Numerical experiments

Abstract and 1. Introduction

2. Mixed integer and constraint programming models

   2.1 Mixed-integer linear programming model

   2.2 Constraint Programming model

3. Constructive Heuristics

4. Benchmark instances

5. Numerical experiments

   5.1 Experiments with the constructive heuristics

   5.2 Solving the proposed models with a commercial solver

6. Conclusions and References

5 Numerical experiments

In this section we present numerical experiments. First, we wish to evaluate the two introduced constructive heuristics. Second, we wish to assess the correctness of the MILP and CP models and attempt to infer which of the two, or rather which of the exact commercial solvers applied to each of them, is more effective in finding proven optimal solutions. Third, we wish to determine the usefulness of providing a feasible solution to the exact solvers. It should be noted that all efforts are to build a set of test instances with proven optimal solutions. The models and constructive heuristics presented in this paper are intended to contribute in that respect and are not intended to construct a solution method per se, for a known difficult problem. In all cases we considered the 110 instances introduced in Section 4 with the learning rate α ∈ {0.1, 0.2, 0.3} for a total of 330 instances.

The experiments were carried out in an Intel i9-12900K (12th Gen) processor operating at 5.200GHz and 128 GB of RAM. The constructive heuristics were implemented in C++ programming language. Models were solved using IBM ILOG CPLEX Optimization Studio version 22.1, using default parameters, with concert library and C++. The code was compiled using g++

10.2.1. Benchmark instances and code are available at https://github.com/kennedy94/FJS.