Metaheuristics for hard optimization : methods and case studies
Résumé
Metaheuristics for Hard Optimization comprises of three parts. The first part is devoted to the detailed presentation of the four most widely known metaheuristics: - the simulated annealing method; - the tabu search; - the genetic and evolutionary algorithms; - the ant colony algorithms. Each one of these metaheuristics is actually a family of methods, of which we try to discuss the essential elements. Some common features clearly appear in most metaheuristics, such as the use of diversification, to force the exploration of regions of the search space, rarely visited until now, and the use of intensification, to go thoroughly into some promising regions. Another common feature is the use of memory to archive the best encountered solutions. One common drawback for most metaheuristics still is the delicate tuning of numerous parameters; theoretical results available by now are not sufficient to really help in practice the user facing a new hard optimization problem. In the second part, we present some other metaheuristics, less widespread or emergent: some variants of simulated annealing; noising method; distributed search; Alienor method; particle swarm optimization; estimation of distribution methods; GRASP method; cross-entropy method; artificial immune systems; differential evolution. Then we describe some extensions of metaheuristics for continuous optimization, multimodal optimization, multiobjective optimization and contrained evolutionary optimization. We present some of the existing techniques and some ways of research. The last chapter is devoted to the problem of the choice of a metaheuristic; we describe an unifying method called "Adaptive Memory Programming", which tends to attenuate the difficulty of this choice. The delicate subject of a rigorous statistical comparison between stochastic iterative methods is also discussed. The last part of the book concentrates on three case studies: - the optimization of the 3G mobile networks (UMTS) using the genetic algorithms. After a brief presentation of the operation of UMTS networks and of the quantities involved in the analysis of their performances, the chapter discusses the optimization problem for planning the UMTS network; an efficient method using a genetic algorithm is presented and illustrated through one example of a realistic network; - the application of genetic algorithms to the problems of management of the air traffic. One details two problems of air traffic management for which a genetic algorithm based solution has been proposed: the first application deals with the en route conflict resolution problem; the second one discusses the traffic management in an airport platform; - constrained programming and ant colony algorithms applied to vehicle routing problems. It is shown that constraint programming provides a modelling procedure, making it possible to represent the problems in an expressive and concise way; the use of ant colony algorithms allows to obtain heuristics which can be simultaneously robust and generic in nature. One appendix of the book is devoted to the modeling of simulated annealing through the Markov chain formalism. Another appendix gives a complete implementation in C++ language for robust tabu search method