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
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- 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 \(\forall m \in \left\{ 1,\ldots ,M \right\} : u_{m} \le v_{m} (1+ {\varepsilon } )\).
References
Deb, K.: Multi-objective optimization using evolutionary algorithms, vol. 16. Wiley, New York (2001)
Cohon, J.L.: Multiobjective programming and planning. Courier Corporation (2013)
Charnes, A., Cooper, W.W., Ferguson, R.O.: Optimal estimation of executive compensation by linear programming. Manag. Sci. 1(2), 138–151 (1955)
Wierzbicki, A.P.: The use of reference objectives in multiobjective optimization. Multiple Criteria Decision Making Theory and Application, pp. 468–486. Springer, Berlin (1980)
Korhonen, P.J., Laakso, J.: A visual interactive method for solving the multiple criteria problem. Eur. J. Oper. Res. 24(2), 277–287 (1986)
Jaszkiewicz, A., Słowiński, R.: The light beam search approach-an overview of methodology applications. Eur. J. Oper. Res. 113(2), 300–314 (1999)
Zitzler, E.: Evolutionary Algorithms for Multiobjective Optimization: Methods and Applications, vol. 63. Citeseer (1999)
Miettinen, K.: Nonlinear Multiobjective Optimization, vol. 12. Springer Science & Business Media (2012)
Deb, K., Kumar, A.: Interactive evolutionary multi-objective optimization and decision-making using reference direction method. In: Proceedings of the 9th Annual Conference on Genetic and Evolutionary Computation, pp. 781–788. ACM (2007)
Korhonen, P., Laakso, J.: Solving generalized goal programming problems using a visual interactive approach. Eur. J. Oper. Res. 26(3), 355–363 (1986)
Korhonen, P., Yu, G.Y.: A reference direction approach to multiple objective quadratic-linear programming. Eur. J. Oper. Res. 102(3), 601–610 (1997)
Korhonen, P.: The specification of a reference direction using the analytic hierarchy process. Math. Modell. 9(3), 361–368 (1987)
Schaffer, J.D.: Multiple objective optimization with vector evaluated genetic algorithms. In: Proceedings of the 1st International Conference on Genetic Algorithms, pp. 93–100. L. Erlbaum Associates Inc. (1985)
Richardson, J.T., Palmer, M.R., Liepins, G.E., Hilliard, M.: Some guidelines for genetic algorithms with penalty functions. In: Proceedings of the Third International Conference on Genetic Algorithms, pp. 191–197. Morgan Kaufmann Publishers Inc. (1989)
Kursawe, F.: A variant of evolution strategies for vector optimization. Parallel Problem Solving from Nature, pp. 193–197. Springer, Berlin (1990)
Hajela, P., Lin, C.-Y.: Genetic search strategies in multicriterion optimal design. Struct. Optim. 4(2), 99–107 (1992)
Fonseca, C.M., Fleming, P.J.: Genetic algorithms for multiobjective optimization: Formulation discussion and generalization. In: ICGA, vol. 93, pp. 416–423, Citeseer (1993)
Horn, J., Nafpliotis, N., Goldberg, D.E.: A niched pareto genetic algorithm for multiobjective optimization. In: Proceedings of the First IEEE Conference on Evolutionary Computation, 1994. IEEE World Congress on Computational Intelligence, pp. 82–87, IEEE (1994)
Srinivas, N., Deb, K.: Muiltiobjective optimization using nondominated sorting in genetic algorithms. Evol. Comput. 2(3), 221–248 (1994)
Holland, J.H.: Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence. U Michigan Press (1975)
Bechikh, S., Chaabani, A., Said, L.B.: An efficient chemical reaction optimization algorithm for multiobjective optimization. IEEE Trans. Cybern. 45(10), 2051–2064 (2015)
Zitzler, E., Thiele, L.: Multiobjective evolutionary algorithms: a comparative case study and the strength pareto approach. Evol. Comput. Trans. IEEE 3(4), 257–271 (1999)
Zitzler, E., Laumanns, M., Thiele, L.: Spea2: Improving the Strength Pareto Evolutionary Algorithm (2001)
Deb, K., Agrawal, S., Pratap, A., Meyarivan, T.: A fast elitist non-dominated sorting genetic algorithm for multi-objective optimization: Nsga-ii. In: Parallel Problem Solving from Nature PPSN VI, pp. 849–858. Springer, New York (2000)
