Search Techniques for Multi-Objective Optimization of Mixed Variable Systems having Stochastic Responses

A research approach is presented for solving stochastic, multi-objective optimization problems. First, the class of mesh adaptive direct search (MADS) algorithms for nonlinearly constrained optimization is extended to mixed variable problems. The resulting algorithm, MV-MADS, is then extended to stochastic problems (MVMADS-RS), via a ranking and selection procedure. Finally, a two-stage method is developed that combines the generalized pattern search/ranking and selection (MGPS-RS) algorithms for single-objective, mixed variable, stochastic problems with a multi-objective approach that makes use of interactive techniques for the specification of aspiration and reservation levels, scalarization functions, and multi-objective ranking and selection. A convergence analysis for the general class of algorithms establishes almost sure convergence of an iteration subsequence to stationary points appropriately defined in the mixed-variable domain. Seven specific instances of the new algorithm are implemented and tested on 11 multi-objective test problems from the literature and an engineering design problem