“It’s not just about gaming; it’s about blending different cultural elements, like fashion, and coherent values, like freedom of self-expression, into the gaming world,” says Antonio Palma, Business Director at My Neighbor Alice. We invited Antonio to discuss the story behind one of Web3’...

‘Crossover Potential in Web3 MMOs is Huge’, A Chat With My Neighbor Alice Business Director, Antonio Palma - TheStreet Crypto: Bitcoin and cryptocurrency news, advice, analysis and more

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The Noonification: Will Data Centers Ruin Your Neighborhood? (9/28/2024)

Data centers have become an integral part of the digital age. Unfortunately, many communities realize they are loud, resource-intensive, and visually unappealing only after they’ve been built. Are these buildings neighborhood-ruiners, or are peoples’ concerns overblown? Are Data Centers Already Ruining Neighborhoods? The residents of the sleepy, tree-lined subdivision of Great Oak didn’t realize what was in store for them when construction began for an Amazon Web Services (AWS) data center. This small community in Prince William County, Virginia, soon became the epicenter of an ongoing quarrel between a multinational tech giant and a local homeowners association. Dale Browne, the president of the Great Oak Homeowners Association, said the building’s “constant whir” was “obnoxious” and regularly exceeded 60 decibels (dB), according to measurements taken by some of the neighborhood’s residents. Community members went as far as to stage protests out front, holding signs condemning the noise. Others didn’t object to the building’s construction or operation. While some saw it as an innovative move, others were apathetic because their once-rural oasis had already become a minimetropolis. After all, what’s one data center among highways, power lines, and supersized shopping centers? Still, many residents were unhappy seeing these massive server warehouses pop up nearby. In the neighboring Loudoun County, companies have built them as close as 50 feet — a mere backyard away — from residential properties. Construction has picked up pace in the United States, prompting similar quarrels and concerns nationwide. Why Are Data Centers Popping up Everywhere? Data centers are proliferating despite pockets of concern. The artificial intelligence market — which experts expect will reach $407 billion by 2027 — is one of the main drivers of this trend. Cloud computing technology and the Internet of Things (IoT) are also pushing demand exponentially higher. Many modern technologies are power-hungry and water-thirsty. They need cutting-edge servers and a tremendous amount of storage to function. Whether companies train a machine learning model or store 8K videos on cloud servers, they need data centers. While data center proliferation has been on the rise for years, it only became a well-known point of contention recently when AI’s popularity prompted firms to reinvest in server warehouses. Why are data centers being built in Virginia? Decision-makers are quickly making this state the so-called “data center capital of the world” for good reason. While some counties are inviting tech companies in hopes of inspiring a second Silicon Valley, others are just in convenient locations — the land and labor are cheap in rural areas. Of course, the robust electric and telecommunications infrastructure helps. How These Buildings Impact Nearby Neighborhoods Why are people against data centers? One of the public’s biggest complaints is noise — many don’t realize how loud these buildings are until they live next to one. Other common concerns include resource usage, greenhouse gas emissions, traffic congestion, and potential pollution. Water Drainage Cooling a massive warehouse packed to the brim with servers, routers, storage systems, and processors takes a lot of water. Research shows one large data center can use up between 1 million and 5 million gallons of water daily — which is enough to supply a town of 10,000-50,000 people. Noise Pollution Many data centers have on-site generators. Their cooling systems — essential for keeping hardware operational — contain intake and exhaust fans, which are objectionably loud. They produce between 55 and 85 dB typically. The noise is even more noticeable in rural areas where massive, nondescript buildings replace spaces that used to be forests or farmland. Are data centers noisy at night? Most are since they run around the clock. Even if their volume doesn’t increase after hours, their loudness is more noticeable when it gets quiet. People often describe the noise as a buzzing, tinny whining or low-pitched roar. Even 60 dB — the low end of the typical spectrum — sounds like overlapping conversations or background music. Power Depletion Do data centers use a lot of energy? They are among the most energy-intensive buildings in existence, consuming up to 50 times more power than standard offices. Although some have on-site power sources — diesel generators are a common choice — many rely on the local electrical infrastructure. The Implications of Having a Data Center Nearby Many people are concerned about having a structure that constantly produces 55-85 dB in their backyards — and for good reason. How loud is a data center? While 60 dB is equivalent to conversation, 70 dB seems as loud as a packed business, and 80 dB sounds as loud as a police siren or power tools. At 85 dB and above, hearing loss occurs. There is also concern about intense resource usage. In Maryland, a proposed 70-mile power line that would cut across the state recently angered residents. While environmental advocates and homeowners have vehemently opposed the $424 million project on the grounds of ecosystem and property preservation, it could be up and running as early as 2027. The health of local communities and ecosystems may also be at stake. If data centers use generators for on-site power, they could produce toxic pollutants like nitrogen oxide or diesel exhaust. The cooling system’s noise alone could drive local wildlife away, damaging