent Neighborhood Search (CNS) introduced by Buljubaˇsi´c and Vasquez [10], which solved 99.81% of the studied instances. 1.2 Our Contributions In this article, we study the CBPP using five initial construction heuristics. The first two are adaptations of heuristics of the BPP called Best Fit Decreasing and Minimum Bin Slack. The last three are heuristics proposed by us called Good Ordering, Hard BFD, and Two-by-Two. In sequence, we present a meta-heuristic approach for CBPP using the VNS, which uses the previous heuristics to build the initial solution. Lastly, we propose a new matheuristic that mixes linear programming with the meta-heuristics VNS and Greedy Randomized Adaptive Search (GRASP). Our results show that our approaches can find near-optimal solutions for instances of up to 104 items in seconds. In particular, for all instances studied of up to 2 × 103 items and with the known optimal solution, our approaches, in 60 seconds, find solutions that use at most one extra bin than an optimal solution. The article is organized as follows. In Section 2, we present a formal definition for CBPP. Next, in Section 3, we present some convenient notations and prove a proposition that provides easy handling of color constraints. In Section 4, we propose an Auxiliary Algorithm, which we use as a subroutine in some of our algorithms. The initial heuristics, the VNS, and the matheuristic are introduced, respectively, in Sections 5, 6, and 7. Finally, the computational results and conclusion are present in Sections 8 and 9. This paper is available on arxiv under CC 4.0 license. Authors: (1) Renan F. F. da Silva, Institute of Computing, University of Campinas; (2) Yulle G. F. Borges, Institute of Computing, University of Campinas; (3) Rafael C. S. Schouery, Institute of Computing, University of Campinas. Authors: (1) Renan F. F. da Silva, Institute of Computing, University of Campinas; (2) Yulle G. F. Borges, Institute of Computing, University of Campinas; (3) Rafael C. S. Schouery, Institute of Computing, University of Campinas. Abstract The Colorful Bin Packing Problem (CBPP) is a generalization of the Bin Packing Problem (BPP). The CBPP consists of packing a set of items, each with a weight and a color, in bins of limited capacity, minimizing the number of used bins and satisfying the constraint that two items of the same color cannot be packed side by side in the same bin. In this article, we proposed an adaptation of BPP heuristics and new heuristics for the CBPP. Moreover, we propose a set of fast neighborhood search algorithms for CBPP. These neighborhoods are applied in a meta-heuristic approach based on the Variable Neighborhood Search (VNS) and a matheuristic approach that mixes linear programming with the meta-heuristics VNS and Greedy Randomized Adaptive Search (GRASP). The results indicate that our matheuristic is superior to VNS and that both approaches can find near-optimal solutions for a large number instances, even for instances with many items. Keywords: Cutting; Packing; Meta-heuristic; Matheuristic; Neighborhood Search Keywords: 1 Introduction In the Bin Packing Problem (BPP), there is a set of items and an unlimited set of bins of equal capacity. The objective is to allocate the items in bins, respecting their capacities and minimizing the number of used bins. A generalization of BPP is the Colorful Bin Packing Problem (CBPP), where each item also has a color, and there is an additional constraint that two items of the same color cannot be packed side by side in the same bin. The CBPP was proposed independently by B¨ohm et al [5] and D´osa and Epstein [17], being studied in these articles only from the point of view of online algorithms and approximation algorithms. In particular, B¨ohm et al. show that the adaptations of the BPP classic algorithms First Fit, Best Fit, and Worst Fit for the CBPP have unbounded approximation ratios. Moreover, the authors prove that any online algorithm has an asymptotic competitive ratio of at least 2.5 and show an (absolute) 3.5-competitive algorithm. Also, some years before these works, Balogh et al [2] introduced the Black and White Bin Packing Problem (BWBPP), a particular case of CBPP with only two colors. Just like Balogh et al [2], the following works Chen et al [13], Balogh et al [3], and B¨ohm et al [6] studied approximation algorithms for online and offline versions of BWBPP and CBPP. An exact and linear algorithm for CBPP was proposed by Alsarhan et al [1] for the particular case where all items have zero weight. Later, Borges and Schouery [7], Borges et al [8] proposed four exact algorithms for the CBPP. The first two are pseudo-polynomial formulations based on Arc Flow Formulation for the BPP proposed by Carvalho [11]. On the other hand, the last two are set-partition formulations solved by the VRPSolver framework proposed by Pessoa et al [30]. Balogh et al [2] presents two applications for CBPP. The first one is in packing problems of twodimensional objects of similar widths that must be packed alternately. For example, consider the contents of information and advertisement on video-content sharing portals (like YouTube) and Social Media, which should fit under each other due to the tiny display of smartphones. Thus, the maximum content that fits in one screen is the bin capacity, the content height is the item size, the information contents have the color white, and advertisement contents have the color black. The second application is commercial breaks on radio or TV, where commercials of different lengths and genres must be scheduled for commercial blocks. In this case, the length of the commercial blocks represents the bin capacity, and the commercial duration is the item size. Two commercials of the same genre have the same color to prohibit them from being transmitted in sequence. The CBPP is an NP-hard problem since it is a generalization of BPP (Karp [25]). For dealing with NP-hard problems, in addition to the exact algorithm approach, another interesting approach is heuristic algorithms, in particular, the meta-heuristic approach, which commonly finds high-quality solutions in reasonable computational time. In this article, we study CBPP using meta-heuristic and matheuristic approaches, and, as far as we know, it is the first study in the literature to use this approach. Next, we present a literature review of heuristic approaches to BPP and present our contribution to CBPP. 1.1 Literature Review Many authors have studied BPP and its variants in the literature, using much as exact algorithms as meta-heuristic algorithms. Next, we present a review of the best-known algorithms for BPP and its generalization called the Cutting Stock Problem (CSP). Also, we introduce the main studies that utilize the VNS in the BPP. The BPP exact algorithms are based on two main formulation types: the formulation of Gilmore and Gomory [21] and the Arc Flow Formulation of Carvalho [11]. Other works that use Gilmore and Gomory Formulation are Vance [31], Belov and Scheithauer [4], and Wei et al [32]. On the other hand, for the arc flow, there are the following works Brand˜ao and Pedroso [9], Delorme and Iori [14], and de Lima et al [26]. Conversely, in the heuristic algorithm approach, Fleszar and Hindi [19] study the Variable Neighborhood Search (VNS) meta-heuristic applied to BPP. In this work, the authors use a variation of the heuristic called Minimum Bin Slack, proposed by Gupta and Ho [23] as an initial solution for VNS. This combination proved to be quite powerful and is able to find the optimal solution in 1329 of the 1370 instances evaluated. Sequentially, Loh et al [27] use the Weight Annealing meta-heuristic in the BPP, which finds optimal solutions in all instances used by Fleszar and Hindi. Castelli and Vanneschi [12] propose a BPP heuristic called BPHS, which is used as the initial solution of the VNS. Despite promising results, this combination has shown a lower performance than two previous studies. Finally, Gonz´alez-San-Mart´ın et al [22] presents a comparative study among nineteen heuristic algorithms proposed in the last two decades. The best algorithm in the study was the Consistent Neighborhood Search (CNS) introduced by Buljubaˇsi´c and Vasquez [10], which solved 99.81% of the studied instances. 1.2 Our Contributions In this article, we study the CBPP using five initial construction heuristics. The first two are adaptations of heuristics of the BPP called Best Fit Decreasing and Minimum Bin Slack. The last three are heuristics proposed by us called Good Ordering, Hard BFD, and Two-by-Two. In sequence, we present a meta-heuristic approach for CBPP using the VNS, which uses the previous heuristics to build the initial solution. Lastly, we propose a new matheuristic that mixes linear programming with the meta-heuristics VNS and Greedy Randomized Adaptive Search (GRASP). Our results show that our approaches can find near-optimal solutions for instances of up to 104 items in seconds. In particular, for all instances studied of up to 2 × 103 items and with the known optimal solution, our approaches, in 60 seconds, find solutions that use at most one extra bin than an optimal solution. The article is organized as follows. In Section 2, we present a formal definition for CBPP. Next, in Section 3, we present some convenient notations and prove a proposition that provides easy handling of color constraints. In Section 4, we propose an Auxiliary Algorithm, which we use as a subroutine in some of our algorithms. The initial heuristics, the VNS, and the matheuristic are introduced, respectively, in Sections 5, 6, and 7. Finally, the computational results and conclusion are present in Sections 8 and 9. This paper is available on arxiv under CC 4.0 license. This paper is available on arxiv under CC 4.0 license. available on arxiv

