Multi-Objective Simulated Annealing Algorithms for General Problems

Multi-Objective Simulated Annealing Algorithms for General Problems

Juan Frausto Solís (Tecnológico Nacional de México, Mexico), Héctor Joaquín Fraire (Tecnológico Nacional de México, Mexico), José Carlos Soto-Monterrubio (Tecnológico Nacional de México, Mexico) and Rodolfo Pazos-Rangel (Tecnológico Nacional de México, Mexico)
DOI: 10.4018/978-1-4666-9779-9.ch014
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Simulated Annealing is an analogy with the annealing of solids, which foundations come from a physical area known as statistical mechanics. This chapter presents a review of the literature on multi-objective simulated annealing (MOSA). There are several multi-objective approaches to solve optimization problems with simulated annealing such as hybridizations, implementation of strategies from different metaheuristics. Modern MOSA research includes populations and adaptive rules, and are briefly described in this chapter. We discuss different approaches in multi-objective and we revise the modern MOSA framework.
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1. Introduction

Optimization has many applications in almost any area of the human activity and has two kind of research areas: single optimization and multi-objective optimization. These areas study single-objective problems or SOP (with only one objective function) and multi-objective problems or MOP (with more than one objective functions) respectively (Coello Coello, Lamont, & Van Veldhuizen, 2007). Even though single optimization is far to be a closed research area, many deterministic and stochastic strategies have been studied since the second world war. In addition, several reviews are available for the problems of this area. In the case of problems belonging to multi-objective optimization area, nature and physical principles are applied to develop algorithm for solve them. Multi-objective Evolutionary Algorithms (MOEAs) and multi-objective Simulated Annealing (MOSA) are among the most common of these algorithms (Deb, 2001). We will use the next model for distinguish single to multi-objective optimization problems:

subject to

In single optimization problems, 978-1-4666-9779-9.ch014.m05is always equal to one, while978-1-4666-9779-9.ch014.m06is always greater than one for multi-objective optimization problems. The rest of this model is the same for SOP and MOP with the next features: There are 978-1-4666-9779-9.ch014.m07 decision variables978-1-4666-9779-9.ch014.m08. There are two set of algebraic expressions978-1-4666-9779-9.ch014.m09and978-1-4666-9779-9.ch014.m10known as inequality and equality constraints respectively. The number of these constraints are978-1-4666-9779-9.ch014.m11and978-1-4666-9779-9.ch014.m12. Finally, 978-1-4666-9779-9.ch014.m13and978-1-4666-9779-9.ch014.m14are respectively the lower and upper bound of each decision variable978-1-4666-9779-9.ch014.m15.

Most of the practical problems belongs to the second category and the NP-Hard problems. For the last kind of problems, many multi-objective evolutionary algorithms (MOEAs) have been published since their review (Deb, 2001); the most popular MOEAs are using Pareto Archived Evolution Strategy (PAES), this use a file where dominated solutions, which are employed for new solutions (Knowles & Corne, 2000), are updated.

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