environmentally sensitive areas. Counties that initially welcomed large technology and cloud computing companies with open arms have wavered after realizing how loud and resource-intensive these structures are. Many may soon raise taxes on hardware, revise their noise ordinances, or enforce strict project review processes to make it worthwhile. Are Communities’ Data Center Fears Justified? The worst-case scenario is using 5 million gallons of water, outputting 85 dB, and producing toxic diesel exhaust daily. That said, most data centers will be noisy and resource-intensive. Air cooling is loud but standard, accounting for 99% of methods in use today. However, that doesn’t mean engineers and operators are unwilling to change to help their unhappy neighbors. The Great Oak Homeowners Association is an excellent example of this fact. While Amazon initially denied the residents’ claims its building was outputting 60 dB — even going as far as to conduct a strategically engineered study to back its claim — it eventually took action. One year after the spat between the AWS data centers and the Great Oak community made headlines, Amazon lengthened its exhaust tubes and directed airflow vertically. Measurements from it and the Homeowners Association revealed the noise leveldropped by 10 dB to about 50 dB, effectively cutting it in half. Currently, it seems decision-makers aren’t considering the long-term repercussions of building near neighborhoods — they’re quickly seizing whatever land is cheap and available. To ease communities’ fears, they should consider their projects’ long-term viability, accounting for how construction and operation will affect nearby residents and local ecosystems. When considering all of the negatives in a vacuum, data centers sound like one of the worst structures a company could ever build. However, they support essential services and help connect people around the world. Most of today’s problems are growing pains — now that engineers and operators know what not to do, they can build better or retrofit existing buildings. For example, while air cooling generates significant noise, immersion cooling — which involves submerging hardware in a non-conductive liquid — apparently sounds considerably quieter in comparison. Engineers could also use on-site renewables to reduce their reliance on the city’s power and water supply, further easing residents’ concerns. What Companies and Communities Can Do Going Forward Gathering and implementing feedback is the only way to permanently ease communities’ concerns. This strategy may even pay off for technology companies because it streamlines site research and lets them know what interventions to prioritize. For example, if people worry about unsightly power lines but don’t care about noise, firms only need to build on-site power. Data centers have become an integral part of the digital age. Unfortunately, many communities realize they are loud, resource-intensive, and visually unappealing only after they’ve been built. Are these buildings neighborhood-ruiners, or are peoples’ concerns overblown? Data centers have become an integral part of the digital age. Unfortunately, many communities realize they are loud, resource-intensive, and visually unappealing only after they’ve been built. Are these buildings neighborhood-ruiners, or are peoples’ concerns overblown? Are Data Centers Already Ruining Neighborhoods? Are Data Centers Already Ruining Neighborhoods? The residents of the sleepy, tree-lined subdivision of Great Oak didn’t realize what was in store for them when construction began for an Amazon Web Services (AWS) data center. This small community in Prince William County, Virginia, soon became the epicenter of an ongoing quarrel between a multinational tech giant and a local homeowners association. Dale Browne, the president of the Great Oak Homeowners Association, said the building’s “constant whir” was “obnoxious” and regularly exceeded 60 decibels (dB), according to measurements taken by some of the neighborhood’s residents. Community members went as far as to stage protests out front, holding signs condemning the noise. regularly exceeded 60 decibels regularly exceeded 60 decibels Others didn’t object to the building’s construction or operation. While some saw it as an innovative move, others were apathetic because their once-rural oasis had already become a minimetropolis. After all, what’s one data center among highways, power lines, and supersized shopping centers? Still, many residents were unhappy seeing these massive server warehouses pop up nearby. In the neighboring Loudoun County, companies have built them as close as 50 feet — a mere backyard away — from residential properties. Construction has picked up pace in the United States, prompting similar quarrels and concerns nationwide. as close as 50 feet as close as 50 feet Why Are Data Centers Popping up Everywhere? Data centers are proliferating despite pockets of concern. The artificial intelligence market — which experts expect will reach $407 billion by 2027 — is one of the main drivers of this trend. Cloud computing technology and the Internet of Things (IoT) are also pushing demand exponentially higher. Many modern technologies are power-hungry and water-thirsty. They need cutting-edge servers and a tremendous amount of storage to function. will reach $407 billion will reach $407 billion Whether companies train a machine learning model or store 8K videos on cloud servers, they need data centers. While data center proliferation has been on the rise for years, it only became a well-known point of contention recently when AI’s popularity prompted firms to reinvest in server warehouses. Why are data centers being built in Virginia? Decision-makers are quickly making this state the so-called “data center capital of the world” for good reason. While some counties are inviting tech companies in hopes of inspiring a second Silicon Valley, others are just in convenient locations — the land and labor are cheap in rural areas. Of course, the robust electric and telecommunications infrastructure helps. land and