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Multi-objective Optimization: Classical and Evolutionary Approaches

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Recent Advances in Evolutionary Multi-objective Optimization

Part of the book series: Adaptation, Learning, and Optimization ((ALO,volume 20))

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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 sha** the field. Furthermore, we suggest a classification of the most popular performance indicators that have been used to evaluate the performance of MOEAs.

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Notes

  1. 1.

    We present the additive version of the \(\varepsilon \)-dominance. The multiplicative epsilon dominance is defined as follows: A solution u is said to epsilon-dominate a solution v (\(u \preceq _{\varepsilon } v\)) if and only if \(\forall m \in \left\{ 1,\ldots ,M \right\} : u_{m} \le v_{m} (1+ {\varepsilon } )\).

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Author information

Authors and Affiliations

  1. SOIE Lab, Computer Science Department, ISG-Tunis, University of Tunis, Bouchoucha City, 2000, Le Bardo, Tunis, Tunisia

    Maha Elarbi, Slim Bechikh & Lamjed Ben Said

  2. 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

    Rituparna Datta

  3. Department of Mechanical Engineering, Indian Institute of Technology Kanpur, Kanpur, Uttar Pradesh, India

    Rituparna Datta

Authors
  1. Maha Elarbi
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  2. Slim Bechikh
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  3. Lamjed Ben Said
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  4. Rituparna Datta
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Correspondence to Maha Elarbi .

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Editors and Affiliations

  1. SOIE lab, Computer Science Department, University of Tunis, ISG-Tunis , Bouchoucha, Le Bardo, Tunisia

    Slim Bechikh

  2. Department of Mechanical Engineering, Institute of Technology, Kalyanpur, Kanpur, Uttar Pradesh, India

    Rituparna Datta

  3. School of Computer Engineering, Nanyang Technological University, Singapore, Singapore

    Abhishek Gupta

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Elarbi, M., Bechikh, S., Ben Said, L., Datta, R. (2017). Multi-objective Optimization: Classical and Evolutionary Approaches. In: Bechikh, S., Datta, R., Gupta, A. (eds) Recent Advances in Evolutionary Multi-objective Optimization. Adaptation, Learning, and Optimization, vol 20. Springer, Cham. https://doi.org/10.1007/978-3-319-42978-6_1

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  • DOI: https://doi.org/10.1007/978-3-319-42978-6_1

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