Fast Neighborhood Search Heuristics for the Colorful Bin Packing Problem

Go (aka Golang) came to life at Google in 2009. It was designed by a few big names: , who had a large hand in the development of the Java Virtual Machine. Robert Griesemer , who holds a U.S. patent for windowing UI systems, helped build the Plan 9 operating system at Bell Labs. (In fact, the mascots and are remarkably similar because Pike’s wife, Renée French, is a renowned illustrator.) Rob Pike for Plan 9 for Golang , who designed and implemented a little thing called Unix. Ken Thompson In this article, we’ll demonstrate how simple it is to build a RESTful web service in Go. Then, we’ll demonstrate how to deploy this application with Heroku. But before we embark on this journey, let’s talk briefly about you might want to use Go. why Why Go? To build a web service in 2024, why would you choose to Go over another language, like Python or TypeScript? Go’s biggest advantage over those two languages is . Go is a compiled-to-machine-code language. It’s not interpreted like Python, Ruby, or JavaScript. It’s not even compiled into bytecode and run on a virtual machine like Java. Lots of benchmarks show Go to be 40x or 50x faster than applications written in interpreted languages. When it comes to speed, Go applications perform similarly to those written in Rust or C++. speed Go has a , often with only one particular way of doing something. This is appealing to many developers, especially any who have ever been in a development team setting, where squabbles over various ways of doing things eat up precious time. This simplicity drives conformity in a codebase and offers less perplexity when the code. (Believe it or not, most developers spend more of their time code rather than writing it.) simple syntax reading reading Go is a young language, so it comes packed with modern features out of the nursery. You get automatic garbage collection like in Java or Python. You get . You get a . And perhaps most beneficial to network programmers: You get an called . built-in linters, formatters, and unit testing rich network stack in the standard library easy-to-use multi-threading toolkit Goroutines Yes, there are some reasons why not everyone is hot on Go. One common complaint revolves around error handling in Go. Functions in Go can return multiple values, one of which is an error code. This hearkens back to the days of C—before exceptions—and feels admittedly archaic. It is easy to forget to check error codes for every function. It’s also tedious to percolate errors from down in the depths—when you awaken a balrog deep inside your application—up to somewhere manageable. You know you’ve done that. Alright, the Go cheerleading is done. Let’s get to building. Building a simple RESTful web service in Go We’ll build a small API service that provides some text operations that applications commonly need, such as: Encode a given string using a basic Caesar Cipher Determine if a string is a palindrome (Perhaps most importantly) SpongeBob-encode a zinging retort. If you’d rather skip ahead to the finished code for this application, you can find it in this . We’re not going to go through line by line, but we’ll talk about the important bits. GitHub repo main.go Let’s start with the main function, the bootstrapping code of the service: func main() {
	http.HandleFunc("/is-palindrome", palindromeHandler)
	http.HandleFunc("/rot13", rot13Handler)
	http.HandleFunc("/spongebob", spongebobHandler)
	http.HandleFunc("/health", healthHandler)

	appPort := ":" + os.Getenv("PORT")
	if appPort == ":" {
		appPort = ":8080"
	}
	err := http.ListenAndServe(appPort, nil)
	if err != nil {
		return
	}
} As we mentioned, one of Go’s powerful features is the expressive standard library. You don’t need any third-party dependencies to quickly get a basic RESTful service up and running. With , you can easily define your routes and assign handlers to the requests that are routed to those URIs. net/http http.HandleFunc The method kicks off the server, binding it to the port you specify. When we deploy to Heroku, . For our local deployment, we default to . http.ListenAndServe Heroku will handle setting the PORT var in the environment 8080 Let’s look at a handler: func spongebobHandler(w http.ResponseWriter, r *http.Request) {
	decoder := json.NewDecoder(r.Body)
	var t requestPayload
	err := decoder.Decode(&t)
	if err != nil {
		panic(err)
	}

	result := map[string]string{
		"original":  *t.Input,
		"spongebob": spongebob(*t.Input),
	}