labor are cheap land and labor are cheap How These Buildings Impact Nearby Neighborhoods Why are people against data centers? One of the public’s biggest complaints is noise — many don’t realize how loud these buildings are until they live next to one. Other common concerns include resource usage, greenhouse gas emissions, traffic congestion, and potential pollution. Water Drainage Cooling a massive warehouse packed to the brim with servers, routers, storage systems, and processors takes a lot of water. Research shows one large data center can use up between 1 million and 5 million gallons of water daily — which is enough to supply a town of 10,000-50,000 people. between 1 million and 5 million gallons between 1 million and 5 million gallons Noise Pollution Many data centers have on-site generators. Their cooling systems — essential for keeping hardware operational — contain intake and exhaust fans, which are objectionably loud. They produce between 55 and 85 dB typically. The noise is even more noticeable in rural areas where massive, nondescript buildings replace spaces that used to be forests or farmland. produce between 55 and 85 dB produce between 55 and 85 dB Are data centers noisy at night? Most are since they run around the clock. Even if their volume doesn’t increase after hours, their loudness is more noticeable when it gets quiet. People often describe the noise as a buzzing, tinny whining or low-pitched roar. Even 60 dB — the low end of the typical spectrum — sounds like overlapping conversations or background music. Power Depletion Do data centers use a lot of energy? They are among the most energy-intensive buildings in existence, consuming up to 50 times more power than standard offices. Although some have on-site power sources — diesel generators are a common choice — many rely on the local electrical infrastructure. up to 50 times more power up to 50 times more power The Implications of Having a Data Center Nearby Many people are concerned about having a structure that constantly produces 55-85 dB in their backyards — and for good reason. How loud is a data center? While 60 dB is equivalent to conversation , 70 dB seems as loud as a packed business, and 80 dB sounds as loud as a police siren or power tools. At 85 dB and above, hearing loss occurs. is equivalent to conversation is equivalent to conversation There is also concern about intense resource usage. In Maryland, a proposed 70-mile power line that would cut across the state recently angered residents. While environmental advocates and homeowners have vehemently opposed the $424 million project on the grounds of ecosystem and property preservation, it could be up and running as early as 2027. proposed 70-mile power line proposed 70-mile power line The health of local communities and ecosystems may also be at stake. If data centers use generators for on-site power, they could produce toxic pollutants like nitrogen oxide or diesel exhaust. The cooling system’s noise alone could drive local wildlife away, damaging environmentally sensitive areas. Counties that initially welcomed large technology and cloud computing companies with open arms have wavered after realizing how loud and resource-intensive these structures are. Many may soon raise taxes on hardware, revise their noise ordinances, or enforce strict project review processes to make it worthwhile. Are Communities’ Data Center Fears Justified? The worst-case scenario is using 5 million gallons of water, outputting 85 dB, and producing toxic diesel exhaust daily. That said, most data centers will be noisy and resource-intensive. Air cooling is loud but standard, accounting for 99% of methods in use today. However, that doesn’t mean engineers and operators are unwilling to change to help their unhappy neighbors. accounting for 99% of methods accounting for 99% of methods The Great Oak Homeowners Association is an excellent example of this fact. While Amazon initially denied the residents’ claims its building was outputting 60 dB — even going as far as to conduct a strategically engineered study to back its claim — it eventually took action. conduct a strategically engineered study conduct a strategically engineered study One year after the spat between the AWS data centers and the Great Oak community made headlines, Amazon lengthened its exhaust tubes and directed airflow vertically. Measurements from it and the Homeowners Association revealed the noise level dropped by 10 dB to about 50 dB, effectively cutting it in half. dropped by 10 dB dropped by 10 dB Currently, it seems decision-makers aren’t considering the long-term repercussions of building near neighborhoods — they’re quickly seizing whatever land is cheap and available. To ease communities’ fears, they should consider their projects’ long-term viability, accounting for how construction and operation will affect nearby residents and local ecosystems. When considering all of the negatives in a vacuum, data centers sound like one of the worst structures a company could ever build. However, they support essential services and help connect people around the world. Most of today’s problems are growing pains — now that engineers and operators know what not to do, they can build better or retrofit existing buildings. For example, while air cooling generates significant noise, immersion cooling — which involves submerging hardware in a non-conductive liquid — apparently sounds considerably quieter in comparison. Engineers could also use on-site renewables to reduce their reliance on the city’s power and water supply, further easing residents’ concerns. apparently sounds considerably quieter apparently sounds considerably quieter What Companies and Communities Can Do Going Forward Gathering and implementing feedback is the only way to permanently ease communities’ concerns. This strategy may even pay off for technology companies because it streamlines site research and lets them know what interventions to prioritize. For example, if people worry about unsightly power lines but don’t care about noise, firms only need to build on-site power.

