We present a diversity-oriented hybrid evolutionary approach for the graph coloring problem. This approach is based on both generally applicable strategies and specifically tailored techniques. Particular attention is paid to ensuring population diversity by carefully controlling spacing among individuals. Using a distance measure between potential solutions, the general population management strategy decides whether an offspring should be accepted in the population, which individual needs to be replaced and when mutation is applied. Furthermore, we introduce a special grouping-based multi-parent crossover operator which relies on several relevant features to identify meaningful building blocks for offspring construction. The proposed approach can be generally characterized as “well-informed”, in the sense that the design of each component is based on the most pertinent information which is identified by both experimental observation and careful analysis of the given problem. The resulting algorithm proves to be highly competitive when it is applied on the whole set of the DIMACS benchmark graphs.

Graph partitioning is one of the most studied NPcomplete problems. Given a graph G = (V, E), the task is to partition the vertex set V into k disjoint subsets of about the same size, such that the number of edges with endpoints in different subsets is minimized. In this work, we present a highly effective multilevel memetic algorithm, which integrates a new multiparent crossover operator and a powerful perturbation-based tabu search algorithm. The proposed crossover operator tends to preserve the backbone with respect to a certain number of parent individuals, i.e. the grouping of vertices which is common to all parent individuals. Extensive experimental studies on numerous benchmark instances from the Graph Partitioning Archive show that the proposed approach, within a time limit ranging from several minutes to several hours, performs far better than any of the existing graph partitioning algorithm in terms of solution quality.

Abstract—The balanced graph partitioning consists in dividing the vertices of an undirected graph into a given number of subsets of approximately equal size, such that the number of edges crossing the subsets is minimized. In this work, we present a multilevel memetic algorithm for this NP-hard problem that relies on a powerful grouping recombination operator and a dedicated local search procedure. The proposed operator tends to preserve the backbone with respect to a set of parent individuals, i.e. the grouping of vertices which is same throughout each parent individual. Although our approach requires significantly longer computing time compared to some current state-of-art graph partitioning algorithms such as SCOTCH, METIS, CHACO, JOSTLE, etc., it competes very favorably with these approaches in terms of solution quality. Moreover, it easily reaches or improves on the best partitions ever reported in the literature. Index Terms—Graph partitioning, grouping recombination operator, local search, backbone. I.

Abstract This chapter is dedicated to Memetic Algorithms for Discrete Optimization. It begins with a general survey, and then explains in depth the key ingredients of a successful MA. A particular attention is given to the following issues: Design of semantic combination operators, development of dedicated local search procedures and management of population diversity. Several other important issues are also discussed such as design of rich evaluation function and constraint handling techniques. This chapter includes two case studies with the purpose of showing how these issues can be effectively implemented in practice. 1

Abstract. We present a multi-parent hybrid genetic–tabu algorithm (denoted by GTA) for the Unconstrained Binary Quadratic Programming (UBQP) problem, by incorporating tabu search into the framework of genetic algorithm. In this paper, we propose a new multi-parent combination operator for generating offspring solutions. A pool updating strategy based on a quality-and-distance criterion is used to manage the population. Experimental comparisons with leading methods for the UBQP problem on 25 large public instances demonstrate the efficacy of our proposed algorithm in terms of both solution quality and computational efficiency.

Abstract Graph vertex coloring is one of the most studied NP-hard combinatorial optimization problems. Given the hardness of the problem, various heuristic algorithms have been proposed for practical graph coloring, based on local search, population-based approaches and hybrid methods. The research in graph coloring heuristics is very active and improved results have been obtained recently, notably for coloring large and very large graphs. This chapter surveys and analyzes graph coloring heuristics with a focus on the most recent advances. 1

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Given an undirected graph G = (V, E), the minimum sum coloring problem (MSCP) is to find a legal vertex coloring of G, using colors represented by natural numbers (1, 2,...) such that the total sum of the colors assigned to the vertices is minimized. In this paper, we present EXSCOL, a heuristic algorithm based on independent set extraction for this NP-hard problem. EXSCOL identifies iteratively collections of disjoint independent sets of equal size and assign to each independent set the smallest available color. For the purpose of computing large independent sets, EXSCOL employs a tabu search based heuristic. Experimental evaluations on a collection of 52 DIMACS and COLOR2 benchmark graphs show that the proposed approach achieves highly competitive results. For more than half of the graphs used in the literature, our approach improves the current best known upper bounds.

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