	w.Header().Set("Content-Type", "application/json")
	err = json.NewEncoder(w).Encode(result)
	if err != nil {
		return
	}
} Our handler needs to do the work of taking the JSON body of the request and parsing it into a Go struct defined outside of this snippet. Then, it needs to build the result from other functions that transform the input string into a SpongeBob utterance. Again, none of the libraries here are third-party dependencies; they all come standard with Go. You can see the prevalence of error handling here via error codes, as working with takes up a large part of the code real estate. err $ go run main.go Then, we send a GET request to : /health $ curl -s http://localhost:8080/health We receive a JSON response indicating the service is up and healthy. That’s it—one file with roughly 100 lines of actual code, and you have a working Go RESTful microservice! Deploying your Go service to Heroku Running the service on your laptop is OK, I guess. But you know what would be really cool? Running it on the web, that’s what. These days, we have lots of options for how to host a service like this. You could build out your own infrastructure using AWS or Azure, but that quickly gets complicated and expensive. Lately, I’ve been turning more and more to . As a platform-as-a-service (PaaS), it’s a low-hassle, low-cost option that allows me to deploy applications to the cloud quickly. Heroku When I’m doing testing and development, I use their Eco Dyno plan to get 1000 dyno hours per month for $5. To deploy basic apps to production, I use their Basic Dyno Plan, which costs a max of $7 per month. For frameworks that Heroku supports, the process of deploying right from your local machine to the web is quick and painless. After setting up a Heroku account, I installed the and logged in from the command line. Heroku CLI You can create a new app directly through the CLI, or you can use the web UI. I named my application the same as my GitHub repo: . We’ll think of something snazzier before our IPO, but for now, this will do. golang-text-demo To deploy our GitHub repo to Heroku, we first need to add a remote repository. $ heroku git:remote -a golang-text-demo This creates a new remote location in our GitHub repo, pointing it to the Heroku application we just created. Now, whenever we push our branch to that remote ( ), it will kick off a flurry of activity as Heroku gets to work. git push heroku main Lastly, we add one file called , which specifies our app’s build dependencies (we don’t have any) and build configurations for Heroku. Our file is short and sweet; simply setting the Go version we want Heroku to use: go.mod module golang-text-demo

go 1.22 When we push to our Heroku remote, Heroku initializes all the required resources in the cloud. This may take a minute or two the first time you deploy your app, but the results appear to be cached, reducing the time in subsequent deploys. When your app has successfully deployed, you’ll see output that looks similar to this: This gives us the URL for our deployed Heroku app. Sweet! With a single command, we’ve deployed a Go microservice to the cloud, and it is now accessible anywhere in the world. To interact with it, we simply issue the same curl command we did before, but we use the Heroku app URL instead of . git push localhost The Heroku CLI also gives us access to our application’s logs. It’s almost exactly like working with the tools directly on your local machine. We just run , and we see the latest log lines from Heroku and our application right there in our terminal window. heroku logs -tail Before we finish, let’s briefly highlight the impressive insights that can be gained about your application from the Heroku app dashboard. Sure, there’s the obvious stuff you care about—like how much your resources are costing or whether or not they are functioning. But the metrics section gives you impressive details about the performance of your application in near real time. Somebody better do something about those critical errors… 🥴 Conclusion In this walkthrough, we’ve explored why Go is a great choice for building a modern, low-dependency, and efficient web service. We built a simple API service in Go and demonstrated how to deploy our service using Heroku. As a PaaS, Heroku supports running a wide variety of services, not just Go. With that, you now have the tools needed to get started on your own Go services journey. Don’t wait, get Go-ing! Also published . here

How I Built My First Go App and The Deployed it to Heroku

In nearly all of my recent explorations of Generative AI, I've come to realize how important prompts are. That hasn't necessarily translated me into writing better prompts all the time, but being aware of the problem is at least one step towards correcting it, right? One of the things that I thought would help me personally would be to have a tool to quickly compare and contrast different prompts. Obviously, I could just open up multiple tabs in a browser, but I really wanted something more direct and simplified for my purposes. With that in mind, let me share what I've built. Prompt Tester Prompt Tester is my incredibly imaginatively named tool to... um... test prompts. It begins with one prompt: The idea is that you enter your initial prompt, and then click one or more times to add more prompts. When ready, you can then just click "Generate Results": Before showing some example results, let me talk a bit about how it was built. The Code The backend is an simple Node.js server that handles throwing up the static HTML and responding to the front-end API requests. Once again, I thank Todd Sharp for sharing his initial code with me. Here's the boring simple handling portion: incredibly async function handler(req, res) {
	console.log('Entered handler.', req.method, req.url);

	if(req.method === 'GET' && req.url.indexOf('favicon.ico') === -1) {
		res.writeHead(200, { 'Content-Type':'text/html' });
		res.write(fs.readFileSync('./demo.html'));
		res.end();
	} else if(req.method === 'POST' && req.url === '/api') {

		let body = '';
		req.on('data', chunk => {
			body += chunk.toString();
		});

		req.on('end', async () => {
			body = JSON.parse(body);
			console.log('BODY:\n', JSON.stringify(body, null, '\t'));

			let result = await callGemini(body.prompt);
			res.writeHead(200, { 'Content-Type':'application/json' });
			res.write(JSON.stringify(result));
			res.end();

		});

	}

}

const server = http.createServer(handler);
server.listen(3000);
console.log('Listening on port 3000'); And the part which just passes the prompt off to Google's . In theory, this could be changed to ChatGPT or any other service. callGemini Gemini API const MODEL_NAME = "gemini-pro";
const API_KEY = process.env.GOOGLE_AI_KEY;

const genAI = new GoogleGenerativeAI(API_KEY);
const model = genAI.getGenerativeModel({ model: MODEL_NAME });

async function callGemini(text) {

	const generationConfig = {
		temperature: 0.9,
		topK: 1,
		topP: 1,
		maxOutputTokens: 2048,
	};

	const safetySettings = [
		{ category: HarmCategory.HARM_CATEGORY_HARASSMENT, threshold: HarmBlockThreshold.BLOCK_MEDIUM_AND_ABOVE, },
		{ category: HarmCategory.HARM_CATEGORY_HATE_SPEECH,	threshold: HarmBlockThreshold.BLOCK_MEDIUM_AND_ABOVE, },
		{ category: HarmCategory.HARM_CATEGORY_SEXUALLY_EXPLICIT, threshold: HarmBlockThreshold.BLOCK_MEDIUM_AND_ABOVE, },
		{ category: HarmCategory.HARM_CATEGORY_DANGEROUS_CONTENT, threshold: HarmBlockThreshold.BLOCK_MEDIUM_AND_ABOVE, },
	];

	const parts = [
    	{text},
  	];

	const result = await model.generateContent({
		contents: [{ role: "user", parts }],
		generationConfig,
		safetySettings,
	});

	try {

		if(result.response.promptFeedback && result.response.promptFeedback.blockReason) {

			return { error: `Blocked for ${result.response.promptFeedback.blockReason}` };
		}
		const response = result.response.candidates[0].content.parts[0].text;
		return { response };
	} catch(e) {
		// better handling
		return {
			error:e.message
		}
	}
	