Will Data Centers Ruin Your Neighborhood?

هل مراكز البيانات ستدمر حيّك؟

¿Centros de Datos ukanakax Barrioman jan walt’ayaspati?

ডেটা সেন্টার কি আপনার প্রতিবেশীকে ধ্বংস করবে?

Hoće li data centri uništiti vaše susjedstvo?

¿Los centros de datos arruinarán su vecindario?

آیا مراکز داده محله شما را خراب خواهند کرد؟

データセンターはあなたの近所を台無しにしますか?

Na Disenthara tša Data di tla Senya Tikologo ya Gago?

¿Centros de Datos nisqakuna Barrioykita waqllichinqachu?

Zničia dátové centrá vaše okolie?

Чи центри обробки даних зруйнують ваше сусідство?

Ma'lumot markazlari sizning mahallangizni buzadimi?

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. 7 Matheuristic 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. 7 Matheuristic 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: Matheuristic Algorithms

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. 6 Variable Neighborhood Search 6.1 Objective function Our objective function f has two levels: the primary objective that seeks to minimize the number of used bins and the secondary objective that seeks the lowest lexicographic order in the residual vector. The residual vector consists of the residual capacity of used bins in non-decreasing order. 6.2 Neighborhoods The VNS performs local searches in neighborhoods, as will be explained below. One relevant factor is the heuristic used in the local search. In our VNS, we use the Best Improvement heuristic, which analyzes all neighbors of a solution and changes to the best neighbor (in terms of the objective function). Our VNS has neighborhoods with the moves: Move-Item, Swap-Items, Swap-and-Move, and MoveTwo-to-One. The number of items changed in one move is constant for these neighborhoods, which just change a constant number of bins and elements in the residual vector (of the second objective function). As we can compare two neighborhoods using their variations in the objective function, it can be done in O(1). Next, we present our neighborhoods, showing optimizations to obtain fast algorithms even for large instances. 6.2.1 Move-Item Neighborhood For the CBPP, one possible algorithm for this neighborhood is to adapt the algorithm used by Fleszar and Hindi [19] for the BPP, that have time complexity O(n2). In this, for each item i, we iterate in the bins given in non-ascending order of residual capacity. Then, we check if the move (i, Br) is valid, where Br is the current bin, and evaluate it if so. Besides, we stop the search when we find the first bin Br such that wi > res(r), since the ordering guarantee that the bins forward also do not have space for the item i. However, it is not necessary to evaluate all moves to find the best one. Applying the Auxiliary Algorithm using the current solution B, it returns the best move for each item i ∈ I, so the best one is the best move between them. It gives us an implementation of the Move-Item Neighborhood with time complexity Θ(n). 6.2.2 Swap-Items Neighborhood Fleszar and Hindi [19] propose for the BPP a Swap-Items Neighborhood with complexity O(n+M), where M is the number of valid moves, which can be very fast in some solutions with little free space. We present the pseudocode of this neighborhood in the Algorithm 4. Although the time complexity of this algorithm is O(n log n + M), in our tests, it performed better than Fleszar and Hindi’s algorithm, especially in large instances. Algorithm 5 presents the pseudocode of this algorithm. 6.2.3 Move-Two-to-One Neighborhood 6.2.4 Swap-and-Move Neighborhood The Swap-and-Move Neighborhood selects three items i, j, k from different bins, then swaps i and j, and moves k to B(i) (its bin before the move). This neighborhood has complexity O(n3) when implemented in the completed way, which offers a low cost-benefit, so we use a restricted version from this one. Instead of testing all the possibilities of k, we test only the heaviest item that can be moved to B(i). The first candidate for k is the heaviest item that fits in B(i), and we can use a binary search to find it. 6.3 Shake Algorithm The Shake Algorithm is a function that makes random moves, seeking to escape from local optimal. In particular, our Shake chooses to execute one of two subroutines with equal probability. In the first subroutine, we performed 20 moves with the constraint that each bin belongs to a maximum of one move. The possible moves are to move one item or swap two items. In the second subroutine, we select two bins and then repack their items in a random order using the Best Fit heuristic. Note that we use a very aggressive Shake since its moves can make the solution much worse. Our Shake is based on the one proposed by Fleszar and Hindi [19] for the BPP, which is equal to the first subroutine without the constraint that bins must be distinct in different moves. The second routine was added because the perturbation generated by the first one can be small in instances with little free space. 