Novel frameworks for creating robust multi-objective benchmark problems

Robust optimization deals with considering different types of uncertainties during the optimization process in order to obtain reliable solutions, a critical issue when solving real problems. Multiple objectives are another vital aspect of real problems that should be considered during optimization. In order to benchmark the performance of different meta-heuristics, test problems are essential, as the literature shows. Despite the significant number of studies in developing multi-objective test problems, there is currently neither study on the suitability of the current robust multi-objective benchmark problems, nor standard frameworks to create them. This motivates our attempts to investigate the features of the current robust test problems and propose three novel frameworks to generate various robust multi-objective test problems with alterable parameters. As case studies, Robust Multi-Objective Particle Swarm Optimization (RMOPSO), Robust Non-dominated Sorting Genetic Algorithm (RNSGA-II), Robust Multiobjective Evolutionary Algorithm Based on Decomposition (RMOEA/D), Robust Two Local Best Multi-objective Particle Swarm Optimization (R2LB-MOPSO), and Robust Decomposition-Based Multi-objective Evolutionary Algorithm with an Ensemble of Neighborhood Sizes (RENS-MOEA/D) are benchmarked on the proposed test problems. The results show that the proposed frameworks are able to generate robust multi-objective test problems with different adjustable characteristics and levels of difficulty. In addition, the results show that the test problems generated by the proposed frameworks can provide very challenging test beds for effectively benchmarking the performance of robust meta-heuristics.