Abstract
Most of the derivative-free optimization (DFO) algorithms rely on a comparison function able to compare any pair of points with respect to a black-box objective function. Recently, new dedicated derivative-free optimization algorithms have emerged to tackle multi-objective optimization problems and provide a Pareto front approximation to the user. This work aims at reusing single objective DFO algorithms (such as Nelder-Mead) in the context of multi-objective optimization. Therefore we introduce a comparison function able to compare a pair of points in the context of a set of non-dominated points. We describe an algorithm, MOGEN, which initializes a Pareto front approximation composed of a population of instances of single-objective DFO algorithms. These algorithms use the same introduced comparison function relying on a shared Pareto front approximation. The different instances of single-objective DFO algorithms are collaborating and competing to improve the Pareto front approximation. Our experiments comparing MOGEN with the state-of the-art Direct Multi-Search algorithm on a large set of benchmarks shows the practicality of the approach, allowing to obtain high quality Pareto fronts using a reasonably small amount of function evaluations.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Bandyopadhyay, S., Pal, S., Aruna, B.: Multiobjective gas, quantitative indices, and pattern classification. IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics 34(5), 2088–2099 (2004)
Ben Abdelaziz, F., Lang, P., Nadeau, R.: Dominance and efficiency in multicriteria decision under uncertainty. Theory and Decision 47, 191–211 (1999)
Conn, A., Scheinberg, K., Vicente, L.: Introduction to Derivative-Free Optimization. Society for Industrial and Applied Mathematics, Mps-siam Series on Optimization (2009)
Custódio, A., Emmerich, M., Madeira, J.: Recent Developments in Derivative-Free Multiobjective Optimization (2012)
Custódio, A.L., Madeira, J.F.A., Vaz, A.I.F., Vicente, L.N.: Direct multisearch for multiobjective optimization. SIAM Journal on Optimization 21(3), 1109–1140 (2011)
Deb, K., Pratap, A., Agarwal, S., Meyarivan, T.: A fast and elitist multiobjective genetic algorithm: Nsga-ii. IEEE Transactions on Evolutionary Computation 6(2), 182–197 (2002)
Dennis Jr, J.E., Torczon, V.: Direct search methods on parallel machines. SIAM Journal on Optimization 1, 448–474 (1991)
Dolan, E.D., Moré, J.J.: Benchmarking optimization software with performance profiles. Mathematical programming 91(2), 201–213 (2002)
Echagüe, E., Delbos, F., Dumas, L.: A global derivative-free optimization method for expensive functions with bound constraints. In: Proceedings of Global Optimization Workshop, pp. 65–68 (2012)
Fourer, R., Gay, D.M., Kernighan, B.W.: A modeling language for mathematical programming. Management Sci. 36, 519–554 (1990)
Kollat, J., Reed, P., Kasprzyk, J.: A new epsilon-dominance hierarchical bayesian optimization algorithm for large multiobjective monitoring network design problems. Advances in Water Resources 31(5), 828–845 (2008)
Mor, J., Wild, S.: Benchmarking derivative-free optimization algorithms. SIAM Journal on Optimization 20(1), 172–191 (2009)
Nelder, J.A., Mead, R.: A simplex method for function minimization. In Comput. J. 7 (1965)
Voorneveld, M.: Characterization of pareto dominance. Operations Research Letters 31(1), 7–11 (2003)
Zitzler, E., Brockhoff, D., Thiele, L.: The hypervolume indicator revisited: On the design of pareto-compliant indicators via weighted integration. In: Obayashi, S., Deb, K., Poloni, C., Hiroyasu, T., Murata, T. (eds.) EMO 2007. LNCS, vol. 4403, pp. 862–876. Springer, Heidelberg (2007)
Zitzler, E., Knowles, J., Thiele, L.: Quality assessment of pareto set approximations. In: Branke, J., Deb, K., Miettinen, K., Słowiński, R. (eds.) Multiobjective Optimization. LNCS, vol. 5252, pp. 373–404. Springer, Heidelberg (2008)
Zitzler, E., Thiele, L., Laumanns, M., Fonseca, C., da Fonseca, V.: Performance assessment of multiobjective optimizers: an analysis and review. IEEE Transactions on Evolutionary Computation 7(2), 117–132 (2003)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this paper
Cite this paper
Dejemeppe, C., Schaus, P., Deville, Y. (2015). Derivative-Free Optimization: Lifting Single-Objective to Multi-Objective Algorithm. In: Michel, L. (eds) Integration of AI and OR Techniques in Constraint Programming. CPAIOR 2015. Lecture Notes in Computer Science(), vol 9075. Springer, Cham. https://doi.org/10.1007/978-3-319-18008-3_9
Download citation
DOI: https://doi.org/10.1007/978-3-319-18008-3_9
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-18007-6
Online ISBN: 978-3-319-18008-3
eBook Packages: Computer ScienceComputer Science (R0)