Stable Matching Theory in Multiobjective Evolutionary Algorithm based on Decomposition (MOEA/D)

Evolutionary multiobjective optimization (EMO) is one of the most active research areas in evolutionary computation and multiple criteria decision making. Multiobjective evolutionary algorithm based on decomposition (MOEA/D), which bridges the traditional techniques and population-based methods, has been widely accepted as one of the three major EMO frameworks and been successfully applied in various domains. However, a number of fundamental issues, such as 1) how to select solution for each subproblem, 2) how to handle decision maker (DM)’s preferences, and 3) how to mate parents for offspring generation, still need to be addressed before this approach can be widely accepted and used in industry. In principle, all these three issues can be regarded as matching problems, which are subproblem-solution, preference-solution and solution-solution matching, respectively.Stable matching theory, first proposed and studied in a Nobel Prize winning paper, can effectively resolve conflicts of interests among selfish agents in the market. In this research, focusing on the aforementioned three issues, we will develop and investigate EMO methodologies from the perspective of stable matching theory. Specifically, we will first develop a novel selection strategy, which assigns each subproblem with its appropriate solution, based on a stable marriage model (one-to-one matching) under certain fairness criteria. Then, we will extend the stable marriage model, used for selection strategy, from a one-to-one matching to a many-to-one matching, and apply it to accommodate DM’s preferences. Finally, we will develop a novel mating scheme, which can balance the exploration and exploitation of the evolutionary search, based on a many-to-many matching model. It is more general than the one-to-one and many-to- one matchings.In the long run, this research will bring a completely new approach for designing and analyzing EMO methodologies in a systematic and rational manner. Moreover, its significant impacts are not only limited to the developments of EMO, but also to the design and analysis of other evolutionary search methods, metaheuristics and even traditional optimization. In the meanwhile, its outputs will provide more powerful tools for real-life optimization problems.