Multi-objective cooperation search algorithm based on decomposition for complex engineering optimization and reservoir operation problems

This study introduces a novel multi-objective cooperation search algorithm based on decomposition (MOCSA/D) to address multi-objective competitive challenges in engineering problem. Inspired by the optimization strategy of single-objective Cooperation Search Algorithm (CSA) and the decomposition framework of MOEA/D, MOCSA/D algorithm randomly generates initial solutions in the optimization space, and then repeatedly executes four search strategies until the end of iteration: Cooperative updating strategy gathers high-quality information to update solutions with balanced distribution. Reflective adjustment strategy expands the exploration range of the population, enabling the acquisition of solutions with strong optimization capabilities. Internal competition strategy selects superior individuals with better performance for subsequent optimization. Density updating strategy improves the competitiveness of optimized individuals within the population, fostering a more diverse solution set. Three numerical experiments (including DTLZ, WFG unconstrained test problems, ZXH_CF constrained test problems and RWMOP real-world multi-objective optimization problems) are tested to further comprehensively evaluate the dominant performance of MOCSA/D. The test results in different problem scenarios show that compared with the existing excellent evolutionary algorithms, MOCSA/D can always obtain a better, stable and uniform distribution of non-dominated solutions, and has higher solving efficiency and optimization quality under different performance evaluation metrics with the increasing difficulty of solving problems. Finally, the proposed algorithm is applied to the multi-objective reservoir engineering optimization problem to verify the feasibility of the decision scheme and the comprehensive benefit optimization of MOCSA/D. Overall, MOCSA/D can simplify the problem optimization difficulty based on decomposition mechanism, and improve the global optimization of population, path diversity and individual competition through different search strategies, which provides an advantageous tool for addressing multi-objective competitive challenges.