Una Benlic

A Multilevel Memetic Approach for Improving Graph k-Partitions

Graph partitioning is one of the most studied NP-complete 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 paper, 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 algorithms in terms of solution quality.

Breakout Local Search for maximum clique problems

The maximum clique problem (MCP) is one of the most popular combinatorial optimization problems with various practical applications. An important generalization of MCP is the maximum weight clique problem (MWCP) where a positive weight is associate to each vertex. In this paper, we present Breakout Local Search (BLS) which can be applied to both MC and MWC problems without any particular adaptation. BLS explores the search space by a joint use of local search and adaptive perturbation strategies. Extensive experimental evaluations using the DIMACS and BOSHLIB benchmarks show that the proposed approach competes favourably with the current state-of-art heuristic methods for MCP. Moreover, it is able to provide some new improved results for a number of MWCP instances. This paper also reports for the first time a detailed landscape analysis, which has been missing in the literature. This analysis not only explains the difficulty of several benchmark instances, but also justifies to some extent the behaviour of the proposed approach and the used parameter settings.

Breakout local search for the quadratic assignment problem

The quadratic assignment problem (QAP) is one of the most studied combinatorial optimization problems with various practical applications. In this paper, we present breakout local search (BLS) for solving QAP. BLS explores the search space by a joint use of local search and adaptive perturbation strategies. Experimental evaluations on the set of QAPLIB benchmark instances show that the proposed approach is able to attain current best-known results for all but two instances with an average computing time of less than 4.5hours. Comparisons are also provided to show the competitiveness of the proposed approach with respect to the best-performing QAP algorithms from the literature.

An effective multilevel tabu search approach for balanced graph partitioning

Graph partitioning is one of the fundamental NP-complete problems which is widely applied in many domains, such as VLSI design, image segmentation, data mining, etc. Given a graph G=(V,E), the balanced k-partitioning problem consists in partitioning the vertex set V into k disjoint subsets of about the same size, such that the number of cutting edges is minimized. In this paper, we present a multilevel algorithm for balanced partition, which integrates a powerful refinement procedure based on tabu search with periodic perturbations. Experimental evaluations on a wide collection of benchmark graphs show that the proposed approach not only competes very favorably with the two well-known partitioning packages METIS and CHACO, but also improves more than two thirds of the best balanced partitions ever reported in the literature.

Breakout Local Search for the Max-Cutproblem

Given an undirected graph G=(V,E) where each edge of E is weighted with an integer number, the maximum cut problem (Max-Cut) is to partition the vertices of V into two disjoint subsets so as to maximize the total weight of the edges between the two subsets. As one of Karps 21 NP-complete problems, Max-Cut has attracted considerable attention over the last decades. In this paper, we present Breakout Local Search (BLS) for Max-Cut. BLS explores the search space by a joint use of local search and adaptive perturbation strategies. The proposed algorithm shows excellent performance on the set of well-known maximum cut benchmark instances in terms of both solution quality and computational time. Out of the 71 benchmark instances, BLS is capable of finding new improved results in 34 cases and attaining the previous best-known result for 35 instances, within computing times ranging from less than 1s to 5.6h for the largest instance with 20,000 vertices.

Memetic search for the quadratic assignment problem

We present a memetic algorithm (called BMA) for the well-known QAP.BMA integrates BLS within the population-based evolutionary computing framework.BMA is able to attain the best-known results for 133 out of 135 QAP benchmark instances.We provide insights on search landscapes and crossover operators for QAP. The quadratic assignment problem (QAP) is one of the most studied NP-hard problems with various practical applications. In this work, we propose a powerful population-based memetic algorithm (called BMA) for QAP. BMA integrates an effective local optimization algorithm called Breakout Local Search (BLS) within the evolutionary computing framework which itself is based on a uniform crossover, a fitness-based pool updating strategy and an adaptive mutation procedure. Extensive computational studies on the set of 135 well-known benchmark instances from the QAPLIB revealed that the proposed algorithm is able to attain the best-known results for 133 instances and thus competes very favorably with the current most effective QAP approaches. A study of the search landscape and crossover operators is also proposed to shed light on the behavior of the algorithm.

A study of breakout local search for the minimum sum coloring problem

Given an undirected graph G=(V,E), the minimum sum coloring problem (MSCP) is to find a legal assignment of colors (represented by natural numbers) to each vertex of G such that the total sum of the colors assigned to the vertices is minimized. In this paper, we present Breakout Local Search (BLS) for MSCP which combines some essential features of several well-established metaheuristics. BLS explores the search space by a joint use of local search and adaptive perturbation strategies. Tested on 27 commonly used benchmark instances, our algorithm shows competitive performance with respect to recently proposed heuristics and is able to find new record-breaking results for 4 instances.

Iterated local search based on multi-type perturbation for single-machine earliness/tardiness scheduling

We propose an iterated local search based on a multi-type perturbation (ILS-MP) approach for single-machine scheduling to minimize the sum of linear earliness and quadratic tardiness penalties. The multi-type perturbation mechanism in ILS-MP probabilistically combines three types of perturbation strategies, namely tabu-based perturbation, construction-based perturbation, and random perturbation. Despite its simplicity, experimental results on a wide set of commonly used benchmark instances show that ILS-MP performs favourably in comparison with the current best approaches in the literature.

An Effective Multilevel Memetic Algorithm for Balanced Graph Partitioning

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.

Hybrid Metaheuristics for the Graph Partitioning Problem

The Graph Partitioning Problem (GPP) is one of the most studied NP-complete problems notable for its broad spectrum of applicability such as in VLSI design, data mining, image segmentation, etc. Due to its high computational complexity, a large number of approximate approaches have been reported in the literature. Hybrid algorithms that are based on adaptations of popular metaheuristic techniques have shown to provide outstanding performance in terms of partition quality. In particular, it is the hybrids between well-known metaheuristics and multilevel strategies that report partitions of the minimal cut-size value. However, metaheuristic hybrids generally require more computing time than those based on greedy heuristics which can generate partitions of acceptable quality in a matter of seconds even for very large graphs. This chapter is dedicated to a review on some representative hybrid metaheuristic approaches including genetic local search, basic multilevel search and recent development on hybrid multilevel search.