6.4 Algorithm 6.5 Neighborhood Ordering 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. 6 Variable Neighborhood Search 6.1 Objective function Our objective function f has two levels: the primary objective that seeks to minimize the number of used bins and the secondary objective that seeks the lowest lexicographic order in the residual vector. The residual vector consists of the residual capacity of used bins in non-decreasing order. 6.2 Neighborhoods The VNS performs local searches in neighborhoods, as will be explained below. One relevant factor is the heuristic used in the local search. In our VNS, we use the Best Improvement heuristic, which analyzes all neighbors of a solution and changes to the best neighbor (in terms of the objective function). Our VNS has neighborhoods with the moves: Move-Item, Swap-Items, Swap-and-Move, and MoveTwo-to-One. The number of items changed in one move is constant for these neighborhoods, which just change a constant number of bins and elements in the residual vector (of the second objective function). As we can compare two neighborhoods using their variations in the objective function, it can be done in O(1). Next, we present our neighborhoods, showing optimizations to obtain fast algorithms even for large instances. 6.2.1 Move-Item Neighborhood For the CBPP, one possible algorithm for this neighborhood is to adapt the algorithm used by Fleszar and Hindi [19] for the BPP, that have time complexity O(n2). In this, for each item i, we iterate in the bins given in non-ascending order of residual capacity. Then, we check if the move (i, Br) is valid, where Br is the current bin, and evaluate it if so. Besides, we stop the search when we find the first bin Br such that wi > res(r), since the ordering guarantee that the bins forward also do not have space for the item i. However, it is not necessary to evaluate all moves to find the best one. Applying the Auxiliary Algorithm using the current solution B, it returns the best move for each item i ∈ I, so the best one is the best move between them. It gives us an implementation of the Move-Item Neighborhood with time complexity Θ(n). 6.2.2 Swap-Items Neighborhood Fleszar and Hindi [19] propose for the BPP a Swap-Items Neighborhood with complexity O(n+M), where M is the number of valid moves, which can be very fast in some solutions with little free space. We present the pseudocode of this neighborhood in the Algorithm 4. Although the time complexity of this algorithm is O(n log n + M), in our tests, it performed better than Fleszar and Hindi’s algorithm, especially in large instances. Algorithm 5 presents the pseudocode of this algorithm. 6.2.3 Move-Two-to-One Neighborhood 6.2.4 Swap-and-Move Neighborhood The Swap-and-Move Neighborhood selects three items i, j, k from different bins, then swaps i and j, and moves k to B(i) (its bin before the move). This neighborhood has complexity O(n3) when implemented in the completed way, which offers a low cost-benefit, so we use a restricted version from this one. Instead of testing all the possibilities of k, we test only the heaviest item that can be moved to B(i). The first candidate for k is the heaviest item that fits in B(i), and we can use a binary search to find it. 6.3 Shake Algorithm The Shake Algorithm is a function that makes random moves, seeking to escape from local optimal. In particular, our Shake chooses to execute one of two subroutines with equal probability. In the first subroutine, we performed 20 moves with the constraint that each bin belongs to a maximum of one move. The possible moves are to move one item or swap two items. In the second subroutine, we select two bins and then repack their items in a random order using the Best Fit heuristic. Note that we use a very aggressive Shake since its moves can make the solution much worse. Our Shake is based on the one proposed by Fleszar and Hindi [19] for the BPP, which is equal to the first subroutine without the constraint that bins must be distinct in different moves. The second routine was added because the perturbation generated by the first one can be small in instances with little free space. 6.4 Algorithm 6.5 Neighborhood Ordering 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

