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2017 | OriginalPaper | Buchkapitel

A Constraint Partitioning Method Based on Minimax Strategy for Constrained Multiobjective Optimization Problems

verfasst von : Xueqiang Li, Shen Fu, Han Huang

Erschienen in: Simulated Evolution and Learning

Verlag: Springer International Publishing

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Abstract

Constrained multiobjective optimization problem (CMOP) is an important research topic in the field of evolutionary computation. In terms of constraint handling, most of the existing evolutionary algorithms consider more about the proportion of infeasible solutions in population, but less concern about the distribution of infeasible solutions. Therefore, we propose a constraint partitioning method based on minimax strategy (CPM/MS) to solve CMOP. Firstly, we analyze the impact of the distribution of infeasible solutions on selecting solutions and give a preconditioning method for infeasible solutions. Secondly, we divide the preconditioned solutions into different regions by minimax strategy. Finally, we update individuals based on feasibility criteria method in each region. The effectiveness of CPM/MS algorithm is extensively evaluated on a suite of 10 bound-constrained numerical optimization problems, where the results show that CPM/MS algorithm is able to obtain considerably better fronts for some of the problems compared with some the state-of-the-art multiobjective evolutionary algorithms.

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Literatur
1.
Zurück zum Zitat Deb, K.: An efficient constraint handling method for genetic algorithms. Comput. Methods Appl. Mech. Eng. 186(2–4), 311–338 (2000)CrossRefMATH Deb, K.: An efficient constraint handling method for genetic algorithms. Comput. Methods Appl. Mech. Eng. 186(2–4), 311–338 (2000)CrossRefMATH
2.
Zurück zum Zitat Cai, X., Hu, Z., Fan, Z.: A novel memetic algorithm based on invasive weed optimization and di_erential evolution for constrained optimization. Soft. Comput. 17(10), 1893–1910 (2013)CrossRef Cai, X., Hu, Z., Fan, Z.: A novel memetic algorithm based on invasive weed optimization and di_erential evolution for constrained optimization. Soft. Comput. 17(10), 1893–1910 (2013)CrossRef
3.
Zurück zum Zitat Hu, Z., Cai, X., Fan, Z.: An improved memetic algorithm using ring neighborhood topology for constrained optimization. Soft. Comput. 18(10), 2023–2041 (2013)CrossRef Hu, Z., Cai, X., Fan, Z.: An improved memetic algorithm using ring neighborhood topology for constrained optimization. Soft. Comput. 18(10), 2023–2041 (2013)CrossRef
4.
Zurück zum Zitat Li, Z.Y., Huang, T., Chen, S.M., Li, R.F.: Overview of constrained optimization evolutionary algorithms. J. Softw. (2017) Li, Z.Y., Huang, T., Chen, S.M., Li, R.F.: Overview of constrained optimization evolutionary algorithms. J. Softw. (2017)
5.
Zurück zum Zitat Farmani, R., Wright, J.A.: Self-adaptive fitness formulation for constrained optimization. IEEE Trans. Evol. Comput. 7(5), 445–455 (2003)CrossRef Farmani, R., Wright, J.A.: Self-adaptive fitness formulation for constrained optimization. IEEE Trans. Evol. Comput. 7(5), 445–455 (2003)CrossRef
6.
Zurück zum Zitat Xiao, J.H., Xu, J., Shao, Z., Jiang, C.F., Pan, L.: A genetic algorithm for solving multi-constrained function optimization problems based on KS function. In: Proceedings of the 2007 IEEE Congress on Evolutionary Computation, Singapore, pp. 4497–4501. IEEE Press (2007) Xiao, J.H., Xu, J., Shao, Z., Jiang, C.F., Pan, L.: A genetic algorithm for solving multi-constrained function optimization problems based on KS function. In: Proceedings of the 2007 IEEE Congress on Evolutionary Computation, Singapore, pp. 4497–4501. IEEE Press (2007)
7.
