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.
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Notes
- 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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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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