} I'm proud to say that I'm now, finally, doing some basic error handling and trying to expose to the user (me) why a prompt was blocked. The front end is relatively simple. I used for the core CSS (again, thank you Todd) and some vanilla JavaScript to handle adding new prompts and making the calls. Here's the HTML (minus the inline CSS): Milligram <h1>Prompt Tester</h1>

<p>
This tool helps you see the result of multiple prompts at the same time. The idea is to use similar prompts with different phrasing 
to see how it impacts the result.
</p>

<div id="prompts">
</div>

<template id="promptRow">
<div class="row">
	<div class="column column-33"><textarea placeholder="Enter your prompt."></textarea></div>
	<div class="column column-67 result"></div>
</div>
<hr>
</template>


<div class="float-right">
<button id="addPrompt">Add Prompt</button> <button id="generateResults">Generate Results</button>
</div> And then the JavaScript. Notice I used above to handle the prompt layout. This is the first time I've used that tag, and it was relatively easy. <template> let $template, $prompts, $addPromptsBtn, $generateResultsBtn;
let promptCount = 0;

document.addEventListener('DOMContentLoaded', init, false);
async function init() {
	
	$addPromptsBtn = document.querySelector('#addPrompt');
	$addPromptsBtn.addEventListener('click',  addPrompt, false);
	$generateResultsBtn = document.querySelector('#generateResults')
	$generateResultsBtn.addEventListener('click',  generateResults, false);
	$template = document.querySelector('#promptRow');
	$prompts = document.querySelector('#prompts');

	addPrompt();
}

function addPrompt() {
	promptCount++;
	const newPrompt = $template.content.cloneNode(true);
	$prompts.append(newPrompt);
}

async function generateResults() {
	// disable add prompt and generate
	$addPromptsBtn.setAttribute('disabled', 'disabled');
	$generateResultsBtn.setAttribute('disabled', 'disabled');

	let $results = document.querySelectorAll('div.result');
	// clear any previous results
	$results.forEach(r => r.innerHTML = '');

	/*
	gather prompts from the inputs
	*/
	let prompts = [];
	let $fields = document.querySelectorAll('#prompts textarea');
	for(f of $fields) prompts.push(f.value);

	let promises = [];
	for(p of prompts) promises.push(getResult(p));
	let results = await Promise.all(promises);

	// assign results to result area for each, handle errors - later
	// there's a one to one correspondance between our array of results and the result div
	for(let i=0;i<results.length;i++) {
		if(results[i].response) $results[i].innerHTML = marked.parse(results[i].response);
		else if(results[i].error) $results[i].innerHTML = `<strong>Error with Prompt: </strong> ${results[i].error}`;
	}

	$addPromptsBtn.removeAttribute('disabled');
	$generateResultsBtn.removeAttribute('disabled');

