A memetic algorithm for the minimum sum coloring problem

Given an undirected graph $G$, 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. This paper presents a memetic algorithm for MSCP based on a tabu search procedure with two neighborhoods and a multi-parent crossover operator. Experiments on a set of 77 well-known DIMACS and COLOR 2002-2004 benchmark instances show that the proposed algorithm achieves highly competitive results in comparison with five state-of-the-art algorithms. In particular, the proposed algorithm can improve the best known results for 17 instances. We also provide upper bounds for 18 additional instances for the first time.Comment: Submitted manuscrip

Algorithms for the minimum sum coloring problem: a review

The Minimum Sum Coloring Problem (MSCP) is a variant of the well-known vertex coloring problem which has a number of AI related applications. Due to its theoretical and practical relevance, MSCP attracts increasing attention. The only existing review on the problem dates back to 2004 and mainly covers the history of MSCP and theoretical developments on specific graphs. In recent years, the field has witnessed significant progresses on approximation algorithms and practical solution algorithms. The purpose of this review is to provide a comprehensive inspection of the most recent and representative MSCP algorithms. To be informative, we identify the general framework followed by practical solution algorithms and the key ingredients that make them successful. By classifying the main search strategies and putting forward the critical elements of the reviewed methods, we wish to encourage future development of more powerful methods and motivate new applications

Sum Coloring : New upper bounds for the chromatic strength

The Minimum Sum Coloring Problem (MSCP) is derived from the Graph Coloring Problem (GCP) by associating a weight to each color. The aim of MSCP is to find a coloring solution of a graph such that the sum of color weights is minimum. MSCP has important applications in fields such as scheduling and VLSI design. We propose in this paper new upper bounds of the chromatic strength, i.e. the minimum number of colors in an optimal solution of MSCP, based on an abstraction of all possible colorings of a graph called motif. Experimental results on standard benchmarks show that our new bounds are significantly tighter than the previous bounds in general, allowing to reduce substantially the search space when solving MSCP .Comment: pre-prin

Some Experiences with Hybrid Genetic Algorithms in Solving the Uncapacitated Examination Timetabling Problem

This paper provides experimental experiences on two local search hybridized genetic algorithms in solving the uncapacitated examination timetabling problem. The proposed two hybrid algorithms use partition and priority based solution representations which are inspired from successful genetic algorithms proposed for graph coloring and project scheduling problems, respectively. The algorithms use a parametrized saturation degree heuristic hybridized crossover scheme. In the experiments, the algorithms firstly are calibrated with a Design of Experiments approach and then tested on the well-known Toronto benchmark instances. The calibration shows that the hybridization prefers an intensive local search method. The experiments indicate the vitality of local search in the proposed genetic algorithms, however, experiments also show that the hybridization benefits local search as well. Interestingly, although the structures of the two algorithms are not alike, their performances are quite similar to each other and also to other state-of-the-art genetic-type algorithms proposed in the literature