Constraint Consensus for Solving Large-scale Constrained Optimization Problems

Addressing large-scale optimization problems with numerous variables and constraints poses difficulties. Ineffectively handling the constraints can result in solutions that are either not optimal or infeasible. In our research, we utilized the constraint-objective cooperative coevolution framework with the FDfar (Feasibility distance-far) method, which is a constraint consensus approach. Our proposed algorithm involves decomposing a complex problem into smaller, more manageable subproblems (subcomponents) using the Recursive Differential Grouping technique, which assigns interrelated variables to the same subcomponent. Then, the FDfar method is selectively applied to a randomly chosen solution to enhance its feasibility. Subsequently, the population is updated while considering the newly generated solution from the FDfar method. We then assess the impact of each subcomponent on both the objective function and the constraints to identify the most effective subcomponent for evolution. The chosen subcomponent then undergoes further evolution using Differential Evolution. We tested our algorithm on a set of 12 benchmark problems. The results from these tests consistently indicated that our approach outperforms other leading methods, not only in making solutions feasible but also in improving their overall quality.