}

async function getResult(p) {
	console.log('get result for',p);
	// quick return on empty prompt
	if(p.trim() === '') return { response:'<strong>Enter a prompt.</strong>' };
	let req = await fetch('/api', { method:'POST', body: JSON.stringify({prompt:p.trim()})});
	let result = await req.json();
	return result;
} I that's all pretty simple DOM manipulation and API calling, but definitely let me know in a comment below if something doesn't make sense. Notice I fire off all my API calls at once and wait for them to finish. think Promise.all Also, note I use the library. The results from Google typically have Markdown, and this helps render them nicely in my little web app. marked All of this isn't terribly interesting I think, but let's look at some testing. As I said, I the style of prompt was important. Having it presented directly to me in a tool went a of a long way to reinforcing that. knew heck Sample Result - Gravity Let's start with a simple idea - explaining gravity but for different age groups. Because of the large size of the results, I'm going to use a bit of CSS here to help keep things sane. Prompt: explain gravity to me but make it appropriate for a child in 1st grade Gravity is a superpower that our planet has! It's like an invisible force that makes everything on Earth stay on the ground. Imagine you have a ball in your hand. When you drop it, what happens? It falls down, right? That's because of gravity. Gravity pulls the ball towards the center of the Earth, and so it falls to the ground. Gravity is also what keeps us on the ground. It's what keeps our feet planted firmly on the Earth and prevents us from floating away! Gravity is a very important force. It keeps everything in place and helps things work the way they do. Without gravity, we would all be floating around in space, and things would be very chaotic! Here's a fun way to think about gravity: imagine that the Earth is a giant magnet, and everything on Earth is made of metal. The magnet pulls the metal objects towards it, and that's what keeps them on the ground. Gravity is a very important and interesting force. It's one of the things that makes our planet such a unique and special place to live! Prompt: explain gravity to me but make it appropriate for a child in 7th grade Imagine you're playing with a ball. You toss it up in the air, and it comes back down to you. This is because of gravity. Gravity is a force that pulls things toward each other. It's what keeps you on the ground and what makes things fall down. The amount of gravity between two objects depends on their mass. The more mass an object has, the stronger its gravity is. That's why things like planets and stars have more gravity than things like people and cars. Gravity is also what keeps the planets in orbit around the sun. The sun's gravity is much stronger than the Earth's, so it pulls the Earth towards it. This keeps the Earth moving in a circle around the sun. Gravity is a very important force in our universe. It keeps things in place and makes things move. Without gravity, the planets would fly off into space, and we would all float away. Here are some fun facts about gravity: Gravity is responsible for the tides. The moon's gravity pulls on Earth's oceans, causing them to rise and fall. Gravity is the reason why we have an atmosphere. Without gravity, the air would just float away into space. Gravity is what makes it possible for us to walk. When we walk, our feet push against the ground, and the ground pushes back. This is what propels us forward. Gravity is the reason why we don't float away into space. Earth's gravity pulls us towards its center, keeping us on the ground. Note the typo in the prompt below. Gemini handled it just fine. Prompt: explain gravity to me but make it appropriate for a college-aged student Gravity: The Force of Attraction Gravity is a fundamental force in the universe responsible for keeping celestial bodies, such as planets, moons, and stars, in motion. It is also what keeps us firmly planted to the ground and allows objects to fall when dropped. Newton's Law of Universal Gravitation: The law of universal gravitation states that every object in the universe attracts every other object with a force proportional to the product of their masses and inversely proportional to the square of the distance between them. Mathematically, it can be expressed as: F = Gm1m2/r^2 Where: F is the gravitational force between two objects. G is the gravitational constant (6.674 × 10^-11 N m^2/kg^2). m1 and m2 are the masses of the two objects. r is the distance between the centers of the two objects. Significance of Gravity: The gravitational pull of larger celestial bodies keeps smaller ones revolving around them. For example, Earth's gravity keeps the moon in orbit, while Sun's gravity keeps Earth and other planets in their respective orbits. Keeps Celestial Bodies in Orbit: Gravity between the Earth and the moon causes ocean tides. As the moon orbits Earth, its gravitational pull creates a bulge in the ocean's water on the side facing the moon. Another bulge forms on the opposite side of Earth due to the inertial forces. As the Earth rotates, these bulges move across the planet's surface, resulting in high and low tides. Responsible for Tides: Gravity pulls objects towards Earth's center, preventing them from floating away. This phenomenon allows us to walk, stand, and interact with our environment. Keeps Objects on Earth: Gravity plays a crucial role in the formation of stars and galaxies. The gravitational collapse of massive clouds of gas and dust leads to the creation of new stars. Similarly, the gravitational pull of galaxies keeps them bound together, preventing them from dispersing. Formation of Stars and Galaxies: Albert Einstein's general relativity theory provides a more comprehensive understanding of gravity. It explains that gravity is not a force but rather a curvature of spacetime caused by the presence of mass or energy. This curvature affects the motion of objects, causing them to follow curved paths rather than straight lines. Relativity Theory: In conclusion, gravity is a fundamental force responsible for keeping celestial bodies in motion, tides, and the behavior of objects on Earth. It is a complex phenomenon that has been studied extensively over the centuries, and it continues to fascinate scientists and researchers to this day. Sample Result - Pets For my second test, I started with a basic prompt and then a better version that asked for specific types of details: (Quick editorial note - the tabular data below is a bit messy, but was messy in the original output.) not Prompt: why are cats so much better than dogs? Cats and dogs are both popular pets, and there is no definitive answer to the question of which one is better. Both cats and dogs have their own unique set of advantages and disadvantages, and the best pet for you will depend on your individual needs and preferences. Some people prefer cats because they are generally more independent than dogs. Cats are typically happy to entertain themselves, and they don't need to be walked or taken outside for exercise. This can be a big advantage for people who live in apartments or who have busy schedules. Cats are also known for being clean and tidy animals. They groom themselves regularly, and they typically use the litter box without any problems. This can be a big advantage for people who don't want to deal with the mess and smell of a dog. Of course, there are also some disadvantages to having a cat. Cats can be more expensive than dogs, and they can be more difficult to train. Cats are also more likely to scratch furniture and other household items. Ultimately, the decision of whether to get a cat or a dog is a personal one. There is no right or wrong answer, and the best pet for you will depend on your individual needs and preferences. Here is a table summarizing the key differences between cats and dogs: Characteristic Cat Dog Independence More independent Less independent Exercise needs Does not need to be walked or taken outside Needs to be walked or taken outside Cleanliness Cleans itself regularly Needs to be bathed regularly Training Can be difficult to train Easier to train Scratching May scratch furniture and other household items Does not typically scratch furniture Cost More expensive Less expensive Prompt: why are cats so much better than dogs? explain with a bulleted list of reasons that cover emotional well being and financial aspects Emotional well-being: Independence: Cats are more independent than dogs, which can be a good thing for people who want a pet that doesn't require a lot of attention. Low maintenance: Cats are generally lower maintenance than dogs. They don't need to be walked or groomed as often, and they can be left alone for longer periods of time. Quiet: Cats are generally quieter than dogs, which can be ideal for people who live in apartments or have noise-sensitive neighbors. Therapeutic: Studies have shown that cats can have a calming effect on humans, and they can help to reduce stress and anxiety. Financial aspects: Lower cost: Cats are generally less expensive to own than dogs. They eat less food, they need fewer vet visits, and they don't require as much grooming. Easier to travel with: Cats are easier to travel with than dogs. They can be transported in a carrier, and they don't need to be walked or exercised while you're away. Longer lifespan: Cats have a longer lifespan than dogs, on average. This means that you can enjoy your cat's companionship for many years to come. Sample Result - Chain of Thought Prompting The following test came from an presentation from AWS re:Invent: . I found a lot of great advice from this session, including a good overview of Chain of Thought prompting, where the idea is you provide information about the steps used to solve a problem to help the GenAI engine better solve a prompt. excellent AWS re:Invent 2023 - Prompt engineering best practices for LLMs on Amazon Bedrock (AIM377) Now, the example given in that presentation went like so: Q: Roger has 5 tennis balls. he buys 2 more cans of tennis balls. Each 
can has 3 tennis balls. How many tennis balls does he have now?

A: The answer is 11.

Q. The cafeteria had 23 apples. If they used 20 to make lunch and 
bought 6 more, how many apples do they have? In the presentation, the model in use incorrectly returned 27. In my test, it worked correctly, but I absolutely saw issues with math back when I built my last November. generative AI blackjack advice demo As I said, Gemini handled it fine: But in Prompt Tester, I tried the suggested CoT prompt: A: The answer is 9. Q: Roger has 5 tennis balls. he buys 2 more cans of tennis balls. Each 
can has 3 tennis balls. How many tennis balls does he have now?

A: Roger started with 5 balls. 2 cans of 3 tennis balls each is 6 
tennis balls. 5 + 6 = 11. The answer is 11.

Q. The cafeteria had 23 apples. If they used 20 to make lunch and 
bought 6 more, how many apples do they have? And the result was improved, showing how it got to the answer: A: The cafeteria had 23 apples. They used 20 apples for lunch, which 
means they have 3 apples left. They then bought 6 more apples, so 
they now have a total of 3 + 6 = 9 apples.

The answer is 9. The difference is pretty significant. The Code If this seems useful to you at all, feel free to grab the code from here: . As I mentioned, it shouldn't be that difficult to add or some such and use a different service. If you do, let me know! https://github.com/cfjedimaster/ai-testingzone/tree/main/prompt_tester callChatGPT

