Abstract
We present a new multiobjective evolutionary algorithm (MOEA), called fast Pareto genetic algorithm (FastPGA), for the simultaneous optimization of multiple objectives where each solution evaluation is computationally- and/or financially-expensive. This is often the case when there are time or resource constraints involved in finding a solution. FastPGA utilizes a new ranking strategy that utilizes more information about Pareto dominance among solutions and niching relations. New genetic operators are employed to enhance the proposed algorithm’s performance in terms of convergence behavior and computational effort as rapid convergence is of utmost concern and highly desired when solving expensive multiobjective optimization problems (MOPs). Computational results for a number of test problems indicate that FastPGA is a promising approach. FastPGA yields similar performance to that of the improved nondominated sorting genetic algorithm (NSGA-II), a widely-accepted benchmark in the MOEA research community. However, FastPGA outperforms NSGA-II when only a small number of solution evaluations are permitted, as would be the case when solving expensive MOPs.
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April, J., Glover, F., Kelly, J., Laguna, M.: Practical introduction to simulation optimization. In: Chick, S. (ed.) Proceedings of the 2003 Winter Simulation Conference, pp. 71–78. Institute of Electrical and Electronics Engineers, Piscataway (2003)
Bui, L.T., Hussein, A.A., Essam, D.: Fitness inheritance for noisy evolutionary multi-objective optimization. In: Beyer, H.-G. (ed.) Proceedings of the 2005 Genetic and Evolutionary Computation Conference, vol. 1, pp. 779–785. ACM Press, New York (2005)
Coello, C.A.C., Lamont, G.B.: Applications of Multi-Objective Evolutionary Algorithms. World Scientific, Singapore (2004)
Coello, C.A.C., Pulido, G.T., Lechuga, M.S.: Handling multiple objectives with particle swarm optimization. IEEE Trans. Evol. Comput. 8(3), 256–279 (2004)
Coello, C.A.C., Van Veldhuizen, D.A., Lamont, G.B.: Evolutionary Algorithms for Solving Multi-Objective Problems, 1st edn. Kluwer Academic, New York (2002)
Czyzac, P., Jaszkiewicz, A.: Pareto simulated annealing—a metaheuristic technique for multiple objective combinatorial optimization. J. Multicriteria Decis. Anal. 7, 34–47 (1998)
Deb, K.: Multi-Objective Optimization Using Evolutionary Algorithms, 1st edn. Wiley, Chichester (2001)
Deb, K., Agrawal, R.B.: Simulated binary crossover for continuous search space. Complex Syst. 9, 115–148 (1995)
Deb, K., Goyal, M.: A combined genetic adaptive search (GeneAS) for engineering design. Comput. Sci. Inform. 26(4), 30–45 (1996)
Deb, K., Pratap, A., Agarval, S., Meyarivan, T.A.: Fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans. Evol. Comput. 6, 182–197 (2002)
Deb, K., Mohan, M., Mishra, S.: Evaluating the epsilon-domination based multi-objective evolutionary algorithm for a quick computation of Pareto-optimal solutions. Evol. Comput. 13(4), 501–525 (2005)
Erbas, C., Cerav-Erbas, S., Pimentel, A.D.: Multiobjective optimization and evolutionary algorithms for the application mapping problem in multiprocessor system-on-chip design. IEEE Trans. Evol. Comput. (2006, to appear)
Farina, M., Deb, K., Amato, P.: Dynamic multiobjective optimization problems: test cases, approximations, and applications. IEEE Trans. Evol. Comput. 8(5), 425–442 (2004)
Fonseca, C.M., Flemming, P.J.: Genetic algorithms for multiobjective optimization: formulation, discussion and generalization. In: Proceedings of the Fifth International Conference on Genetic Algorithms, pp. 416–423, San Mateo, CA, 1993
Goldberg, D.E.: Genetic Algorithms in Search, Optimisation and Machine Learning. Addison–Wesley, Reading (1989)
Goldberg, D.E., Deb, K.: A comparison of selection schemes used in genetic algorithms. Found. Genet. Algorithms 1, 69–93 (1991)
