Abstract
This paper presents a new toolkit for creating scalable multi-objective test problems. The WFG Toolkit is flexible, allowing characteristics such as bias, multi-modality, and non-separability to be incorporated and combined as desired. A wide variety of Pareto optimal geometries are also supported, including convex, concave, mixed convex/concave, linear, degenerate, and disconnected geometries.
All problems created by the WFG Toolkit are well defined, are scalable with respect to both the number of objectives and the number of parameters, and have known Pareto optimal sets. Nine benchmark multi-objective problems are suggested, including one that is both multi-modal and non-separable, an important combination of characteristics that is lacking among existing (scalable) multi-objective problems.
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References
Deb, K.: Multi-objective genetic algorithms: Problem difficulties and construction of test problems. Evolutionary Computation 7, 205–230 (1999)
Van Veldhuizen, D.A.: Multiobjective Evolutionary Algorithms: Classifications, Analyses, and New Innovations. PhD thesis, Air Force Institute of Technology, Wright-Patterson AFB, Ohio (1999)
Zitzler, E., Deb, K., Thiele, L.: Comparison of multiobjective evolutionary algorithms: Empirical results. Evolutionary Computation 8, 173–195 (2000)
Deb, K., Thiele, L., Laumanns, M., Zitzler, E.: Scalable test problems for evolutionary multi-objective optimization. KanGAL Report 2001001, Kanpur Genetic Algorithms Laboratory, Indian Institute of Technology, Kanpur, India (2001)
Whitley, D., Mathias, K., Rana, S., Dzubera, J.: Building better test functions. In: 6th International Conference on Genetic Algorithms, pp. 239–246. Morgan Kaufmann, San Francisco (1995)
Bäck, T., Michalewicz, Z.: Test landscapes. In: Handbook of Evolutionary Computation, vol. B2.7, pp. 14–20. Institute of Physics Publishing (1997)
Fogel, D.B., Beyer, H.G.: A note on the empirical evaluation of intermediate recombination. Evolutionary Computation 3, 491–495 (1995)
Deb, K., Thiele, L., Laumanns, M., Zitzler, E.: Scalable multi-objective optimization test problems. In: CEC 2002, vol. 1, pp. 825–830. IEEE, Los Alamitos (2002)
Van Veldhuizen, D.A., Lamont, G.B.: Multiobjective evolutionary algorithm test suites. In: 1999 ACM Symposium on Applied Computing, pp. 351–357. ACM, New York (1999)
Zitzler, E., Laumanns, M., Thiele, L.: SPEA2: Improving the strength Pareto evolutionary algorithm for multiobjective optimization. In: EUROGEN 2001, CIMNE, Barcelona, Spain, pp. 95–100 (2001)
Bentley, P.J., Wakefield, J.P.: Finding acceptable solutions in the pareto-optimal range using multiobjective genetic algorithms. In: Soft Computing in Engineering Design and Manufacturing, pp. 231–240. Springer, Heidelberg (1998)
Knowles, J.D., Corne, D.W.: Approximating the nondominated front using the Pareto archived evolution strategy. Evolutionary Computation 8, 149–172 (2000)
Deb, K., Pratap, A., Agarwal, S., Meyarivan, T.: A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Transactions on Evolutionary Computation 6, 182–197 (2002)
Fonseca, C.M., Fleming, P.J.: On the performance assessment and comparison of stochastic multiobjective optimizers. In: Ebeling, W., Rechenberg, I., Voigt, H.-M., Schwefel, H.-P. (eds.) PPSN 1996. LNCS, vol. 1141, pp. 584–593. Springer, Heidelberg (1996)
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Huband, S., Barone, L., While, L., Hingston, P. (2005). A Scalable Multi-objective Test Problem Toolkit. In: Coello Coello, C.A., Hernández Aguirre, A., Zitzler, E. (eds) Evolutionary Multi-Criterion Optimization. EMO 2005. Lecture Notes in Computer Science, vol 3410. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-31880-4_20
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DOI: https://doi.org/10.1007/978-3-540-31880-4_20
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