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Accurate Peak Detection in Multimodal Optimization via Approximated Landscape Learning

Zeyuan Ma, Hongqiao Lian, Wenjie Qiu, Yue-Jiao Gong

TL;DR

APDMMO addresses the challenge of locating all optima in MMOPs by learning a global surrogate landscape and using it for peak detection before parallel local refinement. It introduces the Landscape Learner, an ANN with a diverse set of activation units, to approximate the problem landscape; peak areas are identified via gradient-based search on the surrogate and clustered, followed by refinement with SEP-CMAES in parallel. The approach achieves superior performance on the CEC 2013 MMOP benchmark compared with a wide range of baselines, with ablations confirming the value of each stage (GLF, FPD, PLS). The work demonstrates that leveraging landscape knowledge through a surrogate model can effectively guide MMOP search, offering a scalable framework that combines gradient-based and evolutionary techniques for robust peak detection and optimization.

Abstract

Detecting potential optimal peak areas and locating the accurate peaks in these areas are two major challenges in Multimodal Optimization problems (MMOPs). To address them, much efforts have been spent on developing novel searching operators, niching strategies and multi-objective problem transformation pipelines. Though promising, existing approaches more or less overlook the potential usage of landscape knowledge. In this paper, we propose a novel optimization framework tailored for MMOPs, termed as APDMMO, which facilitates peak detection via fully leveraging the landscape knowledge and hence capable of providing strong optimization performance on MMOPs. Specifically, we first design a novel surrogate landscape model which ensembles a group of non-linear activation units to improve the regression accuracy on diverse MMOPs. Then we propose a free-of-trial peak detection method which efficiently locates potential peak areas through back-propagation on the learned surrogate landscape model. Based on the detected peak areas, we employ SEP-CMAES for local search within these areas in parallel to further improve the accuracy of the found optima. Extensive benchmarking results demonstrate that APDMMO outperforms several up-to-date baselines. Further ablation studies verify the effectiveness of the proposed novel designs. The source-code is available at ~\href{}{https://github.com/GMC-DRL/APDMMO}.

Accurate Peak Detection in Multimodal Optimization via Approximated Landscape Learning

TL;DR

APDMMO addresses the challenge of locating all optima in MMOPs by learning a global surrogate landscape and using it for peak detection before parallel local refinement. It introduces the Landscape Learner, an ANN with a diverse set of activation units, to approximate the problem landscape; peak areas are identified via gradient-based search on the surrogate and clustered, followed by refinement with SEP-CMAES in parallel. The approach achieves superior performance on the CEC 2013 MMOP benchmark compared with a wide range of baselines, with ablations confirming the value of each stage (GLF, FPD, PLS). The work demonstrates that leveraging landscape knowledge through a surrogate model can effectively guide MMOP search, offering a scalable framework that combines gradient-based and evolutionary techniques for robust peak detection and optimization.

Abstract

Detecting potential optimal peak areas and locating the accurate peaks in these areas are two major challenges in Multimodal Optimization problems (MMOPs). To address them, much efforts have been spent on developing novel searching operators, niching strategies and multi-objective problem transformation pipelines. Though promising, existing approaches more or less overlook the potential usage of landscape knowledge. In this paper, we propose a novel optimization framework tailored for MMOPs, termed as APDMMO, which facilitates peak detection via fully leveraging the landscape knowledge and hence capable of providing strong optimization performance on MMOPs. Specifically, we first design a novel surrogate landscape model which ensembles a group of non-linear activation units to improve the regression accuracy on diverse MMOPs. Then we propose a free-of-trial peak detection method which efficiently locates potential peak areas through back-propagation on the learned surrogate landscape model. Based on the detected peak areas, we employ SEP-CMAES for local search within these areas in parallel to further improve the accuracy of the found optima. Extensive benchmarking results demonstrate that APDMMO outperforms several up-to-date baselines. Further ablation studies verify the effectiveness of the proposed novel designs. The source-code is available at ~\href{}{https://github.com/GMC-DRL/APDMMO}.

Paper Structure

This paper contains 23 sections, 3 equations, 5 figures, 1 table, 2 algorithms.

Table of Contents

  1. INTRODUCTION
  2. RELATED WORKS
  3. Evolutionary Multimodal Optimization
  4. Niching Technique
  5. New Evolutionary Operator
  6. Multi-objective Problem Transformation
  7. Learning for EC
  8. MetaBBO
  9. SAEA
  10. Methodology
  11. Global Landscape Fitting
  12. Landscape Learner
  13. Training Workflow
  14. Free-of-trial Peak Detection
  15. Parallel Local Search
  16. ...and 8 more sections

Figures (5)

  • Figure 1: The overall workflow of APDMMO, with three sequential stages, from left to right.
  • Figure 2: Architecture design of the Landscape Learner.
  • Figure 3: Comparison of prediction accuracies of different Landscape Learner model architecture designs.
  • Figure 4: Average peak ratio over $f_1 \sim f_{20}$ achieved by different function evaluations allocation settings.
  • Figure 5: Importance analysis of FPD and PLS stages.