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An Evolutionary Optimization Method Based on Scalarization for Multi-objective Problems

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Abstract

In this paper, we perform some computational experiments on the new global scalarization method for multi-objective optimization problems. Its main idea is to construct, for a given multi-objective optimization problem, a global scalarization function whose values are non-negative real numbers. The points where the scalarization function attains the zero value are exactly weak Pareto stationary points for the original multi-objective problem.
We apply two different evolutionary algorithms to minimize the scalarization function; both of them are designed for solving scalar optimization problems. The first one is the classical Genetic Algorithm (GA). The second one is a new algorithm called Dissimilarity and Similarity of Chromosomes (DSC), which has been designed by the authors.
The computational results presented in this paper show that the DSC algorithm can find more minimizers of the scalarization function than the classical GA.

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Literatur
1.
Zurück zum Zitat Coello, C.A.C.: Evolutionary Algorithms for Solving Multi-Objective Problems, 2nd edn. Springer, Science+Business Media, LLC All, Heidelberg (2007)MATH Coello, C.A.C.: Evolutionary Algorithms for Solving Multi-Objective Problems, 2nd edn. Springer, Science+Business Media, LLC All, Heidelberg (2007)MATH
2.
Zurück zum Zitat Deb, K.: Multi-Objective Optimization Using Evolutionary Algorithms. Wiley, New York (2001)MATH Deb, K.: Multi-Objective Optimization Using Evolutionary Algorithms. Wiley, New York (2001)MATH
3.
Zurück zum Zitat Michalewicz, Z.: Genetic Algorithms + Data Structures = Evolution Programs. Artificial Intelligence, 3rd edn. Springer, Heidelberg (1996)MATH Michalewicz, Z.: Genetic Algorithms + Data Structures = Evolution Programs. Artificial Intelligence, 3rd edn. Springer, Heidelberg (1996)MATH
4.
Zurück zum Zitat Deb, K., Member, A., Pratap, A., Agarwal, S., Meyarivan, T.: A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans. Evol. Comput. 6(2), 182–197 (2002)CrossRef Deb, K., Member, A., Pratap, A., Agarwal, S., Meyarivan, T.: A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans. Evol. Comput. 6(2), 182–197 (2002)CrossRef
5.
Zurück zum Zitat Rahmo, E., Studniarski, M.: A new global scalarization method for multiobjective optimization with an arbitrary ordering cone. Appl. Math. 8, 154–163 (2017)CrossRef Rahmo, E., Studniarski, M.: A new global scalarization method for multiobjective optimization with an arbitrary ordering cone. Appl. Math. 8, 154–163 (2017)CrossRef
6.
Zurück zum Zitat Al-Jawadi, R., Studniarski, M., Younus, A.: A New Genetic Algorithm Based on Dissimilarities and Similarities. Submitted for publication Al-Jawadi, R., Studniarski, M., Younus, A.: A New Genetic Algorithm Based on Dissimilarities and Similarities. Submitted for publication
7.
Zurück zum Zitat Ehrgot, M., Gandibleux, X.: Multiple Criteria Optimization State of the Art Annoteted Bibligraphic Surveys. Kluwer Academic Publishers, Dordrecht (2003) Ehrgot, M., Gandibleux, X.: Multiple Criteria Optimization State of the Art Annoteted Bibligraphic Surveys. Kluwer Academic Publishers, Dordrecht (2003)
8.
Zurück zum Zitat Ehrgott, M.: Multicriteria Optimization. Springer, Berlin (2005) Ehrgott, M.: Multicriteria Optimization. Springer, Berlin (2005)
10.
Zurück zum Zitat Caramia, M., Dell’Olmo, P.: Multi-objective Optimization Managment in Freight Logistic Increasing Capacity (2008) Caramia, M., Dell’Olmo, P.: Multi-objective Optimization Managment in Freight Logistic Increasing Capacity (2008)
11.
Zurück zum Zitat Voß, T., Beume, N., Igel, C.: Scalarization versus indicator-based selection in multi-objective CMA evolution strategies. In: IEEE Congress on Evolutionary Computation, pp. 3036–3043. IEEE (2008) Voß, T., Beume, N., Igel, C.: Scalarization versus indicator-based selection in multi-objective CMA evolution strategies. In: IEEE Congress on Evolutionary Computation, pp. 3036–3043. IEEE (2008)
12.
Zurück zum Zitat Man, K.F., Tang, K.S., Kwong, S.: Genetic algorithms: concepts and applications. IEEE Trans. Ind. Electron. 43(5), 519–534 (1996)CrossRef Man, K.F., Tang, K.S., Kwong, S.: Genetic algorithms: concepts and applications. IEEE Trans. Ind. Electron. 43(5), 519–534 (1996)CrossRef
13.
Zurück zum Zitat Chudasama, C.: Comparison of parents selection methods of genetic algorithm for TSP. In: International Conference on Computer Communications and Networks, CSI- COMNET, pp. 85–87 (2011) Chudasama, C.: Comparison of parents selection methods of genetic algorithm for TSP. In: International Conference on Computer Communications and Networks, CSI- COMNET, pp. 85–87 (2011)
14.
Zurück zum Zitat Iquebal, M.A.: Genetic Algorithms and their Applications: An Overview. Ph.D. Agricultural Stat. Roll No. 9068 I.A.S.R.I., Libr. Ave. New Delhi-110012, pp. 1–11 Iquebal, M.A.: Genetic Algorithms and their Applications: An Overview. Ph.D. Agricultural Stat. Roll No. 9068 I.A.S.R.I., Libr. Ave. New Delhi-110012, pp. 1–11
15.
Zurück zum Zitat Liang, Y., Leung, K.: Genetic Algorithm with adaptive elitist-population strategies for multimodal function optimization. Appl. Soft Comput. J. 11(2), 2017–2034 (2010)CrossRef Liang, Y., Leung, K.: Genetic Algorithm with adaptive elitist-population strategies for multimodal function optimization. Appl. Soft Comput. J. 11(2), 2017–2034 (2010)CrossRef
16.
Zurück zum Zitat Minami, M.: Weak Pareto-optimal necessary conditions in a nondifferentiable multiobjective program on a Banach space. J. Optim. Theory Appl. 41(3), 451–461 (1983)MathSciNetCrossRefMATH Minami, M.: Weak Pareto-optimal necessary conditions in a nondifferentiable multiobjective program on a Banach space. J. Optim. Theory Appl. 41(3), 451–461 (1983)MathSciNetCrossRefMATH
17.
Zurück zum Zitat Clarke, F.H.: Optimization and Nonsmooth Analysis. Wiley, New York (1983)MATH Clarke, F.H.: Optimization and Nonsmooth Analysis. Wiley, New York (1983)MATH
18.
Zurück zum Zitat Younus, A.: Converting a Multi-Objective Optimization Problem to a Single-Objective Optimization Problem by Using a New Scalarization Method. M.Sc. Thesis, University of Łódź (2016) Younus, A.: Converting a Multi-Objective Optimization Problem to a Single-Objective Optimization Problem by Using a New Scalarization Method. M.Sc. Thesis, University of Łódź (2016)
19.
Zurück zum Zitat Optimization Toolbox, User’s Guide. The MathWorks (2008) Optimization Toolbox, User’s Guide. The MathWorks (2008)
Metadaten
Titel
An Evolutionary Optimization Method Based on Scalarization for Multi-objective Problems
verfasst von
Marcin Studniarski
Radhwan Al-Jawadi
Aisha Younus
Copyright-Jahr
2018
DOI
https://doi.org/10.1007/978-3-319-67220-5_5