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

Problem
This paper addresses the limitations of existing niching-based evolutionary algorithms in multimodal optimization, particularly their reliance on distance metrics or density estimators that fail to accurately recover the peak-basin structure of the decision space. This often results in pseudo-multimodality, where diverse individuals converge into a limited number of basins, undermining the goal of identifying multiple optima. The authors propose a novel framework, Chaotic Landscape-Decoding Evolution (CLDE), to enhance the exploration and exploitation of multimodal landscapes. This work is presented as a preprint and has not yet undergone peer review.

Method
CLDE introduces a decision-space-centric approach that operates through a closed-loop mechanism of decode, value, allocate, and refine. The framework employs a logistic chaotic map for controlled global exploration, which features a decaying step size to balance exploration and exploitation. A $k$-nearest-neighbor graph is constructed on a decoding canvas, facilitating persistence-guided basin growing. This method merges peaks only when they are not separated by deep valleys, thus preserving the integrity of distinct basins. An adaptive persistence threshold is utilized to dynamically adjust the decoding resolution, preventing over-fragmentation and over-merging of basins. The authors instantiate CLDE in two variants: CLDE-S for single-objective and CLDE-M for multi-objective multimodal optimization.

Results
Experimental evaluations on 20 CEC2013 benchmark functions demonstrate that CLDE-S achieves a peak ratio of 0.85, outperforming established baselines such as NSGA-II and SPEA2 under the same evaluation budget. For multi-objective optimization, CLDE-M shows competitive performance on the DTLZ and MMMOP suites, achieving an Inverted Generational Distance (IGD) of 0.02 and IGDx of 0.03, with significant improvements noted on strongly multimodal problems compared to traditional methods. These results indicate that CLDE effectively enhances both the quality of solutions and the coverage of basins.

Limitations
The authors acknowledge that the performance of CLDE may be sensitive to the choice of parameters, such as the decay rate of the chaotic map and the adaptive persistence threshold. Additionally, the framework’s reliance on a $k$-nearest-neighbor graph may introduce computational overhead, particularly in high-dimensional spaces. The paper does not address the scalability of CLDE to more complex or real-world multimodal optimization problems, which may present additional challenges.

Why it matters
The introduction of CLDE represents a significant advancement in multimodal optimization by providing a structured approach to navigating complex fitness landscapes. By effectively maintaining basin diversity while improving solution quality, CLDE has the potential to enhance various applications in optimization, including engineering design, resource allocation, and machine learning hyperparameter tuning. This work lays the groundwork for future research into more robust and efficient multimodal optimization techniques, particularly in scenarios where the landscape is highly complex and multimodal.

Authors: Meng Xiang, Pei Yan
Source: arXiv:2605.18351
URL: https://arxiv.org/abs/2605.18351v1