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Local Search Techniques: Focus on Tabu Search

Local Search Techniques: Focus on Tabu Search

Edited by

Wassim Jaziri

I-Tech

IV

Published by In-Teh

In-Teh is Croatian branch of I-Tech Education and Publishing KG, Vienna, Austria. Abstracting and non-profit use of the material is permitted with credit to the source. Statements and opinions expressed in the chapters are these of the individual contributors and not necessarily those of the editors or publisher. No responsibility is accepted for the accuracy of information contained in the published articles. Publisher assumes no responsibility liability for any damage or injury to persons or property arising out of the use of any materials, instructions, methods or ideas contained inside. After this work has been published by the In-Teh, authors have the right to republish it, in whole or part, in any publication of which they are an author or editor, and the make other personal use of the work. 2008 In-teh www.in-teh.org Additional copies can be obtained from: publication@ars-journal.com First published September 2008 Printed in Croatia

A catalogue record for this book is available from the University Library Rijeka under no. 111230015 Local Search Techniques: Focus on Tabu Search, Edited by Wassim JAZIRI p. cm. ISBN 978-3-902613-34-9 1. Local Search Techniques: Focus on Tabu Search, Wassim JAZIRI

PrefaceIn real-world optimization applications, stakeholders require multiple and complex constraints, which are difficult to satisfy and make complicated to find satisfactory solutions. In the most cases, we face over-constrained optimization problems (no satisfactory solution can be found) because of the stakeholders multiple requirements and the various and complex constraints to be satisfied. Solving over-constrained problems is based on the relaxation of some constraints according to values of preferences in order to favour the satisfaction of the most relevant. In addition, some methods have been developed, such as Branch and Bound method and Filtering techniques, which allow avoiding an enumeration of all potential solutions but are very expensive in computation times. Two types of actors are involved in the optimization problems: the stakeholders who express their needs and the analyst who models and manages these needs. The choice of appropriate resolution methods depends on the stakeholders needs and the number of criterion to take into account. The definition and the formulation of stakeholders needs are among the major preoccupations to resolve an optimization problem. The quality of a solution depends on the efficiency of this step, which must model all aspects of the problem, in particular those related to the objectives of the application. However, in majority of optimization works, the interest concerns the choice and the development of appropriate optimization approaches rather than the modelling of the stakeholders needs. An optimisation approach consists in exploring the search space to find the best solution according to an objective function and satisfying some constraints. It expresses a value of cost to reduce or of benefit to maximize. The optimization framework is adapted to the problems with multiple solutions. In traditional optimization problems, the objective function comprises a single criterion able to determine the optimum. Otherwise, the objective consists in finding a good compromise regarding multiple criteria. The problem is then a case of multicriteria optimization. In practice, optimization problems can reach a high complexity and require considerable computation times because of the number of potential solutions. The approximate methods are generally used to resolve this class of problems. These methods are based on an iterative exploration of the search space to find a solution of good quality in reasonable computation times. Among the most known approximate methods, we mention the neighbourhood methods, such as Local Search, Simulated Annealing, Threshold Algorithms, Noising Method and Tabu Search as well as the algorithms based on the

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evolution approach, such as Evolutionary Programming, Strategies of Evolution, Genetic Algorithms and Genetic Programming. In the last decade, optimization problems have been among the most studied problems and they are still an active area of research. Algorithmic advances as well as the needs to solve complex real-world optimization problems have provided an excellent framework on which to develop and design new optimization techniques. The field of Neighborhood search methods has grown considerably. Researchers have demonstrated the ability of these methods to solve hard combinatorial problems within reasonable computation times. Neighborhood search methods are iterative procedures, which consist in constructing from a current solution a next solution with a better quality regarding an objective function. Among the Neighborhood search methods, Tabu Search is one of the most prominent, widely used, and successful approaches for solving optimization problems from artificial intelligence and operations research. Tabu Search is a meta-heuristic algorithm, which can be used for solving combinatorial optimization problems. Tabu Search has found its usefulness in a vast area of applications such as scheduling, vehicle routing problems, resources planning, regional development, location problems, integer programming problems, traveling salesman, graph coloring, knapsack problems, network design etc. Tabu Search has now become a reputable optimization technique and has proved highly effective in solving a wide range of optimization problems. Several works presenting applications of Tabu Search to various combinatorial problems have proved that Tabu Search provides good solutions very close to optimality. These successes have made Tabu Search extremely popular among those interested in finding good solutions to the large combinatorial problems encountered in many practical settings. Tabu Search uses a local search procedure to iteratively move from a current solution x to a neighbor solution x' in the neighborhood of x, until some stopping criterion has been satisfied. The search process starts with an initial solution and moves from neighbor to neighbor as long as possible while improving the objective function value. Tabu Search improves the performance of the search process by using memory structures: the last explored configurations are kept in a short-term memory (Tabu list) in order to prohibit moves that lead to one of them. Overall objective of the book The goal of this book is to report original researches on algorithms and applications of Tabu Search to real-world problems as well as recent improvements and extensions on its concepts and algorithms. The book Chapters identify useful new implementations and ways to integrate and apply the principles of Tabu Search, to hybrid it with others optimization methods, to prove new theoretical results, and to describe the successful application of optimization methods to real world problems. Chapters were selected after a careful review process by reviewers, based on the originality, relevance and their contribution to local search techniques and more precisely to Tabu Search. Audience The book Local Search Techniques: Focus on Tabu Search provides a broad spectrum of advances in applied optimization with a focus on Tabu Search. It is designed to be useful and accessible to researchers, engineers, graduate students and all scientists and practitioners in computer science, operations research and artificial intelligence as well as

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other applications specialists who need local search techniques to model and solve combinatorial optimization problems. Preview This book consists of two main parts: Tabu Search algorithms and applications. In the first part, the state of the art and novel advances of Tabu Search algorithms are described. The purpose of the applications section is to provide the practitioners with a description of the relevant optimization issues in a number of specific application areas. This book is organized as follows. Chapter 1 Tabu Search: a Comparative Study provides an overall view of the local search area and describes Tabu Search and some other meta-heuristics to which Tabu Search will be compared: Simulated Annealing, Genetic Algorithms, Ant Colony Optimization, Greedy Randomized Adaptive Search Procedure and Particle Swarm Optimization. The authors identify the different problems for which Tabu Search was used to generate solutions, such as scheduling problems, routing problems, and assignment problems. Chapter 2 A Multiobjective Tabu Framework for the Optimization and Evaluation of Wireless Systems provides an insight on the use of Tabu Search for the resolution of multiobjective optimization problems and its performance for real-world optimization problems. The main concepts of multiobjective optimization are presented as well as an overview of the main multiobjective strategies. Chapter 3 SOS-Heuristic for Intelligent Exploration of the Search Space in CSOP proposes an intelligent search heuristic called SOS-Heuristic (Heuristic for Satisfactory and Optimized Solutions) to guide the resolution of constraints satisfaction and optimization problem. The objective of the SOS-Heuristic is to improve the value of the objective function without damaging the satisfaction of constraints. Experiments on a spatial optimization problem using a hybrid method provided interesting results and prove the efficiency of the proposed approach in comparison to another optimization approach based on Tabu Search. Chapter 4 Symbiotic Tabu Search explains the use of the Tabu Search metaheuristic and proposes a hybrid Tabu Search approach with symbiotic evolution, called Symbiotic Tabu Search. Implementation and test results on three Benchmark

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