Many-Modal Optimization by Difficulty-Based Cooperative Co-evolution

Evolutionary multimodal optimization has received considerable attention in the past decade. Most existing evolutionary multimodal optimization algorithms are designed to solve problems with relatively few global optima. However, in real-world applications, the problems can possess a lot of global optima (and sometimes acceptable local optima). Finding more global optima can help us learn more about their landscapes and distributions. However, solving these problems with limited computational resources is a challenge for current algorithms.In this paper, many-modal optimization problems are studied, and each of them has more than 100 global optima. We first present a benchmark with 10 many-modal problems based on the existing multimodal optimization benchmarks. The numbers of global optima of these 10 problems vary from 108 to 7776. Second, we propose the difficulty-based cooperative co-evolution (DBCC) strategy for solving many-modal optimization problems. DBCC comprises four primary steps: problem separation, resource allocation, optimization, and solution reconstruction. The clonal selection algorithm is selected as the optimizer in DBCC. Experimental results demonstrate that DBCC provides satisfactory performance.