Zurück zum Zitat Tessema, B., Yen, G.G.: A adaptive penalty formulation for constrained evolutionary optimization. IEEE Trans. Syst. Man Cybern. (A) 39(3), 565–578 (2009)CrossRef Tessema, B., Yen, G.G.: A adaptive penalty formulation for constrained evolutionary optimization. IEEE Trans. Syst. Man Cybern. (A) 39(3), 565–578 (2009)CrossRef
8.
Zurück zum Zitat Surry, P.D., Radcliffe, N.J.: The COMOGA method: Constrained optimization by multiobjective genetic algorithm. Control Cybern. 26(3), 391–412 (1997)MATH Surry, P.D., Radcliffe, N.J.: The COMOGA method: Constrained optimization by multiobjective genetic algorithm. Control Cybern. 26(3), 391–412 (1997)MATH
9.
Zurück zum Zitat Wang, Y., Cai, Z.X., Guo, G., Zhou, Y.R.: A dynamic hybrid framework for constrained evolutionary optimization. IEEE Trans. Syst. Man Cybern. (B) 42(1), 203–217 (2012)CrossRef Wang, Y., Cai, Z.X., Guo, G., Zhou, Y.R.: A dynamic hybrid framework for constrained evolutionary optimization. IEEE Trans. Syst. Man Cybern. (B) 42(1), 203–217 (2012)CrossRef
10.
Zurück zum Zitat Cai, Z.X., Wang, Y.: Combining multiobjective optimization with differential evolution to solve constrained optimization problems. IEEE Trans. Evol. Comput. 16(1), 117–134 (2012)CrossRef Cai, Z.X., Wang, Y.: Combining multiobjective optimization with differential evolution to solve constrained optimization problems. IEEE Trans. Evol. Comput. 16(1), 117–134 (2012)CrossRef
11.
Zurück zum Zitat Gong, W.Y., Cai, Z.H.: A multiobjective differential evolution algorithm for constrained optimization. In: Proceedings of the 2008 IEEE Congress on Evolutionary Computation, Hong Kong, pp. 181–188. IEEE Press (2008) Gong, W.Y., Cai, Z.H.: A multiobjective differential evolution algorithm for constrained optimization. In: Proceedings of the 2008 IEEE Congress on Evolutionary Computation, Hong Kong, pp. 181–188. IEEE Press (2008)
12.
Zurück zum Zitat Gao, W.F., Yen, G., Liu, S.Y.: A dual-population differential evolution with coevolution for constrained optimization. IEEE Trans. Cybern. 45(5), 1108–1121 (2014) Gao, W.F., Yen, G., Liu, S.Y.: A dual-population differential evolution with coevolution for constrained optimization. IEEE Trans. Cybern. 45(5), 1108–1121 (2014)
13.
Zurück zum Zitat Zielinski, R., Laur, R.: Constrained single-objective optimization using differential evolution. In: Proceedings of the 2006 IEEE International Conference on Evolutionary Computation, Vancouver, pp. 223–230. IEEE Press (2006) Zielinski, R., Laur, R.: Constrained single-objective optimization using differential evolution. In: Proceedings of the 2006 IEEE International Conference on Evolutionary Computation, Vancouver, pp. 223–230. IEEE Press (2006)
14.
Zurück zum Zitat Sarker, R.A., Elsayed, S.M., Ray, T.: Differential evolution with dynamic parameters selection for optimization problems. IEEE Trans. Evol. Comput. 18(5), 689–707 (2014)CrossRef Sarker, R.A., Elsayed, S.M., Ray, T.: Differential evolution with dynamic parameters selection for optimization problems. IEEE Trans. Evol. Comput. 18(5), 689–707 (2014)CrossRef
15.
Zurück zum Zitat Wang, Y., Wang, B.C., Li, H.X., Yen, G.G.: Incorporating objective function information into the feasibility rule for constrained evolutionary optimization. IEEE Trans. Cybern. 46(12), 2938–2952 (2015)CrossRef Wang, Y., Wang, B.C., Li, H.X., Yen, G.G.: Incorporating objective function information into the feasibility rule for constrained evolutionary optimization. IEEE Trans. Cybern. 46(12), 2938–2952 (2015)CrossRef
16.
Zurück zum Zitat Runarsson, T.P., Yao, X.: Stochastic ranking for constrained evolutionary optimization. IEEE Trans. Evol. Comput. 4(3), 284–294 (2000)CrossRef Runarsson, T.P., Yao, X.: Stochastic ranking for constrained evolutionary optimization. IEEE Trans. Evol. Comput. 4(3), 284–294 (2000)CrossRef
17.