Understanding Variable Neighborhood Search

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. 4 Auxiliary Algorithm 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. 4 Auxiliary Algorithm 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: Auxiliary Algorithm

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. 3 Notations 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. 3 Notations 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: Notations

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

Scientific American Supplement, No. 711, August 17, 1889, by Various, is part of the HackerNoon Books Series. You can jump to any chapter in this book . GIBRALTAR AND NEIGHBORHOOD. here GIBRALTAR AND NEIGHBORHOOD. REPORT BY CONSUL SPRAGUE. Notwithstanding that the political situation of Europe seems to be less threatening among its leading powers, still the uncertainty prevalent among those who are generally considered the arbiters of public affairs has had its influence in contracting the limits of speculative adventure, thereby circumscribing the general course of trade throughout the Mediterranean. In renewing to the department my reports upon the navigation and general commerce of Gibraltar, I beg to state that there has been a tolerably fair current business prevailing in American produce during the past quarter, consisting chiefly in flour, tobacco, and refined petroleum in cases, imported direct from New York. The steady demand for American petroleum confirms the fact that Russian petroleum so far receives but little attention in this market from the regular traders and consumers, so long as supplies from the United States can be regularly imported at reasonable prices. It, however, remains an open question, in the event of lower prices ruling in the Russian petroleum regions, whether American supplies may not later on experience some greater competitive foreign interference. According to the statistical data, steam vessels of all nationalities have continued to make Gibraltar their port of call, not only for orders, but also for replenishing their stock of fuel and provisions, and in larger numbers than ever before, the number in 1888 having reached 5,712 steam vessels, measuring in all 5,969,563 tons, while in 1887 the number was only 5,187 steam vessels, with an aggregate tonnage of 5,372,962. This increase cannot but result in considerable benefit to the coal and maritime traffic, which now forms the most important portion of the general commerce of Gibraltar, in spite of the keen competition it experiences from other British and foreign coaling ports. Freights have also advanced in favor of steamship interests, which, with higher prices in England for coal, have also caused an advance in the price of coal at this port, to the benefit of the coal merchants and others interested in this important trade. At present the ruling price for steam coal is 24 per ton, deliverable from alongside of coal hulks moored in the bay. As near as I have been able to ascertain, the quantity of coal sold in this market during the past year for supplying merchant steam vessels has amounted to about 508,000 tons, which is an increase of about 20,000 tons over the year 1887. s. Notwithstanding that plans have already been submitted to the British government for the construction of a dry dock in Gibraltar, the matter remains somewhat in suspense, since it meets with some opposition on the part of the British government, which, in face of the European fever for general arming, seems more inclined to utilize in another form the expense which such a work would entail upon the imperial government, by replacing the obsolete ordnance recently removed from this fortress and substituting new defenses and guns of the most approved patterns, a matter which has evidently been receiving, for some time past, the special attention of the British military authorities, not doubting that the recent visit to the fortress of the Duke of Cambridge has had some connection with it. In fact, it is reported that the duke has already expressed the opinion that this fortress requires a larger number of artillerymen than are quartered here at present to man its batteries, and it would seem that this recommendation is likely to be carried out. It is yet somewhat too early to venture an opinion regarding the growing crops of cereals in this Spanish neighborhood, but the agricultural and manufacturing interests in Spain have suffered so much in the past years that the