Co-evolutionary algorithm with a region-based diversity enhancement strategy

When addressing constrained multi-objective optimization problems, the presence of complex constraints often results in a non-connected feasible region, segmenting the Pareto front into multiple discrete segments. This fragmentation can significantly limit population diversity. To tackle this issue, we have designed two mechanisms aimed at preserving population diversity and have developed a constrained multi-objective co-evolutionary algorithm (DESCA) based on the framework of a two-population co-evolutionary algorithm. The proposed algorithm consists of two populations: a main population dedicated to exploring the constrained Pareto front and an auxiliary population tasked with exploring the unconstrained Pareto front. To sustain the diversity within both populations, the algorithm dynamically adjusts the genetic operator based on the observed states of the populations. Moreover, when the main population encounters stagnation, a regional mating mechanism is employed between the main population and the auxiliary population, accompanied by a relaxation of the constraints on the main population. Conversely, when the auxiliary population experiences stagnation, a diversity-first individual selection strategy is implemented; this strategy utilizes a regional distribution index to assess individual diversity and mitigates population stagnation by enhancing diversity. The performance of DESCA has been evaluated across 33 benchmark problems and 6 real-world problems. Experimental results demonstrate that DESCA exhibits strong competitiveness compared to seven other typical state-of-the-art algorithms.