A method for simulation based optimization using radial basis functions
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We propose an algorithm for the global optimization of expensive and noisy black box functions using a surrogate model based on radial basis functions (RBFs). A method for RBF-based approximation is introduced in order to handle noise. New points are selected to minimize the total model uncertainty weighted against the surrogate function value. The algorithm is extended to multiple objective functions by instead weighting against the distance to the surrogate Pareto front; it therefore constitutes the first algorithm for expensive, noisy and multiobjective problems in the literature. Numerical results on analytical test functions show promise in comparison to other (commercial) algorithms, as well as results from a simulation based optimization problem.
KeywordsSimulation based optimization Radial basis functions Multiobjective Noise Response surface Surrogate model Black box function
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- Booker AJ, Dennis JE Jr, Frank PD, Serafini DB, Torczon V (1998) Optimization using surrogate objectives on a helicopter test example. In: Computational methods for optimal design and control, Arlington, VA, 1997. Progr systems control theory, vol 24. Birkhäuser Boston, Boston, pp 49–58 Google Scholar
- Deb K, Thiele L, Laumanns M, Zitzler E (2001) Scalable test problems for evolutionary multi-objective optimization. Technical report, Computer engineering and networks laboratory (TIK), Swiss federal institute of technology (ETH) Google Scholar
- Dixon LCW, Szegö G (1978) The global optimization problem: an introduction. North-Holland, Amsterdam Google Scholar
- Hanne T (2006) Applying multiobjective evolutionary algorithms in industrial projects. In: Küfer KH, Rommelfanger H, Tammer C, Winkler K (eds) Multicriteria decision making and fuzzy systems. Theory, methods and applications. Shaker Verlag, Aachen, pp 125–142 Google Scholar
- Jakobsson S, Saif-Ul-Hasnain M, Rundqvist R, Edelvik F, Andersson B, Patriksson M, Ljungqvist M, Lortet D, Wallesten J (2008) Combustion engine optimization: a multiobjective approach. Optim Eng (in press) Google Scholar
- Kohavi R (1999) A study of cross-validation and bootstrap for accuracy estimation and model selection. In: Proceedings of the 14:th international joint conference on artificial intelligence (IJCAI). Morgan Kaufmann, San Mateo, pp 1137–1145 Google Scholar
- Rudholm J, Wojciechowski A (2007) A method for simulation based optimization using radial basis functions. Master’s thesis, Chalmers university of technology, Göteborg, www.chalmers.se/math/EN/research/research-groups/optimization/master-thesis-projects
- Saif-Ul-Hasnain M (2008) Simulation based multiobjective optimization of diesel combustion engines. Master’s thesis, Chalmers university of technology Google Scholar
- Shor NZ (1985) Minimization methods for nondifferentiable functions. Springer series in computational mathematics, vol 3. Springer, Berlin Google Scholar