Multipoint linear approximations for astic chance constrained optimization problems with er design variables

A sequential linearization approach is developed for simulation based optimization problems with integer design variables and stochastic objective function and constraints. Typically, chance constraints are considered, which arise for systems where conditions on, for example, reliability are included. The stochastic functions can only be evaluated at the integer design variable levels via a computationally expensive simulation. This means that a replication of a simulation evaluation for the same design generally gives different results, and that the number of simulations during the optimization is limited. The optimization approach generates a sequence of approximate integer linear programming subprob-lems. It is assumed that design sensitivities are not available. Instead, N experiments are planned in discrete points of the search subregion according to a D-optimal design of experiments. The simulation results are used to fit linear response-surface models. The stochastic behavior is accounted for in the deterministic approximate subproblem by the introduction of safety indices for objective function and constraints. The solution of the integer linear programming subproblem is evaluated by M simulation replications with respect to objective function change and feasibility of the design. A move limit strategy is included to redefine the size and position of the search subregion after each cycle. The performance of the optimization approach and the influence of parameters JV and M will be illustrated via two analytical test problems.