PACE Solver Description: CIMAT_Team

Abstract

This document describes MAEDM-OCM, a first generation memetic algorithm for the one-sided crossing minimization problem (OCM), which obtained the first position at the heuristic track of the Parameterized Algorithms and Computational Experiments Challenge 2024. In this variant of OCM, given a bipartite graph with vertices V = A ∪ B, only the nodes of the layer B can be moved. The main features of MAEDM-OCM are the following: the diversity is managed explicitly through the Best-Non-Penalized (BNP) survivor strategy, the intensification is based on Iterated Local Search (ILS), and the cycle crossover is applied. Regarding the intensification step, the neighborhood is based on shifts and only a subset of the neighbors in the local search are explored. The use of the BNP replacement was key to attain a robust optimizer. It was also important to incorporate low-level optimizations to efficiently calculate the number of crossings and to reduce the requirements of memory. In the case of the longest instances (|B| > 17000) the memetic approach is not applicable with the time constraints established in the challenge. In such cases, ILS is applied. The optimizer is not always applied to the original graph. In particular, twin nodes in B are grouped in a single node.