6. Simulation Optimization

This chapter is organized as follows. Section 6.1 introduces the optimization of real systems that are modeled through either deterministic or random simulation; this optimization we call simulation optimization or briefly optimization. There are many methods for this optimization, but we focus on methods that use specific metamodels of the underlying simulation models; these metamodels were detailed in the preceding chapters, and use either linear regression or Kriging. Section 6.2 discusses the use of linear regression metamodels for optimization. Section 6.2.1 summarizes basic response surface methodology (RSM), which uses linear regression; RSM was developed for experiments with real systems. Section 6.2.2 adapts this RSM to the needs of random simulation. Section 6.2.3 presents the adapted steepest descent (ASD) search direction. Section 6.2.4 summarizes generalized RSM (GRSM) for simulation with multiple responses. Section 6.2.5 summarizes a procedure for testing whether an estimated optimum is truly optimal—using the Karush-Kuhn-Tucker (KKT) conditions. Section 6.3 discusses the use of Kriging metamodels for optimization. Section 6.3.1 presents efficient global optimization (EGO), which uses Kriging. Section 6.3.2 presents Kriging and integer mathematical programming (KrIMP) for the solution of problems with constrained outputs. Section 6.4 discusses robust optimization (RO), which accounts for uncertainties in some inputs. Section 6.4.1 discusses RO using RSM, Sect. 6.4.2 discusses RO using Kriging, and Sect. 6.4.3 summarizes the Ben-Tal et al. approach to RO. Section 6.5 summarizes the major conclusions of this chapter, and suggests topics for future research. The chapter ends with Solutions of exercises, and a long list of references.