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Accelerating Evolution: Integrating PSO Principles into Real-Coded Genetic Algorithm Crossover

Xiaobo Jin, JiaShu Tu

TL;DR

This work introduces PSOX, a PSO-inspired crossover for real-coded GAs that enables cross-generational learning by combining an individual’s current position with both its historical best and the global historical best of others. Implemented as $O = w p_i + c_1 r_1 (pbest_j - p_i) + c_2 r_2 (gbest - p_i)$, PSOX aims to accelerate convergence while preserving diversity. Across 15 30-dimensional benchmark functions and two mutation operators, PSOX generally achieves higher accuracy and stability, with convergence speed benefits demonstrated relative to conventional crossovers; a mutation-rate analysis provides practical guidelines for terrain-aware parameter tuning. The findings offer a concrete method to enhance real-coded GA performance on complex landscapes, while also highlighting scenarios where mutation-rate adjustments are crucial to avoid premature convergence in densely multimodal spaces.

Abstract

This study introduces an innovative crossover operator named Particle Swarm Optimization-inspired Crossover (PSOX), which is specifically developed for real-coded genetic algorithms. Departing from conventional crossover approaches that only exchange information between individuals within the same generation, PSOX uniquely incorporates guidance from both the current global best solution and historical optimal solutions across multiple generations. This novel mechanism enables the algorithm to maintain population diversity while simultaneously accelerating convergence toward promising regions of the search space. The effectiveness of PSOX is rigorously evaluated through comprehensive experiments on 15 benchmark test functions with diverse characteristics, including unimodal, multimodal, and highly complex landscapes. Comparative analysis against five state-of-the-art crossover operators reveals that PSOX consistently delivers superior performance in terms of solution accuracy, algorithmic stability, and convergence speed, especially when combined with an appropriate mutation strategy. Furthermore, the study provides an in-depth investigation of how different mutation rates influence PSOX's performance, yielding practical guidelines for parameter tuning when addressing optimization problems with varying landscape properties.

Accelerating Evolution: Integrating PSO Principles into Real-Coded Genetic Algorithm Crossover

TL;DR

This work introduces PSOX, a PSO-inspired crossover for real-coded GAs that enables cross-generational learning by combining an individual’s current position with both its historical best and the global historical best of others. Implemented as , PSOX aims to accelerate convergence while preserving diversity. Across 15 30-dimensional benchmark functions and two mutation operators, PSOX generally achieves higher accuracy and stability, with convergence speed benefits demonstrated relative to conventional crossovers; a mutation-rate analysis provides practical guidelines for terrain-aware parameter tuning. The findings offer a concrete method to enhance real-coded GA performance on complex landscapes, while also highlighting scenarios where mutation-rate adjustments are crucial to avoid premature convergence in densely multimodal spaces.

Abstract

This study introduces an innovative crossover operator named Particle Swarm Optimization-inspired Crossover (PSOX), which is specifically developed for real-coded genetic algorithms. Departing from conventional crossover approaches that only exchange information between individuals within the same generation, PSOX uniquely incorporates guidance from both the current global best solution and historical optimal solutions across multiple generations. This novel mechanism enables the algorithm to maintain population diversity while simultaneously accelerating convergence toward promising regions of the search space. The effectiveness of PSOX is rigorously evaluated through comprehensive experiments on 15 benchmark test functions with diverse characteristics, including unimodal, multimodal, and highly complex landscapes. Comparative analysis against five state-of-the-art crossover operators reveals that PSOX consistently delivers superior performance in terms of solution accuracy, algorithmic stability, and convergence speed, especially when combined with an appropriate mutation strategy. Furthermore, the study provides an in-depth investigation of how different mutation rates influence PSOX's performance, yielding practical guidelines for parameter tuning when addressing optimization problems with varying landscape properties.
Paper Structure (14 sections, 18 equations, 2 figures, 8 tables)

This paper contains 14 sections, 18 equations, 2 figures, 8 tables.

Table of Contents

  1. Introduction
  2. Literature review
  3. The proposed PSO-Inspired crossover operator
  4. Experimental setup
  5. Accuracy and Stability Test
  6. Convergence speed Test
  7. Effects of Mutation rate Test
  8. Results and discussion
  9. Performance Comparison of Different Crossover Operators
  10. Performance Comparison of Different Operators Combined with the NUM Mutation Operator
  11. Performance Comparison of Different Operators Combined with the GM Mutation Operator
  12. Analysis of the Convergence Speed
  13. The Relationship between PSOX and the Mutation Rate
  14. Conclusion

Figures (2)

  • Figure 1: Comparison of the Convergence Speeds of Different Operators in Four Test Cases
  • Figure 2: The Influence of the Mutation Rate on the GA with the PSOX Operator