Mapping the Fitness Landscape: A Structure-Guided Approach to Multi-Modal Optimization

TL;DR

This paper introduces CLDE, a novel structure-guided framework for multimodal optimization that explicitly recovers the peak-basin organization in decision space, improving solution diversity and quality.

Contribution

The paper presents CLDE, a new decision-space-centric approach that uses chaotic maps and persistence-guided basin growing to enhance multimodal optimization.

Findings

CLDE-S achieves high peak ratio on CEC2013 functions.

CLDE-M attains competitive IGD/IGDx on DTLZ and MMMOP suites.

Significant improvements on strongly multimodal problems.

Abstract

Multimodal optimization requires finding many optima rather than merely keeping a diverse population. Yet most niching-based evolutionary algorithms rely on distances or density estimators without explicitly recovering the underlying peak--basin organization in the decision space, which can lead to pseudo-multimodality: many distinct individuals ultimately collapse into only a few basins. We introduce Chaotic Landscape-Decoding Evolution (CLDE), a decision-space-centric framework that turns multimodal search into a closed loop of decode--value--allocate--refine. CLDE injects controlled global exploration via a logistic chaotic map with a decaying step size, then builds a $k$-nearest-neighbor graph on a decoding canvas and performs persistence-guided basin growing that merges peaks only when they are not separated by deep valleys. An adaptive persistence threshold continuously tunes the decoding resolution online to avoid over-fragmentation and over-merging. Guided by the decoded structure, CLDE carries out basin-wise selection and refinement to improve solution quality while preserving basin coverage. We instantiate CLDE as CLDE-S and CLDE-M for single- and multi-objective multimodal optimization. Experiments on 20 CEC2013 functions show that CLDE-S achieves strong peak ratio under the same evaluation budget, while on DTLZ and MMMOP suites CLDE-M attains competitive IGD/IGDx, with pronounced gains on strongly multimodal problems.