How to Test Multiple Variations of Generative AI Prompts

জেনারেটিভ এআই প্রম্পটগুলির একাধিক বৈচিত্র কীভাবে পরীক্ষা করবেন

So testen Sie mehrere Variationen generativer KI-Eingabeaufforderungen

Cómo probar múltiples variaciones de indicaciones de IA generativa

Comment tester plusieurs variantes d'invites d'IA générative

जेनरेटिव एआई प्रॉम्प्ट के एकाधिक विविधताओं का परीक्षण कैसे करें

生成 AI プロンプトの複数のバリエーションをテストする方法

Generative AI 프롬프트의 다양한 변형을 테스트하는 방법

Como testar múltiplas variações de prompts de IA generativos

Как протестировать несколько вариантов подсказок генеративного ИИ

Üretken Yapay Zeka İstemlerinin Çoklu Varyasyonlarını Test Etme

Cách kiểm tra nhiều biến thể của lời nhắc AI sáng tạo

如何测试生成式 AI 提示的多种变体

Every hardcore VR user knows there are two important things when it comes to daily VR gaming: comfort, and battery. One accessory that can improve both of those things is a headstrap that houses a built-in mobile battery, or a “battery strap”. Let’s face it, the stock strap that comes with the Quest 3 is a complete joke. It almost offends me that Meta raises their prices every year and continues to find materials from the dollar store to make their stock strap. Thus, users have no option but to buy a new one, and Meta bets on that. That’s why they keep doing it and they make it simple to plug and play new straps into the headset; . When it comes to VR accessories, I’ve reviewed almost every major thing on the market. they’re too cheap and lazy to make a quality one of their own For the past month, I've tested KIWI's latest offering – the Now, if you're anything like me, the thrill of diving into VR worlds comes with the nagging dread of seeing that low battery warning pop up just as you're getting into the groove. Single-Point-Charging (SPC) Battery Head Strap for the Quest 3. Battery straps aim to solve these problems. With a bunch of cheap options on the market, I want to show you want $79.99 can get you in today’s VR landscape. What We’ll Cover: Specs Design Features Cons Final Verdict I’ve not been compensated by Kiwi in anyway to write this review. However, they did send me their item for free to test for this article. Disclaimer: Specs 6400mAh lithium polymer battery Provides extra 2-4 hours of playtime 1.89 pounds 10.04 x 9.45 x 2.76 inches Memory foam cushion Cable-holding attachment This strap was manufactured by KIWI Design, a China-based company that's been carving its path in the VR scene since 2015. The company is a culmination of years of VR innovation, backed by over 100 patents. What stands out is its claim to balance comfort with extended playtime, addressing a fundamental flaw in VR headsets: their notorious front-heaviness. This strap aims to redistribute that weight, making long sessions in virtual worlds less of a strain and more of an immersive joy. Design Now, let’s talk about the design. The first thing you'll notice is the memory foam padding. It's like a gentle hug for your head, soft yet supportive, a far cry from the standard straps that are $10-20 on AliExpress or Wish. The overall aesthetic is sleek and modern, a white and black strap that has a fair amount of polish. But it's not just about looks; the functionality is where this design truly shines. The balance achieved with this strap significantly reduces the front-heavy drag, showing that KIWI has not only listened to user feedback but acted on it in a meaningful way. With a closer look at this strap, you can tell it’s a blend of thoughtful ergonomics and subtle aesthetics. The smooth, matte finish coupled with the sleek, curving lines gives the strap a futuristic vibe without trying to stand out too much. Form Factor The contours appear to follow the natural shape of the head, suggesting that comfort was at the forefront of KIWI's design philosophy. The integration of the battery itself is seamless, maintaining the headset’s clean lines—a stark contrast to the often bulky add-ons that can feel tacked on rather than part of a unified whole. And let's talk about that battery housing for a second. The way it's positioned and padded, it’s going to give you that counterbalance for the front-heavy feel of most VR headsets, which is exactly what you want for those marathon sessions. In my opinion, this isn't just another clunky power bank slapped onto a strap. It's meticulously crafted. It’s easy to buy a velcro band and strap an external battery back to a standard Quest 3 strap. I’ve done that for years. However, with this strap, I no longer felt much need to add more counterweights on my own. I may dabble in that just to see how it feels, but this is honestly enough for me in terms of counterweight. Features Focusing on features, KIWI’s SPC Battery Head Strap ticks a lot of the boxes we need for long VR gaming sessions. With a 6400mAh battery, KIWI fulfills the promise of doubling or even tripling your playtime. Built-in Power: It’s a plug-and-play system that allows simultaneous charging of both the headset and the battery strap with a single cable. This convenience is the kind of detail that shows KIWI isn’t just manufacturing accessories; they’re crafting seamless user experiences. Single-Point Charging: VR gamers know that the full adjustability of the strap isn’t just about tightness —it’s about angle and positioning. The freedom to position the back cushion precisely where it feels best is a huge plus. Whether you like it high up near the crown of your head or low for a traditional feel, this strap adapts to your preference. Ergonomic Design: It’s been designed to snuggle right into the official carrying case, and by extension, most aftermarket cases. KIWI recognizes that VR enthusiasts are on the move, and they’ve made sure your power-packed head strap doesn’t tie you down. Compatibility and Portability: Cons Even the best-designed products have their drawbacks, and the SPC Battery Head Strap is no exception. It's a bummer that the SPC's innovative charging feature is limited to the . If you're not on board with this specific dock, you're out of luck, missing out on one of the strap's key conveniences. I guess it could work with another dock that uses a similar magnetic pin connector, but there’s a very low chance you’ll find a non-KIWI dock that works with this. External Compatibility: KIWI RGB Vertical Charging Stand : Although the counterweight design is a step in the right direction, it could do with a bit more heft for an even better balance. Some users might find themselves needing to add an extra counterweight for optimal comfort during those longer sessions. Weight Distribution While the seamless integration with KIWI's charging stand is a plus, it also means you're buying into a specific ecosystem. If you decide to switch to another brand's accessories or docks in the future, this head strap's unique charging feature becomes redundant. Exclusive Ecosystem: , the sticker shock is real. Sure, we're getting a head strap that doubles as a lifeline for our VR sessions, thanks to the integrated battery pack. And when you consider that this strap itself becomes literally half of the headset, the price tag starts to seem more reasonable. However, it’s not just VR. If you want to buy a new PS5 controller, the price is around that $80 mark, so this is standard for the gaming industry. Pricing: At $79.99 I always think VR accessories are too damn expensive. It's perfect for those willing to invest in their , but for budget-conscious gamers, it might be a stretch too far, which is likely why Meta has become criminally cheap with their stock headstraps - they know it costs a lot to make a quality one. But let's not sugarcoat it—if your wallet's feeling light, or you're trying to keep your VR spending in check, this head strap is a luxury rather than a necessity. VR experience Despite these points, it's important to consider them in the context of your specific VR setup and how you use it. These cons may not be dealbreakers for everyone, and for those who are fully invested in the KIWI ecosystem, the advantages might far outweigh the limitations. Final Verdict: 8.5/10 Taking all of this into account, the SPC Battery Head Strap from KIWI is a strong contender in the Quest 3 headstraps market. It's thoughtfully designed with user comfort and convenience in mind, backed by a powerful battery to keep you immersed for hours. The single-point charging capability and the ergonomic design make it stand out from the crowd. . It makes the entire setup more cohesive and user-friendly, turning what could be a tangled mess of cables and charging times into a streamlined process. If you're already using or planning to get the KIWI RGB Vertical Charging Stand, this head strap is practically a must-have Overall, for those committed to the KIWI ecosystem, the SPC Battery Head Strap is a wise investment that enhances your VR experience significantly. It offers a comfortable, long-lasting, and hassle-free solution to one of VR gaming's most persistent issues — battery life. My recommendation? If you're looking for a top-tier VR head strap and you're cool with the KIWI universe, go for it. It's an 8.5/10 from me, earning its place as a staple in my daily VR sessions on the Quest 3.

