Spatial-Temporal Knowledge Transfer for Dynamic Constrained Multiobjective Optimization

Dynamic Constrained Multiobjective Optimization Problems (DCMOPs) are characterized by multiple conflicting optimization objectives and constraints that vary over time. The presence of both dynamism and constraints underscores the importance of preserving population diversity. This diversity is essential not only to escape local optima following environmental changes but also to climb infeasible barriers to approach feasible regions. However, existing constraint-handling techniques for enhancing solution feasibility could steer infeasible solutions toward partially feasible regions, potentially resulting in the loss of diversity. To maintain both diversity and feasibility, this work establishes two synergistic tasks: one task concentrates on exploring the unconstrained search space to preserve diversity, while the other delves into searching the constrained search space to prioritize feasibility. Particularly, in light of evolutionary transfer optimization, two knowledge transfer modules, i.e., the spatial knowledge transfer module and temporal knowledge transfer module are designed. The spatial knowledge transfer module facilitates knowledge transfer between the constrained and unconstrained search spaces to accelerate the exploration of both spaces. On the other hand, the temporal transfer module leverages historical knowledge to enhance search efficiency within the new environment. To advance the test suite toward real-world cases, we designed fourteen test problems with various properties. Experiments conducted on the proposed test problems and a real-world problem have demonstrated the efficacy of our proposed algorithm.