Handling Multiple Scenarios in Evolutionary Multiobjective Numerical Optimization

Solutions to most practical numerical optimization problems must be evaluated for their performance over a number of different loading or operating conditions, which we refer here as scenarios. Therefore, a meaningful and resilient optimal solution must be such that it remains feasible under all scenarios and performs close to an individual optimal solution corresponding to each scenario. Despite its practical importance, multiscenario consideration has received a lukewarm attention, particularly in the context of multiobjective optimization. The usual practice is to optimize for the worst-case scenario. In this paper, we review existing methodologies in this direction and set our goal to suggest a new and potential population-based method for handling multiple scenarios by defining scenario-wise domination principle and scenario-wise diversity-preserving operators. To evaluate, the proposed method is applied to a number of numerical test problems and engineering design problems with a detail explanation of the obtained results and compared with an existing method. This first systematic evolutionary-based multiscenario, multiobjective optimization study on numerical problems indicates that multiple scenarios can be handled in an integrated manner using an evolutionary multiobjective optimization framework to find a well-balanced compromise set of solutions to multiple scenarios and maintain a tradeoff among multiple objectives. In comparison to an existing serial multiple optimization approach, the proposed approach finds a set of compromised tradeoff solutions simultaneously. An achievement of multiobjective tradeoff and multiscenario tradeoff is algorithmically challenging, but due to its practical appeal, further research and application must be spent.