This Quest 3 Battery Strap by Kiwi Design Embarrasses Meta’s Stock Strap

কিউই ডিজাইনের এই কোয়েস্ট 3 ব্যাটারি স্ট্র্যাপটি মেটার স্টক স্ট্র্যাপকে বিব্রত করে

Dieser Quest 3-Batteriegurt von Kiwi Design bringt Metas Schaftgurt in Verlegenheit

Esta correa de batería Quest 3 de Kiwi Design avergüenza a la correa original de Meta

Cette sangle de batterie Quest 3 de Kiwi Design embarrasse la sangle d'origine de Meta

कीवी डिज़ाइन का यह क्वेस्ट 3 बैटरी स्ट्रैप मेटा के स्टॉक स्ट्रैप को शर्मिंदा करता है

Kiwi Design のこの Quest 3 バッテリー ストラップは Meta のストック ストラップを当惑させます

Kiwi Design의 이 Quest 3 배터리 스트랩은 Meta의 스톡 스트랩을 당혹스럽게 합니다.

Esta pulseira de bateria Quest 3 da Kiwi Design embaraça a pulseira de estoque da Meta

Этот ремешок для аккумулятора Quest 3 от Kiwi Design смущает стандартный ремешок Meta

Kiwi Design'ın Bu Quest 3 Pil Kayışı, Meta'nın Stok Kayışını Utandırıyor

Dây đeo pin Quest 3 này của Kiwi Design khiến dây đeo cổ phiếu của Meta xấu hổ

Kiwi Design 设计的这款 Quest 3 电池带让 Meta 的库存表带尴尬不已

While developing products in DevOps teams, we make decisions on which features to develop and how to ship them quite quickly in order to meet customer requirements. Often, these decisions cause more problems in the long run. These kinds of decisions lead to “Technical Debt”. Tech debt is a phenomenon that happens when we prioritize the speed of delivery now, by forgoing everything like code quality or maintainability. Although the agility of delivering products is key to staying relevant in this agile world, we also have to make decisions that ensure the changes are sustainable. In this article, we'll talk about what technical debt is, how to handle quick decisions during development, and give examples to help you understand how to avoid future issues. Tech debt is the extra work that has to be done later because of the technical decisions that we make now. Although it was coined by software developer Ward Cunningham in 1992, it still holds relevance. Usually, Technical debt occurs when teams rush to push new features within deadlines, by writing code without thinking about other considerations such as security, extensibility, etc. Over time, the tech debt increases and becomes difficult to manage. The only way to deal with it then becomes to overhaul the entire system and rewrite everything from scratch. To prevent this scenario, we need to continuously groom the tech debt, and to do that, we need to understand the type of tech debt we are dealing with. Causes of Tech Debt Prudent and deliberate: Prioritizing swift shipping while postponing dealing with their consequences is deliberate debt. This can be taken up when the product is still in the MVP phase or the benefits of quick delivery outweigh potential risks. Reckless and deliberate: Despite knowing how to craft better code, prioritizing rapid delivery over quality leads to reckless and deliberate debt. Prudent and inadvertent: Prudent and inadvertent debt occurs when there's a commitment to producing high-quality code, but this solution was discovered after the feature has been shipped. Reckless and inadvertent: Reckless and inadvertent debt arises when the team tries to implement coding best practices without actually understanding how or why to implement them. This often leads the teams to making a different kind of tech debt. Given these different causes for tech debts, let's try to understand the types of tech debts. These can be broadly categorized under three main heads: Code Related Debts: Code Debt: When we talk about tech debt, code debt is the first thing that comes to mind. It is due to bad coding practices, not following proper coding standards, insufficient code documentation, etc. This type of debt causes problems in terms of maintainability, extensibility, security, etc. Testing Debt: This occurs when the entire testing strategy is inadequate, which includes the absence of unit tests, integration tests, and adequate test coverage. This kind of debt causes us to lose confidence in pushing new code changes and increases the risk of defects and bugs surfacing in production, potentially leading to system failures and customer dissatisfaction. Documentation Debt: This manifests when documentation is either insufficient or outdated. It poses challenges for both new and existing team members in comprehending the system and the rationale behind certain decisions, thereby impeding efficiency in maintenance and development efforts. Architecture Debt: Design Debt: This emerges from flawed or outdated software architecture or design choices. It encompasses overly intricate designs, improper utilization of patterns, and a lack of modularity. Design debt presents obstacles to scalability and the seamless incorporation of new features. Infrastructure Debt: This is linked to the operational environment of the software, encompassing issues such as outdated servers, inadequate deployment practices, or the absence of comprehensive disaster recovery plans. Infrastructure debt can result in performance bottlenecks and increased periods of downtime. Dependency Debt: This arises from reliance on outdated or unsupported third-party libraries, frameworks, or tools. Such dependency exposes the software to potential security vulnerabilities and integration complexities. People/Management Debt: Process Debt: This pertains to inefficient or outdated development processes and methodologies. It encompasses poor communication practices, a deficiency in agile methodologies adoption, and a lack of robust collaboration tools. In addition to this, there is the issue of not automating the process, which greatly increases the agility of software delivery. People/Technical Skills Debt: This is when the team lacks essential skills or knowledge, resulting in the implementation of suboptimal solutions. Investment in training and development initiatives can serve to mitigate this form of debt. Managing and Prioritising the tech debt Technical debt is something that happens when teams are developing products in an agile way. It's like borrowing against the future by taking shortcuts now. But if the team knows about this debt and has a plan to deal with it later, it can actually help prioritize tasks. Whether the debt was intentional or not, it is crucial that the team grooms the technical debt during a backlog refinement session. Here's how you can categorize these tasks: : These are tasks that are crucial for keeping the product running smoothly. Do It Right Away : These tasks contribute to the long-term health of the product, like upgrading outdated systems. A Worthy Investment : These are small tasks that can be fixed easily. They're great for new team members to learn about the product. Quick and Easy Wins : Sometimes, the problem might solve itself or it might not be worth the time and effort to fix, especially if you're planning to upgrade or retire a system. Not Worth Considering When building a new product/feature or facing tight deadlines, it quite common to choose speed delivery over the quality or code sustainability in the long run. Striking balance between the need for quick solutions while maintaining the long term vision for sustainable development practices is the key. Managing technical debt effectively can help ensure the success of your projects in the long term. Like my content? Feel free to reach out to my for interesting content and productive discussions. LinkedIn Also published . here

