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Robust Nonconvex Optimization for Simulation-based Problems

Dimitris Bertsimas(dbertsim***at***mit.edu)
Omid Nohadani(nohadani***at***mit.edu)
Kwong Meng Teo(kmteo***at***alum.mit.edu)

Abstract: In engineering design, an optimized solution often turns out to be suboptimal, when implementation errors are encountered. While the theory of robust convex optimization has taken significant strides over the past decade, all approaches fail if the underlying cost function is not explicitly given; it is even worse if the cost function is nonconvex. In this work, we present a robust optimization method, which is suited for problems with a nonconvex cost function as well as for problems based on simulations such as large PDE solvers, response surface, and kriging metamodels. Moreover, this technique can be employed for most real-world problems, because it operates directly on the response surface and does not assume any specific structure of the problem. We present this algorithm along with the application to an actual engineering problem in electromagnetic multiple-scattering of aperiodically arranged dielectrics, relevant to nano-photonic design. The corresponding objective function is highly nonconvex and resides in a 100-dimensional design space. Starting from an ``optimized" design, we report a robust solution with a significantly lower worst case cost, while maintaining optimality. We further generalize this algorithm to address a nonconvex optimization problem under both implementation errors and parameter uncertainties.

Keywords: Robust optimization; Nonconvex Optimization; Robustness; Implementation errors; Data uncertainty

Category 1: Robust Optimization

Category 2: Applications -- Science and Engineering (Optimization of Systems modeled by PDEs )

Category 3: Other Topics (Optimization of Simulated Systems )

Citation: Submitted to Operations Research; Sloan School of Management and Operations Research Center, Massachusetts Institute of Technology, E40-111, Cambridge, Massachusetts 02139

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Entry Submitted: 08/22/2007
Entry Accepted: 08/22/2007
Entry Last Modified: 08/22/2007

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