Multi-objective Optimization: Classical and Evolutionary Approaches
Problems involving multiple conflicting objectives arise in most real world optimization problems. Evolutionary Algorithms (EAs) have gained a wide interest and success in solving problems of this nature for two main reasons: (1) EAs allow finding several
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Abstract Problems involving multiple conflicting objectives arise in most real world optimization problems. Evolutionary Algorithms (EAs) have gained a wide interest and success in solving problems of this nature for two main reasons: (1) EAs allow finding several members of the Pareto optimal set in a single run of the algorithm and (2) EAs are less susceptible to the shape of the Pareto front. Thus, Multi-objective EAs (MOEAs) have often been used to solve Multi-objective Problems (MOPs). This chapter aims to summarize the efforts of various researchers algorithmic processes for MOEAs in an attempt to provide a review of the use and the evolution of the field. Hence, some basic concepts and a summary of the main MOEAs are provided. We also propose a classification of the existing MOEAs in order to encourage researchers to continue shaping the field. Furthermore, we suggest a classification of the most popular performance indicators that have been used to evaluate the performance of MOEAs. Keywords Multi-objective optimization problems · Performance metrics
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M. Elarbi (B) · S. Bechikh · L. Ben Said SOIE Lab, Computer Science Department, ISG-Tunis, University of Tunis, Bouchoucha City, 2000 Le Bardo, Tunis, Tunisia e-mail: [email protected] S. Bechikh e-mail: [email protected] L. Ben Said e-mail: [email protected] R. Datta Graduate School of Knowledge Service Engineering, Department of Industrial and Systems Engineering, Korean Advanced Institute of Science and Technology (KAIST), 291 Daehak-ro, Yuseong-gu, Daejeon 34141, Republic of Korea e-mail: [email protected]; [email protected] R. Datta Department of Mechanical Engineering, Indian Institute of Technology Kanpur, Kanpur, Uttar Pradesh, India © Springer International Publishing Switzerland 2017 S. Bechikh et al. (eds.), Recent Advances in Evolutionary Multi-objective Optimization, Adaptation, Learning, and Optimization 20, DOI 10.1007/978-3-319-42978-6_1
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1 Introduction Most real world optimization problems involve the optimization of two or more conflicting objectives simultaneously. In order to solve a MOP, there are three goals to pursue: (1) convergence, (2) diversity, and (3) solution distribution uniformity. In fact, the obtained non-dominated solutions should be as close as possible to the Pareto optimal front of the optimization problem. This goal is similar to the demand of convergence to the global optimum in single-objective optimization. Often, there exist an infinite number of Pareto optimal solutions. Naturally, only a finite number of solutions can be generated during an optimization process. Furthermore, the number of generated solutions must be limited otherwise the computational cost would become too large. Nevertheless, the largest possible freedom of choice should be offered to the Decision Maker (DM). Therefore, a well-distributed approximation set is demanded which is a goal that consists itself of two requirements: (1) an extent that is as large as possible and
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