Managing Technical Debt in Agile Environments

This paper is available on under CC 4.0 license. Arxiv Authors: (1) Md Masud Rana, Department of Mathematics, University of Kentucky; (2) Duc Duy Nguyen, Department of Mathematics, University of Kentucky & ducnguyen@uky.edu. Table of Links Abstract & Introduction Datasets and Results Methods Conclusion, Data and Software Availability, Competing interests, Acknowledgments & References 4 Conclusion The study of protein-protein interactions (PPIs) and the prediction of mutation-induced binding free energy changes are of great importance in understanding the molecular basis of biological processes. The application of geometric graph theory and atom-level graph coloring techniques provides a powerful framework for analyzing biomolecules and capturing their intricate relationships. By utilizing the concept of geometric subgraphs and constructing multi-scale weighted colored geometric subgraphs (MWCGS), we can effectively represent the structural and functional properties of PPIs. The site-specific MWCGS features allow us to extract meaningful patterns and characteristics, shedding light on the effects of mutations and the underlying molecular interactions. In this work, we developed a mutation-induced binding free energy change predictor, called GGL-PPI, by incorporating site-specific MWCGS features for PPIs and gradient-boosting trees. Our method demonstrates superior performance compared to existing methods. The model was validated on three datasets: AB-Bind S645, SKEMPI 1.0 S1131, and SKEMPI 2.0 S4169 and S8338, showcasing its robustness and effectiveness. Furthermore, GGL-PPI was evaluated on a blind test set, the Ssym dataset. To prevent data leakage between the test and training sets, the model was trained on a homology-reduced balanced training set Q3488. This approach ensures the reliability and fairness of the evaluation process. GGL-PPI exhibits the most unbiased and superior performance in predicting binding free energy changes for both direct and reverse mutations, outperforming other existing methods, particularly for reverse mutations. Overall, the results highlight the potential of the GGL-PPI approach in accurately predicting mutation-induced binding free energy changes in protein-protein interactions, providing valuable insights into the molecular mechanisms underlying protein-protein interactions and facilitating drug design and discovery efforts. 5 Data and Software Availability The source code is available at Github: https://github.com/NguyenLabUKY/GGL-Mutation. 6 Competing interests No competing interest is declared. 7 Acknowledgments This work is supported in part by funds from the National Science Foundation (NSF: # 2053284, # 2151802, and # 2245903), and the University of Kentucky Startup Fund. References [1] Dana Chuderland and Rony Seger. 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PPIs and the Prediction of Mutation-Induced Binding Free Energy Changes: What It All Means

I recently got into a discussion on Twitter where I suggested that root-level directories don't make much sense when you're creating applications that are a library. It's conventional wisdom in the community, to suggest putting any code you do not want to expose to other applications inside the directory. And it's true if you're creating something that is meant to be important to other people’s code. The truth is, however, that most people are likely not working on other libraries but rather applications (APIs, web servers, etc). internal not Go internal Take this layout, for example: - app
    - cmd
	- app
	    - main.go
    - internal
    - services
    - repository
    .git
    go.mod
    go.sum A standard repository on github, gitlab etc. What does protect against here? Literally, any other package in this application will be on the same level as the directory, all will be able to import from it. The only situation, where this would not hold is if you were to take this entire code and copy it into another repository. And, honestly, when was the last time you did that? internal internal So, yes, it's technically correct (the best kind) that using root-level directories provides encapsulation (which is good). But, in practice, you don't really get any of the benefits of . If we were to add a view package to our application and wanted to start grouping different views in a sub-package, an directory suddenly starts to make sense. internal internal internal Let me illustrate: - app
    ...omitted
    - views
	layouts.go
	- home
	    home.go
	- about
	    about.go When does internal make sense? If we had some layout components (base, dashboard, etc) in the file that aren't exported, and wouldn't be able to import it as both are no longer part of the view package. If we export it, package in the application can import it, obviously not desirable. But, we can add an directory, export the layout components and encapsulate them from the rest of the application, like so: layouts.go home.go about.go any internal - app
    ...omitted
    - views
	- internal
	    - layouts
		base.go
		dashboard.go
	- home
	    home.go
	- about
	    about.go This is kind of a pet peeve of mine; it isn't really that important now that we have gotten modules (pre-modules was one of the reasons for internal which I will get into in a bit) and as long as you stay consistent about what goes into , it's all good. I prefer to use , as that to me at least better communicates what the directory is for. And I've seen quite a few Go applications in my time now, they either use or and most often contain the same kind of code. Auxiliary packages that are needed for the application as a whole but do not contain core business logic. Code to interact with , wrappers around a library to send mails, a etc. To me, for non-library code, this is the most important thing to get right, what do you expect to find in the directory not as much the same (again, you don't get any of the benefits from internal if you place it in the root)? internal pkg internal pkg aws queue Why do we have internal? To answer that question, we have to go back quite a bit. All the way back to the time before modules, when the creators of Go thought it a great idea to force everyone into their (Google's) preferred way of structuring code. You'd be forced into something like this: - $GOPATH
	- src
	- github.com
	    - user
		- repo
		    - cmd
		    - internal
		    - pkg Before Go 1.4, you could only have local and global components which could lead to frustrating situations where you'd like to have code that is only used within the module it’s defined and not part of the public repository. And in Go 1.4, the solution to this was introduced with the introduction of the directory. The Go compiler will verify that the package doing the import is within the same module as the package being imported. internal With the above structure, using as the default makes a ton of sense as it's quite easy to accidentally expose something that otherwise should've been kept private. But with the introduction of modules, this doesn't apply. Reading makes me think of something internal to a not the application as a whole. internal internal package Does all of this really matter? No. I tend to pick this "fight" just because I think it a bit funny how some people will go out of their way to argue that is the only correct way to do it. internal As argued above, if you're building something that is not meant to be imported into other people’s code, this is good advice. If you're building an application, consider using . But most importantly, be consistent. We spend too much time in software focusing on right and wrong as black and white, but it all depends. If the code that I'm arguing should go into a directory feels more natural for to be in an directory, then by all means, do that. pkg pkg you and your team internal Just be consistent. Also published here.

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