An Adaptive Constraint Violation Evaluation Framework for Constrained Multiobjective Evolutionary Optimization

Constrained multiobjective optimization evolutionary algorithms cope with various constraints through the combination of a constraint violation evaluation (CVE) framework with a constraint handling technique. The evaluation of constraint violation is a critical problem that determines how effectively constraint information is utilized. However, this topic has received limited attention in existing research. To bridge this gap, an adaptive CVE (ACVE) framework that considers the evolutionary state is proposed in this paper. ACVE first divides solutions into multiple clusters. Each cluster is then reassigned a constraint violation value. By adjusting the number of clusters based on the evolutionary state, ACVE adaptively utilizes constraint information at different levels of granularity. This design allows ACVE to achieve a more optimal balance between constraint satisfaction and objective optimization, thereby reducing the dependency on constraint handling techniques. Extensive experiments conducted on several benchmark test suites demonstrate the effectiveness of ACVE. Based on ACVE, we develop the dual-population dynamic coevolutionary algorithm (DDCo). In experiments on multiple benchmark test suites, DDCo demonstrates superior or competitive performance compared with state-of-the-art algorithms, as evaluated using indicators such as inverted generational distance and hypervolume. Moreover, DDCo is successfully applied to optimize the charging protocols of lithium-ion batteries.