Zurück zum Zitat Zhang, M., Luo, W.J., Wang, X.: Differential evolution with dynamic stochastic selection for constrained optimization. Inf. Sci. 178(15), 3043–3074 (2008)CrossRef Zhang, M., Luo, W.J., Wang, X.: Differential evolution with dynamic stochastic selection for constrained optimization. Inf. Sci. 178(15), 3043–3074 (2008)CrossRef
18.
Zurück zum Zitat Takahama, T., Sakai, S.: Constrained optimization by the ε constrained differential evolution with gradient-based mutation and feasible elites. In: Proceedings of the 2006 IEEE International Conference on Evolutionary Computation, Vancouver, pp. 372–378. IEEE Press (2006) Takahama, T., Sakai, S.: Constrained optimization by the ε constrained differential evolution with gradient-based mutation and feasible elites. In: Proceedings of the 2006 IEEE International Conference on Evolutionary Computation, Vancouver, pp. 372–378. IEEE Press (2006)
19.
Zurück zum Zitat Bu, C., Luo, W., Zhu, T.: Differential evolution with a species-based repair strategy for constrained optimization. In: Proceedings of the 2014 IEEE Congress on Evolutionary Computation, Beijing, pp. 967–974. IEEE Press (2014) Bu, C., Luo, W., Zhu, T.: Differential evolution with a species-based repair strategy for constrained optimization. In: Proceedings of the 2014 IEEE Congress on Evolutionary Computation, Beijing, pp. 967–974. IEEE Press (2014)
20.
Zurück zum Zitat Takahama, T., Sakai, S.: Efficient constrained optimization by the ε constrained rank-based differential evolution. In: Proceedings of the 2012 IEEE Congress on Evolutionary Computation, Brisbane, pp. 1–8. IEEE Press (2012) Takahama, T., Sakai, S.: Efficient constrained optimization by the ε constrained rank-based differential evolution. In: Proceedings of the 2012 IEEE Congress on Evolutionary Computation, Brisbane, pp. 1–8. IEEE Press (2012)
21.
Zurück zum Zitat Ishibuchi, H., Murata, T.: A Multiobjective genetic local search algorithm and its application to flowshop scheduling. IEEE Trans. Syst. Man Cybern. Part C Appl. Rev. 28(3), 392–403 (1998)CrossRef Ishibuchi, H., Murata, T.: A Multiobjective genetic local search algorithm and its application to flowshop scheduling. IEEE Trans. Syst. Man Cybern. Part C Appl. Rev. 28(3), 392–403 (1998)CrossRef
22.
Zurück zum Zitat 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)CrossRef 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)CrossRef
23.
Zurück zum Zitat Corne, D.W., Jerram, N.R., Knowles, J.D., Oates, M.J.: PESA-II: region-based selection in evolutionary multiobjective optimization. In: Proceedings of the 3rd Annual Conference on Genetic and Evolutionary Computation, pp. 283–290. Morgan Kaufmann Publishers Inc. (2001) Corne, D.W., Jerram, N.R., Knowles, J.D., Oates, M.J.: PESA-II: region-based selection in evolutionary multiobjective optimization. In: Proceedings of the 3rd Annual Conference on Genetic and Evolutionary Computation, pp. 283–290. Morgan Kaufmann Publishers Inc. (2001)
24.
Zurück zum Zitat Zitzler, E., Thiele, L.: Multiobjective evolutionary algorithms: a comparative case study and the strength pareto approach. IEEE Trans. Evol. Comput. 3(4), 257–271 (1999)CrossRef Zitzler, E., Thiele, L.: Multiobjective evolutionary algorithms: a comparative case study and the strength pareto approach. IEEE Trans. Evol. Comput. 3(4), 257–271 (1999)CrossRef
25.
Zurück zum Zitat Ishibuchi, H., Murata, T.: A multiobjective genetic local search algorithm and its application to flowshop scheduling. IEEE Trans. Syst. Man Cybern. Part C Appl. Rev. 28(3), 392–403 (1998)CrossRef Ishibuchi, H., Murata, T.: A multiobjective genetic local search algorithm and its application to flowshop scheduling. IEEE Trans. Syst. Man Cybern. Part C Appl. Rev. 28(3), 392–403 (1998)CrossRef
26.
