Solution merging in matheuristics for resource constrained job scheduling

Matheuristics have been gaining in popularity for solving combinatorial optimisation problems in recent years. This new class of hybrid method combines elements of both mathematical programming for intensification and metaheuristic searches for diversification. A recent approach in this direction has been to build a neighbourhood for integer programs by merging information from several heuristic solutions, namely construct, solve, merge and adapt (CMSA). In this study, we investigate this method alongside a closely related novel approach—merge search (MS). Both methods rely on a population of solutions, and for the purposes of this study, we examine two options: (a) a constructive heuristic and (b) ant colony optimisation (ACO); that is, a method based on learning. These methods are also implemented in a parallel framework using multi-core shared memory, which leads to improving the overall efficiency. Using a resource constrained job scheduling problem as a test case, different aspects of the algorithms are investigated. We find that both methods, using ACO, are competitive with current state-of-the-art methods, outperforming them for a range of problems. Regarding MS and CMSA, the former seems more effective on medium-sized problems, whereas the latter performs better on large problems.