Multiform-based evolutionary framework for large-scale constrained multi-objective optimization

Large-scale constrained multi-objective optimization problems (LSCMOPs) are common in real-world scenarios. These multi-objective problems are characterized by high-dimensional decision spaces and complex constraints, posing a stiff challenge for evolutionary computation methods. However, LSCMOPs remain underexplored since existing constrained or large-scale multi-objective algorithms struggle due to limited scalability and inefficient constraint-handling mechanisms. Inspired by the concept of multiform optimization, which solves the original problem via alternative formulations, this paper proposes a large-scale constrained multiform framework (LSCMF). Firstly, the LSCMOPs are decomposed into three forms, each addressing a core challenge arising from high-dimensional decision spaces, variable linkage, and constraints, respectively. Secondly, we integrate advanced techniques to solve each form. Specifically, a competitive and cooperative swarm optimizer is employed to enhance convergence and maintain diversity in high-dimensional and multimodal decision spaces, a differential evolution search algorithm is applied to decouple implicit variables linkages, and an hybrid environment selection strategy is designed to progressively guide the population from an unconstrained form to the original formulation, enabling effective traversal of infeasible regions. Finally, extensive experiments on multiple benchmark suites and real-world scheduling problems verify the effectiveness and versatility of the proposed framework, which achieves superior performance compared to several representative and state-of-the-art algorithms. • A multiform-based evolutionary framework that decomposes complex problems into simple sub-problems. • Different advanced techniques are designed for different forms. • Competitive results on both benchmark and real-world problems.