Cooperative co-evolutionary algorithm for multi-objective optimization problems with changing decision variables

Multi-objective optimization problems (MOPs) with changing decision variables exist in the actual industrial production and daily life, which have changing Pareto sets and complex relations among decision variables and are difficult to solve. In this study, we present a cooperative co-evolutionary algorithm by dynamically grouping decision variables to effectively tackle MOPs with changing decision variables. In the presented algorithm, decision variables are grouped into a series of groups using maximum entropic epistasis (MEE) at first, with decision variables in different groups owning a weak dependency. Subsequently, a sub-population is generated to solve decision variables in each group with an existing multi-objective evolutionary algorithm (MOEA). Further, a complete solution including all the decision variables is achieved through the cooperation among sub-populations. Finally, when a decision variable is added or deleted from the existing problem, the grouping of decision variables is dynamically adjusted based on the correlation between the changed decision variable and existing groups. To verify the performance of the developed method, the presented method is compared with five popular methods by tackling eight benchmark optimization problems. The experimental results reveal that the presented method is superior in terms of diversity, convergence, and spread of solutions on most benchmark optimization problems.