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Generalized multiobjective evolutionary algorithm guided by descent directions. (English) Zbl 1305.65150

Summary: This paper proposes a generalized descent directions-guided multiobjective algorithm (DDMOA2). DDMOA2 uses the scalarizing fitness assignment in its parent and environmental selection procedures. The population consists of leader and non-leader individuals. Each individual in the population is represented by a tuple containing its genotype as well as the set of strategy parameters. The main novelty and the primary strength of our algorithm is its reproduction operator, which combines the traditional local search and stochastic search techniques. To improve efficiency, when the number of objective is increased, descent directions are found only for two randomly chosen objectives. Furthermore, in order to increase the search pressure in high-dimensional objective space, we impose an additional condition for the acceptance of descent directions found for leaders during local search. The performance of the proposed approach is compared with those produced by representative state-of-the-art multiobjective evolutionary algorithms on a set of problems with up to 8 objectives. The experimental results reveal that our algorithm is able to produce highly competitive results with well-established multiobjective optimizers on all tested problems. Moreover, due to its hybrid reproduction operator, DDMOA2 demonstrates superior performance on multimodal problems.

MSC:

65K05 Numerical mathematical programming methods
90C15 Stochastic programming
90C29 Multi-objective and goal programming

Software:

DDMOA2; MSOPS-II; PISA; jMetal
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References:

[1] Beyer, H.-G., Schwefel, H.-P.: Evolution strategies: a comprehensive introduction. Nat. Comput. 1(1), 3-52 (2002) · Zbl 1014.68134
[2] Bleuler, S., Laumanns, M., Thiele, L., Zitzler, E.: PISA: a platform and programming language independent interface for search algorithms. In: Proceedings of the Conference on Evolutionary Multi-Criterion Optimization, pp. 494-508. EMO’03 (2003) · Zbl 1037.68743
[3] Bosman, P.A.N., Thierens, D.: The balance between proximity and diversity in multiobjective evolutionary algorithms. IEEE Trans. Evol. Comput. 7(2), 174-188 (2003)
[4] Coello Coello, C.A., Lamont, G.B., Van Veldhuizen, D.A.: Evolutionary Algorithms for Solving Multi-Objective Problems. Genetic and Evolutionary Computation, 2 edn. Springer (2007) · Zbl 1142.90029
[5] Costa, L., Espírito Santo, I., Denysiuk, R., Fernandes, E.M.G.P.: Hybridization of a genetic algorithm with a pattern search augmented Lagrangian method. In: Proceedings of the Conference on Conference on Engineering Optimization, p. 1195. EngOpt’10 (2010)
[6] Deb, K.: Multi-Objective Optimization using Evolutionary Algorithms. Wiley-Interscience Series in Systems and Optimization. Wiley (2001)
[7] 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)
[8] Deb, K., Thiele, L., Laumanns, M., Zitzler, E.: Scalable test problems for evolutionary multi-objective optimization. Technical Report 112, Swiss Federal Institute of Technology, Zurich, Switzerland (2001) · Zbl 1078.90567
[9] Denysiuk, R., Costa, L., Espírito Santo, I.: DDMOA: Descent directions based multiobjective algorithm. In: Proceedings of the Conference on Computational and Mathematical Methods in Science and Engineering, pp. 460-471. CMMSE’12 (2012) · Zbl 1305.65150
[10] Denysiuk, R., Costa, L., Espírito Santo, I.: DDMOA2: Improved descent directions-based multiobjective algorithm. In: Proceedings of the Conference on Computational and Mathematical Methods in Science and Engineering. pp. 513-524. CMMSE’13 (2013) · Zbl 1311.90132
[11] Denysiuk, R., Costa, L., Espírito Santo, I.: A new hybrid evolutionary multiobjective algorithm guided by descent directions. J. Math. Model. Algoritm. Oper. Res. 12(3), 233-251 (2013) · Zbl 1311.90132
[12] Durillo, J.J., Nebro, A.J.: jMetal: a Java framework for multi-objective optimization. Adv. Eng. Softw. 42(10), 760-771 (2011)
[13] García, S., Molina, D., Lozano, M., Herrera, F.: A study on the use of non-parametric tests for analyzing the evolutionary algorithms’ behaviour: a case study on the CEC’2005 special session on real parameter optimization. J. Heuristics 15(6), 617-644 (2009) · Zbl 1191.68828
[14] Hughes, E.J.: MSOPS-II: A general-purpose many-objective optimiser. In: Proceedings of the IEEE Congress on Evolutionary Computation, pp. 3944-3951. CEC’07 (2007)
[15] Ishibuchi, H., Doi, T., Nojima, Y.: Incorporation of scalarizing fitness functions into evolutionary multiobjective optimization algorithms. In: In Proceedings of the Conference on Parallel Problem Solving from Nature, pp. 493-502. PPSN’06 (2006)
[16] Khare, V.R., Yao, X., Deb, K.: Performance scaling of multi-objective evolutionary algorithms. In: Proceedings of the Conference on Evolutionary Multi-Criterion Optimization, pp. 376-390. EMO’03 (2003) · Zbl 1036.90541
[17] Knowles, J., Corne, D.: Memetic algorithms for multiobjective optimization: issues, methods and prospects. Recent Adv. Memet. Algoritm. Stud. Fuzziness Soft Comput. 166, 313-352 (2005)
[18] Li, H., Zhang, Q.: Multiobjective optimization problems with complicated Pareto sets, MOEA/D and NSGA-II. IEEE Trans. Evol. Comput. 13(2), 284-302 (2009)
[19] Loh, W.L.: On Latin hypercube sampling. Ann. Stat. 33(6), 2058-2080 (1996) · Zbl 0867.62005
[20] Miettinen, K.: Nonlinear multiobjective optimization. International Series in Operations Research and Management Science, vol. 12. Kluwer Academic Publishers (1999) · Zbl 0949.90082
[21] Purshouse, R.C., Fleming, P.J.: Evolutionary many-objective optimisation: an exploratory analysis. In: Proceedings of the IEEE Congress on Evolutionary Computation, CEC’03, pp. 2066-2073 (2003)
[22] Shukla, P.K., Deb, K.: On finding multiple Pareto-optimal solutions using classical and evolutionary generating methods. Eur. J. Oper. Res. 181(3), 1630-1652 (2007) · Zbl 1123.90048
[23] Torczon, V.: On the convergence of pattern search algorithms. SIAM J. Optim. 7, 1-25 (1997) · Zbl 0884.65053
[24] Zitzler, E., Künzli, S.: Indicator-based selection in multiobjective search. In: Proceedings of the Conference on Parallel Problem Solving from Nature, PPSN’04, pp. 832-842 (2004)
[25] Zitzler, E., Thiele, L.: Multiobjective optimization using evolutionary algorithms - A case comparative case study. In: Proceedings of the Conference on Parallel Problem Solving from Nature, PPSN’98, pp. 292-304 (1998)
[26] Zitzler, E., Thiele, L., Laumanns, M., Fonseca, C.M., Grunert da Fonseca, V.: Performance assessment of multiobjective optimizers: an analysis and review. IEEE Trans. Evol. Comput. 7(2), 117-132 (2003)
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