Modifications of generalized response surface methodology for constrained stochastic optimization problems

Abstract

To optimize problems with a stochastic objective function and some stochastic or deterministic constraints, the generalized response surface methodology (GRSM) is used. This study presents a novel GRSM that is fast and accurate enough to solve constrained stochastic optimization problems containing expensive simulations or too costly real experiments. Basic GRSM is a kind of interior point method which moves toward the optimum from only inside of the feasible region. However, the proposed approach can move toward the optimum from inside or outside the feasible region. In addition, basic GRSM is not always reliable and fails in problems including complicated stochastic functions; we improved the GRSM to enable it to make reliable solutions to complicated problems. We solve two examples: 1- a toy problem with two stochastic constraints, and 2- an optimization problem of $(s,\mathrm{ }S)$ inventory system with one stochastic constraint. The obtained results indicate the optimization method proposed in this study is much more efficient than OPT-QUEST and classic GRSM.

Keywords:

• Stochastic optimization
• Simulation-optimization
• Generalized response surface methodology
• Big-M method
• $(s,\mathrm{ }S)$ inventory systems

Disclosure statement

The authors have no competing interests to declare that are relevant to the content of this article.

Data availability statement

All the data used in the current study are generated applying the random number generating algorithm of the MATLAB software package. Analogous results are repeatable with any random data-sets generated using different seeds.