Construct, Merge, Solve & Adapt A new general algorithm for combinatorial optimization

Abstract

This paper describes a general hybrid metaheuristic for combinatorial optimization labelled Construct, Merge, Solve & Adapt. The proposed algorithm is a specific instantiation of a framework known from the literature as Generate-And-Solve, which is based on the following general idea. First, generate a reduced sub-instance of the original problem instance, in a way such that a solution to the sub-instance is also a solution to the original problem instance. Second, apply an exact solver to the reduced sub-instance in order to obtain a (possibly) high quality solution to the original problem instance. And third, make use of the results of the exact solver as feedback for the next algorithm iteration. The minimum common string partition problem and the minimum covering arborescence problem are chosen as test cases in order to demonstrate the application of the proposed algorithm. The obtained results show that the algorithm is competitive with the exact solver for small to medium size problem instances, while it significantly outperforms the exact solver for larger problem instances.

Construct, Merge, Solve and Adapt: Application to the Repetition-Free Longest Common Subsequence Problem

“…In this work, the CMSA algorithm has been applied to the repetition-free longest common subsequence problem. The general picture of the results, in comparison to CPLEX, is similar to the one observed in earlier applications of CMSA to the minimum common string partition problem and a minimum weight arborescence problem in [1]. CMSA is generally competitive with CPLEX for small to medium size problem instances, whereas it outperforms CPLEX with growing problem instances size.…”

“…Therefore, recent research efforts have focused on ways in which efficient exact solvers can be used within heuristic frameworks even in the context of large problem instances. One of the most recent examples of these research efforts is an algorithm labelled Construct, Merge, Solve & Adapt (CMSA) [1,2]. This algorithm works as follows.…”

Parallel matheuristics for the discrete unit commitment problem with min‐stop ramping constraints

“…For instance, the POPMUSIC framework (partial optimization metaheuristic under special intensification conditions; Taillard and Voss, ) partitions variables and solves independent computations in the partitioned subproblems, and modifying iteratively the partitions of variables. Recently, Blum and Pedro () provided a generic algorithm where operators of construction, merging, and repair have to be implemented.…”

Matheuristics for Variants of the Dominating Set Problem

“…As in the Construct, Merge, Solve & Adapt (CMSA) approach described in Blum et al (2016), the set of promising vertices is selected based on the search history. Moreover, the size of the subproblem is adapted to exploit the capabilities of the solver as efficiently as possible.…”