Constrained multimodal multi-objective optimization for large-scale wind farm layout by tri-population coevolutionary framework

Rational wind farm layout optimization is essential for enhancing wind energy utilization while simultaneously reducing operation and maintenance costs. However, existing methods often focus on performance metrics in the objective space, ignoring the multimodal characteristics of the decision space where structurally distinct layouts can yield similar performance. To address these challenges, a tri-population coevolutionary framework for constrained multimodal multi-objective optimization (TriPCo-CMMO) is proposed. Firstly, a coevolutionary mechanism with three functionally heterogeneous populations is designed. The main population maintains diversity in all spaces. The auxiliary exploration population employs an ε-dominance relaxation strategy to traverse marginally inferior regions in objective space and connect fragmented “feasible islands”. And the auxiliary convergence population focuses on rapid convergence to the Pareto front. Secondly, a dynamic multi-mode elite interaction strategy is proposed. By employing diversity exchange, convergence guidance, and balance exchange modes, the interaction intensity is dynamically adjusted to balance global exploration and local exploitation. Thirdly, a dual-space environmental selection strategy is developed by incorporating a decision space distance metric alongside the traditional objective space crowding distance. Finally, the effectiveness of the proposed approach is validated through extensive wind farm layout optimization experiments. Compared to baseline algorithms, an average Pareto front coverage of over 95% is obtained across diverse wind conditions, and the largest number of equivalent multimodal solutions is identified by TriPCo-CMMO. These results confirm the superior robustness of the framework in multimodal wind farm layout optimization, offering diverse and practical alternatives for engineering decision-making.