CLDE algorithm maps fitness landscapes to find multiple optima efficiently

Multimodal optimization aims to discover all global and local optima of a function, but traditional niching evolutionary algorithms often produce pseudo-multimodality—individuals that appear diverse but collapse into only a few basins. Addressing this, researchers Meng Xiang and Pei Yan propose Chaotic Landscape-Decoding Evolution (CLDE), a decision-space-centric framework that explicitly recovers the underlying peak–basin structure. CLDE operates in a closed loop: decode, value, allocate, refine. It injects controlled global exploration using a logistic chaotic map with decaying step size, then builds a k-nearest-neighbor graph on a decoding canvas. Persistence-guided basin growing merges peaks only when not separated by deep valleys, and an adaptive persistence threshold tunes resolution online to avoid over-fragmentation or over-merging.

The framework has two instantiations: CLDE-S for single-objective and CLDE-M for multi-objective multimodal optimization. Experiments on 20 CEC2013 functions show CLDE-S achieves a strong peak ratio under the same evaluation budget. On DTLZ and MMMOP suites, CLDE-M attains competitive IGD and IGDx metrics, with pronounced gains on strongly multimodal problems. The paper, submitted to arXiv on May 18, 2026, is 9 pages and focuses on neural and evolutionary computing. By moving beyond distance-based or density-based heuristics, CLDE offers a principled way to maintain basin coverage while improving solution quality—a step forward for real-world applications like engineering design and drug discovery where multiple good solutions are needed.