Mathematical programming and the optimization of computer simulations

Mathematical programming techniques can be combined with response surface experimental design methods to optimize simulated systems. A computer simulation model has controllable input variables xi, i=1,…, n and yields responses ηj, j=1,…, m. A simulation trial at a particular set of values xik, i=1,…n produces an estimate yik for the system response ηj. This paper describes several formulations of the so-called “simulation/optimization” problem, including constrained optimization and multiple-objective optimization. It also describes several procedures for obtaining a solution to this problem, including a direct search technique, a first-order response surface method, and a second-order response surface approach. Each of these techniques combines simulation, response surface methodology, and mathematical programming.