Multi-Scenario Multi-Criteria Optimization in Engineering Design

Motivated by applications in engineering design, a mathematical model of the multi-scenario multi-criteria optimization problem is introduced. Theoretical results for the single-scenario case are presented to support a solution methodology developed for the bi-scenario bi-criteria case. Multi-scenario design problems are traditionally solved by aggregation of all objectives of all scenarios into a large multi-criteria problem. The difficulties that arise from this approach are highlighted. The proposed methodology is a scenario-based approach where a design problem is solved for each scenario resulting into multiple sets of solutions. The methodology is developed as an exploration tool of these solution sets in both the design and objective spaces. The methodology is applicable to problems with large numbers of scenarios and/or criteria. Mathematical and structural examples are included to illustrate the implementation of the methodology, its strengths and weaknesses.