Simulation based optimization of stochastic systems with integer design variables by sequential multipoint linear approximation |
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Authors: | SJ Abspoel LFP Etman J Vervoort RA van Rooij AJG Schoofs JE Rooda |
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Affiliation: | (1) Systems, Dynamics, and Control Engineering, Department of Mechanical Engineering, Eindhoven University of Technology, Wh. 4.105, P.O. Box 513, NL-5600 MB Eindhoven, The Netherlands e-mail: l.f.p.etman@tue.nl, NL |
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Abstract: | Optimization problems are considered for which objective function and constraints are defined as expected values of stochastic
functions that can only be evaluated at integer design variable levels via a computationally expensive computer simulation.
Design sensitivities are assumed not to be available. An optimization approach is proposed based on a sequence of linear approximate
optimization subproblems. Within each search subregion a linear approximate optimization subproblem is built using response
surface model building. To this end, N simulation experiments are carried out in the search subregion according to a D-optimal
experimental design. The linear approximate optimization problem is solved by integer linear programming using corrected constraint
bounds to account for any uncertainty due to the stochasticity. Each approximate optimum is evaluated on the basis of M simulation
replications with respect to objective function change and feasibility of the design. The performance of the optimization
approach and the influence of parameters N and M is illustrated via two analytical test problems. A third example shows the
application to a production flow line simulation model.
Received April 28, 2000 |
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Keywords: | : approximation concepts integer design variables stochastic systems simulation optimization nongradient based optimization |
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