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Localized KBO with genetic dynamics for multi-modal optimization

Federica Ferrarese, Claudia Totzeck

TL;DR

A novel approach to multi-modal optimization by enhancing the recently developed kinetic-based optimization method with genetic dynamics with genetic dynamics, addressing a critical need in fields like engineering design, machine learning, and bioinformatics.

Abstract

In this paper, we introduce a novel approach to multi-modal optimization by enhancing the recently developed kinetic-based optimization (KBO) method with genetic dynamics (GKBO). The proposed method targets objective functions with multiple global minima, addressing a critical need in fields like engineering design, machine learning, and bioinformatics. By incorpo rating leader-follower dynamics and localized interactions, the algorithm efficiently navigates high-dimensional search spaces to detect multiple optimal solutions. After providing a binary description, a mean-field approximation is derived, and different numerical experiments are conducted to validate the results.

Localized KBO with genetic dynamics for multi-modal optimization

TL;DR

A novel approach to multi-modal optimization by enhancing the recently developed kinetic-based optimization method with genetic dynamics with genetic dynamics, addressing a critical need in fields like engineering design, machine learning, and bioinformatics.

Abstract

In this paper, we introduce a novel approach to multi-modal optimization by enhancing the recently developed kinetic-based optimization (KBO) method with genetic dynamics (GKBO). The proposed method targets objective functions with multiple global minima, addressing a critical need in fields like engineering design, machine learning, and bioinformatics. By incorpo rating leader-follower dynamics and localized interactions, the algorithm efficiently navigates high-dimensional search spaces to detect multiple optimal solutions. After providing a binary description, a mean-field approximation is derived, and different numerical experiments are conducted to validate the results.

Paper Structure

This paper contains 15 sections, 46 equations, 7 figures.

Table of Contents

  1. Introduction
  2. Localised genetic kinetic based optimization (GKBO)
  3. Binary interaction between agents
  4. Derivation of the mean-field equations equations
  5. Change of labels
  6. Numerical methods
  7. Interaction step.
  8. Labels evolution.
  9. Validation tests
  10. Multi-modal Rastrigin function.
  11. Multi-modal Ackley function.
  12. Test 1: Number of detected minima and leaders dependence
  13. Test 2: Comparison for different dimension and diffusion parameters
  14. Test 3: Comparison between the localized GKBO and the polarized CBO algorithms
  15. Conclusion

Figures (7)

  • Figure 1: Multi-modal Rastrigin function \ref{['eq:multi_rastrigin']}. On the left, with two global minima and on the right with four global minima. We highlight with markers their position.
  • Figure 2: Multi-modal Ackley function \ref{['eq:multi_ackley']}. On the left, with two global minima and on the right with four global minima. We highlight with markers their position.
  • Figure 3: Average number of detected minima as the dimension $d$ varies for $\sigma_F= 2.5$, for the Rastrigin function \ref{['eq:multi_rastrigin']} with $n_{min} = 4$ global minima. The markers denote the average number of detected minima for different values of $d$.
  • Figure 4: Success rate and number of iterations as $N_L$ varies for the Rastrigin function \ref{['eq:multi_rastrigin']} with $n_{min} =4$ minima for $d=2$ and $\sigma_F=2.5$. The markers denote the value of the success rates and mean number of iterations.
  • Figure 5: Success rate and number of iterations as $d$ varies for the Rastrigin function \ref{['eq:multi_rastrigin']} with $n_{min} =2$ minima and $\sigma_F=2.5$. The markers denote the value of the success rates and mean number of iterations.
  • ...and 2 more figures

Theorems & Definitions (1)

  • Remark 1