Zurück zum Zitat Zhang, Q., Li, H.: MOEA/D: a multiobjective evolutionary algorithm based on decomposition. IEEE Trans. Evol. Comput. 11(6), 712–731 (2007)CrossRef Zhang, Q., Li, H.: MOEA/D: a multiobjective evolutionary algorithm based on decomposition. IEEE Trans. Evol. Comput. 11(6), 712–731 (2007)CrossRef
27.
Zurück zum Zitat Liu, H.L., Gu, F., Zhang, Q.: Decomposition of a multiobjective optimization problem into a number of simple multiobjective subproblems. IEEE Trans. Evol. Comput. 18(3), 450–455 (2014)CrossRef Liu, H.L., Gu, F., Zhang, Q.: Decomposition of a multiobjective optimization problem into a number of simple multiobjective subproblems. IEEE Trans. Evol. Comput. 18(3), 450–455 (2014)CrossRef
28.
Zurück zum Zitat Cai, X., Li, Y., Fan, Z., Zhang, Q.: An external archive guided multiobjective evolutionary algorithm based on decomposition for combinatorial optimization. IEEE Trans. Evol. Comput. 19(4), 508–523 (2015)CrossRef Cai, X., Li, Y., Fan, Z., Zhang, Q.: An external archive guided multiobjective evolutionary algorithm based on decomposition for combinatorial optimization. IEEE Trans. Evol. Comput. 19(4), 508–523 (2015)CrossRef
29.
Zurück zum Zitat Cai, X., Yang, Z., Fan, Z., Zhang, Q.: Decomposition-based-sorting and angle-based-selection for evolutionary multiobjective and many-objective optimization. IEEE Trans. Cybern. PP(99), 1–14 (2016) Cai, X., Yang, Z., Fan, Z., Zhang, Q.: Decomposition-based-sorting and angle-based-selection for evolutionary multiobjective and many-objective optimization. IEEE Trans. Cybern. PP(99), 1–14 (2016)
30.
Zurück zum Zitat Jiang, S., Zhang, J., Ong, Y.S., Zhang, A.N., Tan, P.S.: A simple and fast hypervolume indicator-based multiobjective evolutionary algorithm. IEEE Trans. Cybern. 45(10), 2202–2213 (2015)CrossRef Jiang, S., Zhang, J., Ong, Y.S., Zhang, A.N., Tan, P.S.: A simple and fast hypervolume indicator-based multiobjective evolutionary algorithm. IEEE Trans. Cybern. 45(10), 2202–2213 (2015)CrossRef
31.
Zurück zum Zitat Liu, H., Li, X., Chen, Y.: Multiobjective evolutionary algorithm based on dynamical crossover and mutation. In: Proceedings of International Conference on Computational Intelligence and Security, Suzhou, pp. 150–155. IEEE (2008) Liu, H., Li, X., Chen, Y.: Multiobjective evolutionary algorithm based on dynamical crossover and mutation. In: Proceedings of International Conference on Computational Intelligence and Security, Suzhou, pp. 150–155. IEEE (2008)
32.
Zurück zum Zitat Zhang, Q., Zhou, A.M., Suganthan, P.N., et al.: Multiobjective optimization test instances for the CEC 2009 special session and competition. School of Computer Science and Electrical Engineering, University of Essex, Essex (2009) Zhang, Q., Zhou, A.M., Suganthan, P.N., et al.: Multiobjective optimization test instances for the CEC 2009 special session and competition. School of Computer Science and Electrical Engineering, University of Essex, Essex (2009)
33.
Zurück zum Zitat Zitzler, E., Thiele, L., Laumanns, M., et al.: Performance assessment of multiobjective optimizers: an analys is and review. IEEE Trans. Evol. Comput. 7(2), 117–132 (2003)CrossRef Zitzler, E., Thiele, L., Laumanns, M., et al.: Performance assessment of multiobjective optimizers: an analys is and review. IEEE Trans. Evol. Comput. 7(2), 117–132 (2003)CrossRef
34.
Zurück zum Zitat Zhang, Q., Suganthan, P.N.: Final report on CEC’09 MOEA competition. School of Computer Science and Electrical Engineering, University of Essex, Essex (2009) Zhang, Q., Suganthan, P.N.: Final report on CEC’09 MOEA competition. School of Computer Science and Electrical Engineering, University of Essex, Essex (2009)
Metadaten
Titel
A Constraint Partitioning Method Based on Minimax Strategy for Constrained Multiobjective Optimization Problems
verfasst von
Xueqiang Li
Shen Fu
Han Huang
Copyright-Jahr
2017
DOI
https://doi.org/10.1007/978-3-319-68759-9_21