Hanne, T.: Global multiobjective optimization using evolutionary algorithms. J. Heur. 6(3), 347–360 (2000)
Herrera, F., Lozano, M., Verdegay, J.L.: Tackling real-coded genetic algorithms: operators and tolls for behavioral analysis. Artif. Intell. Rev. 12, 265–319 (1998)
Kursawe, F.: A variant of evolution strategies for vector optimization. In: Schwefel, H.P. (ed.) Proceedings of the 1st Parallel Problem Solving from Nature Workshop, pp. 193–197. Springer, Berlin (1990)
Knowles, J.: ParEGO: a hybrid algorithm with on-line landscape approximation for expensive multiobjective optimization problems. IEEE Trans. Evol. Comput. 10(1), 50–66 (2006)
Knowles, J., Corne, D.: The Pareto archived evolution strategy: a new Baseline algorithm for multiobjective optimization. In: Proceedings of the 1999 Congress on Evolutionary Computation (CEC’1999), pp. 98–105, IEEE Service Center, Washington, D.C., July 1999
Knowles, J., Corne, D.: On metrics for comparing nondominated sets. In: Proceedings of the 2002 Congress on Evolutionary Computation (CEC’2002), vol. 1, pp. 711–716, IEEE Service Center, Piscataway, New Jersey, May 2002
Kulturel-Konak, S., Smith, A.E., Norman, B.A.: Multi-objective tabu search using a multinomial probability mass function. Eur. J. Oper. Res. 169(3), 915–931 (2006)
Lu, H., Yen, G.G.: Rank-density-based multiobjective genetic algorithm and benchmark test function study. IEEE Trans. Evol. Comput. 7(4), 325–343 (2003)
Michalewicz, Z.: Genetic Algorithm + Data Structures = Evolution Programs. Springer, New York (1996)
Nafploitis, N., Horn, J., Goldberg, D.E.: A Niched Pareto genetic algorithm for multiobjective optimization. In: Proceedings of the First IEEE Conference on Evolutionary Computation, pp. 82–87, 1994
Nebro, A.J., Luna, F., Alba, E., Beham, A., Dorronsoro, B.: AbYSS: adapting scatter search for multiobjective optimization. Tech-Report: ITI-2006-2, Departamento de Lenguajes y Ciencias de la Computacion, University of Malaga, Malaga, Spain, 2006
Shen, Z.J., Daskin, M.: Tradeoffs between customer service and cost in integrated supply chain design. Manuf. Serv. Oper. Manag. 7(3), 188–207 (2005)
Srinivas, N., Deb, K.: Multiobjective optimization using nondominated sorting in genetic algorithms. Int. J. Evol. Comput. 2(3), 221–248 (1994)
Tan, K.C., Lee, T.H., Khor, E.F.: Evolutionary algorithm with dynamic population size and local exploration for multi-objective optimization. IEEE Trans. Evol. Comput. 5(6), 565–588 (2001)
Van Veldhuizen, D.A., Lamont, G.B.: On measuring multiobjective evolutionary algorithm performance. In: Proceedings of 2000 Congress on Evolutionary Computation, vol. 1, pp. 204–211, IEEE Service Center, Piscataway, New Jersey, July 2000
While, L., Hingston, P., Barone, L., Huband, S.: A faster algorithm for calculating hypervolume. IEEE Trans. Evol. Comput. 10(1), 29–38 (2006)
Zitzler, E., Thiele, L.: Multiobjective evolutionary algorithms: a comparative study and strength Pareto approach. IEEE Trans. Evol. Comput. 3(4), 257–271 (1999)
Zitzler, E., Laumanns, M., Thiele, L.: SPEA2: improving the strength Pareto evolutionary algorithm. Technical Report 103, Computer Engineering and Networks Laboratory (TIK), Swiss Federal Institute of Technology (ETH) Zurich, Gloriastrasse 35, CH-8092 Zurich, Switzerland (2001)
Zitzler, E., Deb, K., Thiele, L.: Comparison of multiobjective evolutionary algorithms: empirical results. Evol. Comput. 8(2), 173–195 (2000)
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Eskandari, H., Geiger, C.D. A fast Pareto genetic algorithm approach for solving expensive multiobjective optimization problems. J Heuristics 14, 203–241 (2008). https://doi.org/10.1007/s10732-007-9037-z
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DOI: https://doi.org/10.1007/s10732-007-9037-z