general feeling in Spain continues to tend toward establishing increased restrictions against foreign competition in her home markets. There is every probability that the provinces of Malaga and Granada may shortly be granted the privilege of cultivating the tobacco plant under government supervision, as an essay. If properly managed, it may form an important and lucrative business for those interested in land and agricultural pursuits. After many consecutive years of heavy outlays, difficulties, and constant disappointments, a new English company has recently succeeded in commencing the construction of a railway from the neighboring Spanish town of Algeciras to join, via Ronda, the railway station of Bobadilla, on the railroad line toward Malaga. It is presumed that when this railroad will be in running order it will greatly benefit this community, especially if the Spanish government should decide to establish custom houses at Algeciras and the Spanish lines outside the gates of this fortress, similar to those existing on the frontiers of France and Portugal. That some idea may be formed of the constant important daily intercourse which exists between this fortress and Spain, I may state that late police statistics show that 1,887,617 passes were issued to visitors entering this fortress on daily permits during the year 1888, 1,608,004 entering by the land route and 279,613 by sea. I must, however, observe that the larger portion of these visitors consists of laborers, coal heavers, market people, and others engaged in general traffic. A new industry in cork has lately sprung up, in which leading Spanish and native commercial firms in Gibraltar are directly interested to a considerable extent. Extensive warehouses for the storing of cork wood and machinery for the manufacture of bottle corks have recently been established at the Spanish lines, about a mile distant from this fortress, in Spanish territory, where large quantities of cork have already been stored. The cork is obtained and collected from the valuable trees, which are owned by the representatives of some of the oldest nobility of Spain, who have sold the products of their extensive woods to private individuals for periods reaching as far on as ten years, for which concession large cash advances have already been made. The woods commence at a distance of about twelve miles from Gibraltar, and are of considerable extent. The railway now in course of construction passes through these woods, which may ere long offer quite picturesque scenery for travelers, especially when the cork trees are bearing acorns, which form the principal food for the fattening of large herds of swine during certain seasons of the year, in this way, also, contributing to the value of this tree, which, like the other kinds of oak trees, is of long and tardy growth. The tree from which the cork is obtained is somewhat abundant in the mountainous districts of Andalusia. It grows to a height of about 30 feet, and resembles the , or evergreen oak, and attains to a great age. After arriving at a certain state of maturity it periodically sheds its bark, but this bark is found to be of better quality when artificially removed from the tree, which may be effected without injury to the tree itself. After the tree has attained twenty-five years it may be barked, and the operation is afterward repeated once in every seven years. The quality of the cork seems to improve with the increasing age of the tree, which is said to live over one hundred and fifty years. The bark is taken off during July and August. Quercus ilex Cork dust is also obtained from this cork wood, and is much used in the packing of grapes, which fruit is largely shipped from the eastern coast of Spain, especially from Almeria, during the vintage seasons, for the American and British markets.— Reports of U.S. Consuls. About HackerNoon Book Series: We bring you the most important technical, scientific, and insightful public domain books. This book is part of the public domain. Various (2004). Scientific American Supplement, No. 711, August 17, 1889. Urbana, Illinois: Project Gutenberg. Retrieved https://www.gutenberg.org/cache/epub/16972/pg16972-images.html This eBook is for the use of anyone anywhere at no cost and with almost no restrictions whatsoever. You may copy it, give it away or re-use it under the terms of the Project Gutenberg License included with this eBook or online at , located at . www.gutenberg.org https://www.gutenberg.org/policy/license.html

