LAUSR

In this paper, we present a two-phase multimodal optimization model designed to efficiently and accurately identify multiple optima. The first phase employs a population-based search algorithm to locate potential optima, while the second phase introduces a novel peak identification (PI) procedure to filter out non-optimal solutions, ensuring that each identified solution represents a distinct optimum. This approach not only enhances the effectiveness of multimodal optimization but also addresses the issue of redundant solutions prevalent in existing algorithms. We propose two PI algorithms: HVPI, which uses a hill–valley approach to distinguish between optima, without requiring prior knowledge of niche radii; and HVPIC, which integrates HVPI with bisecting K-means clustering to reduce the number of fitness evaluations (FEs). The performance of these algorithms was evaluated using the F-measure, a comprehensive metric that accounts for both the accuracy and redundancy in the solution set. Extensive experiments on a suite of benchmark functions and engineering problems demonstrated that our proposed algorithms achieved a high precision and recall, significantly outperforming traditional methods.