Deb, K., Pratap, A., Agarwal, S., Meyarivan, T.: A fast and elitist multiobjective genetic algorithm: Nsga-ii. IEEE Trans. Evol. Comput. 6(2), 182–197 (2002)
Knowles, J., Corne, D.: The pareto archived evolution strategy: A new baseline algorithm for pareto multiobjective optimisation. In: Proceedings of the 1999 Congress on Evolutionary Computation, 1999. CEC 99, vol. 1. IEEE (1999)
Knowles, J.D., Corne, D.W.: Approximating the nondominated front using the pareto archived evolution strategy. Evol. Comput. 8(2), 149–172 (2000)
Corne, D.W., Knowles, J.D., Oates, M.J.: The pareto envelope-based selection algorithm for multiobjective optimization. In: Parallel Problem Solving from Nature PPSN VI, pp. 839–848. Springer (2000)
Corne, D.W., Jerram, N.R., Knowles, J.D., Oates, M.J., et al.: Pesa-ii: Region-based selection in evolutionary multiobjective optimization. In: Proceedings of the Genetic and Evolutionary Computation Conference (GECCO 2001). Citeseer (2001)
Zitzler, E., Künzli, S.: Indicator-based selection in multiobjective search. In: Parallel Problem Solving from Nature-PPSN VIII, pp. 832–842. Springer (2004)
Beume, N., Naujoks, B., Emmerich, M.: Sms-emoa: Multiobjective selection based on dominated hypervolume. Eur. J. Oper. Res. 181(3), 1653–1669 (2007)
Azzouz, N., Bechikh, S., Said, L.B.: Steady state ibea assisted by mlp neural networks for expensive multi-objective optimization problems. In: Proceedings of the 2014 Conference on Genetic and Evolutionary Computation, pp. 581–588. ACM (2014)
Zhang, Q., Li, H.: Moea/d: A multiobjective evolutionary algorithm based on decomposition. IEEE Trans. Evol. Comput. 11(6), 712–731 (2007)
Zitzler, E., Deb, K., Thiele, L.: Comparison of multiobjective evolutionary algorithms: Empirical results. Evol. Comput. 8(2), 173–195 (2000)
Deb, K., Thiele, L., Laumanns, M., Zitzler, E.: Scalable multi-objective optimization test problems. In: Proceedings of the 2002 Congress on Evolutionary Computation, 2002. CEC’02, vol. 1, pp. 825–830. IEEE (2002)
Zitzler, E., Thiele, L., Laumanns, M., Fonseca, C.M., Da Fonseca, V.G.: Performance assessment of multiobjective optimizers: an analysis and review. IEEE Trans. Evol. Comput. 7(2), 117–132 (2003)
Van Veldhuizen, D.A., Lamont, G.B.: On measuring multiobjective evolutionary algorithm performance. In: Proceedings of the 2000 Congress on Evolutionary Computation, 2000, vol. 1, pp. 204–211. IEEE (2000)
Hernández Gómez, R., Coello Coello, C.A.: Improved metaheuristic based on the r2 indicator for many-objective optimization. In: Proceedings of the 2015 on Genetic and Evolutionary Computation Conference, pp. 679–686. ACM (2015)
Bechikh, S., Said, L.B., Ghédira, K.: Negotiating decision makers’ reference points for group preference-based evolutionary multi-objective optimization. In: 2011 11th International Conference on Hybrid Intelligent Systems (HIS), pp. 377–382. IEEE (2011)
Bechikh, S., Said, L.B., Ghédira, K.: Group preference based evolutionary multi-objective optimization with nonequally important decision makers: Application to the portfolio selection problem. Int. J. Comput. Inf. Syst. Ind. Manag. Appl. 5(278–288), 71 (2013)
Kalboussi, S., Bechikh, S., Kessentini, M., Said, L.B.: Preference-based many-objective evolutionary testing generates harder test cases for autonomous agents. In: Search Based Software Engineering, pp. 245–250. Springer (2013)
Bechikh, S., Kessentini, M., Said, L.B., Ghédira, K.: Chapter four-preference incorporation in evolutionary multiobjective optimization: A survey of the state-of-the-art. Adv. Comput. 98, 141–207 (2015)
Bechikh, S.: Incorporating decision makers preference information in evolutionary multi-objective optimization. PhD thesis, University of Tunis, ISG-Tunis, Tunisia (2013)
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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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