GIBRALTAR AND NEIGHBORHOOD

Metaverse has been one of the bright points in this long, gloomy crypto winter. According to a recent report from , in the first half of 2023, VC firms have invested $707 million into metaverse projects, which is 44% of all Web3 investments in Q1 and Q2 of 2023. DappRadar A down market is frequently a time to build out infrastructure, and metaverse makes up the largest portion of infrastructure investments. Even as the price of virtual land in the metaverse and associated tokens have taken a beating on value, the infinite potential of completely virtual space has too much potential for investors to ignore. However, in order for any of this growth and building out the virtual footprint of the metaverse to make sense, we will need users – and virtual societies to give them focus for positive participation.
Recently, in a hosted by market-maker , I interviewed a panel of experts on building communities in Metaverse including Ayana Palermo, CEO of , Jillian Godsil, founder & Editor-in-Chief of , and Danny Brown Wolf, Chief of Staff for . Twitter Spaces Gotbit Be Future Media Blockleaders Upland Building Metaverse Society 101 In our discussion, we tackled the thorny issue of how to take the infinite potential - and potentially liminal and empty landscape of the metaverse - and fill it with life by building societies with a useful purpose that stimulates positive participation. Brown Wolf said: “It’s not about a land grab, it’s about growth – community by community.” She explained that Upland, which is based on real GIS maps, has been growing city by city, with new cities opening regularly. The latest city that Upland added to its virtual world was London, which at peak times experienced 83 NFT mints per second. “Everything in Upland is an NFT which can be sold, traded or swapped, but not all of the NFTs are created by the platform, increasingly more and more are created by the community. So this level of activity shows the popularity,” Brown Wolf said. Brown Wolf has a background in international relations and cited by Balaji Srinivasan. Network State addresses how the formation of communities tends to focus on common values and interests, which are happening organically in Upland as people gravitate toward specific ‘neighborhoods’ or nodes. Once these people congregate, they tend to work jointly on projects. How to Start a New Country The Network State: The concept of organic communities was addressed by Godsil, who is Recipient of the Order of Merit of Liberland and Editor-In-Chief of Liberland Press, talked about the contested micronation’s leap into the Liberverse. As the digital twin of the micronation formed 8 years ago on the banks of the Danube River by Czech politician and economist Vit Jedlicka, Liberverse has all the room and the global reach that the small nation lacks in real life. “This digital reflection of Liberland allows world citizens to interact over the metaverse despite vast geographic discrepancies.” Liberland has attracted some attention by offering diplomatic status to world citizens willing to recognize the 2.7 square-mile island as a sovereign nation. Palermo commented that Be Future Media builds infrastructure in metaverses such as Sandbox and Decentraland. She observed that brands “Seemed to be entering the metaverse last year for general PR awareness – but this year they came for the experience.” Brown Wolf concurred and observed that the difference between Web2 and Web3 was in the interactions. “ People are strollers not scrollers in Web3. They don’t want advertising, they want interaction,” Brown Wolf said. “And they want co-creation.” Upland is apparently already delivering in monetization. Brown Wolf gave the example of Cafes owned by players in the metaverse. If they host events they might decide to have token-gated events or have free entry with tipping included. So what makes a successful Neighborhood in Metaverse? According to Brown Wolf, the key is to provide a system of governance and let a focus on collective good lead them forward. “They need a place to communicate and they need to build their own governance systems in terms of how decisions are made. Some neighborhoods have delegated decisions to a governing body, or even elected a Mayor. Others meet up to make collective decisions. We're still at the stage of experimentation, where there isn't one right answer.” However, like any sort of society, the incentives for gain need to be there. “Part of what makes neighborhoods successful is that they were able to add value to their property just like in real life and eventually monetize it. If you have a shady neighborhood you start building it with everything decorated and beautiful, with community events, buyers will want to be a part of that and you will pay a premium on that property. The hard work that was put into building this neighborhood translates into monetary value. And that creates incentive,” Brown Wolf said.

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