Jean-Philippe Hamiez

Scatter Search for Graph Coloring

In this paper, we present a first scatter search approach for the Graph Coloring Problem (GCP). The evolutionary strategy scatter search operates on a set of configurations by combining two or more elements. New configurations are improved before replacing others according to their quality (fitness), and sometimes, to their diversity. Scatter search has been applied recently to some combinatorial optimization problems with promising results. Nevertheless, it seems that no attempt of scatter search has been published for the GCP. This paper presents such an investigation and reports experimental results on some well-studied DIMACS graphs.

Solving the Sports League Scheduling Problem with Tabu Search

In this paper we present a tabu approach for a version of the Sports League Scheduling Problem. The approach adopted is based on a formulation of the problem as a Constraint Satisfaction Problem (CSP). Tests were carried out on problem instances of up to 40 teams representing 780 integer variables with 780 values per variable. Experimental results show that this approach outperforms some existing methods and is one of the most promising methods for solving problems of this type.

Recent Advances in Graph Vertex Coloring

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.

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 15 instances.

An analysis of solution properties of the graph coloring problem

This paper concerns the analysis of solution properties of the Graph Coloring Problem. For this purpose, we introduce a property based on the notion of representative sets which are sets of vertices that are always colored the same in a set of solutions. Experimental results on well-studied DIMACS graphs show that many of them contain such sets and give interesting information about the diversity of the solutions. We also show how such an analysis may be used to improve a tabu search algorithm.

A Study of Tabu Search for Coloring Random 3-Colorable Graphs Around the Phase Transition

The authors present an experimental investigation of tabu search (TS) to solve the 3-coloring problem (3-COL). Computational results reveal that a basic TS algorithm is able to find proper 3-colorings for random 3-colorable graphs with up to 11000 vertices and beyond when instances follow the uniform or equipartite well-known models, and up to 1500 vertices for the hardest class of flat graphs. This study also validates and reinforces some existing phase transition thresholds for 3-COL.

A linear-time algorithm to solve the Sports League Scheduling Problem (prob026 of CSPLib)

In this paper, we present a repair-based linear-time algorithm to solve a version of the Sports League Seheduling Problem (SLSP) where the number T of teams is such that (T - 1) mod 3 ≠ 0. Starting with a conflicting schedule with particular properties, the algorithm removes iteratively the conflicts by exchanging matches. The properties of the initial schedule make it possible to take the optimal exchange at each iteration, leading to a linear-time algorithm. This algorithm can find thus valid schedules for several thousands of teams in less than 1 min. It is still an open question whether the SLSP can be solved efficiently when (T - 1) mod 3 = 0.

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.

Sports league scheduling: enumerative search for prob026 from CSPLib

This paper presents an enumerative approach for a sports league scheduling problem. This simple method can solve some instances involving a number T of teams up to 70 while the best known constraint programing algorithm is limited to T < 40. The proposed approach relies on interesting properties which are used to constraint the search process.