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TOPSIS-like metaheuristic for LABS problem

Aleksandra Urbańczyk, Bogumiła Papiernik, Piotr Magiera, Piotr Urbańczyk, Aleksander Byrski

TL;DR

The paper addresses the Low Autocorrelation Binary Sequence (LABS) problem, which seeks binary sequences that minimize the autocorrelation energy $E(S)$. It introduces TOPSIS-inspired socio-cognitive mutation operators that emulate following the best solutions and avoiding the worst, integrated into an elitist Genetic Algorithm. Experiments on LABS with $L=50$ show improved performance over a baseline GA, with the best variant achieving end energies near $281$, significantly outperforming the base. The findings highlight the potential of observational learning-inspired mutations to enhance exploration and convergence in combinatorial optimization and motivate applications to other domains.

Abstract

This paper presents the application of socio-cognitive mutation operators inspired by the TOPSIS method to the Low Autocorrelation Binary Sequence (LABS) problem. Traditional evolutionary algorithms, while effective, often suffer from premature convergence and poor exploration-exploitation balance. To address these challenges, we introduce socio-cognitive mutation mechanisms that integrate strategies of following the best solutions and avoiding the worst. By guiding search agents to imitate high-performing solutions and avoid poor ones, these operators enhance both solution diversity and convergence efficiency. Experimental results demonstrate that TOPSIS-inspired mutation outperforms the base algorithm in optimizing LABS sequences. The study highlights the potential of socio-cognitive learning principles in evolutionary computation and suggests directions for further refinement.

TOPSIS-like metaheuristic for LABS problem

TL;DR

The paper addresses the Low Autocorrelation Binary Sequence (LABS) problem, which seeks binary sequences that minimize the autocorrelation energy . It introduces TOPSIS-inspired socio-cognitive mutation operators that emulate following the best solutions and avoiding the worst, integrated into an elitist Genetic Algorithm. Experiments on LABS with show improved performance over a baseline GA, with the best variant achieving end energies near , significantly outperforming the base. The findings highlight the potential of observational learning-inspired mutations to enhance exploration and convergence in combinatorial optimization and motivate applications to other domains.

Abstract

This paper presents the application of socio-cognitive mutation operators inspired by the TOPSIS method to the Low Autocorrelation Binary Sequence (LABS) problem. Traditional evolutionary algorithms, while effective, often suffer from premature convergence and poor exploration-exploitation balance. To address these challenges, we introduce socio-cognitive mutation mechanisms that integrate strategies of following the best solutions and avoiding the worst. By guiding search agents to imitate high-performing solutions and avoid poor ones, these operators enhance both solution diversity and convergence efficiency. Experimental results demonstrate that TOPSIS-inspired mutation outperforms the base algorithm in optimizing LABS sequences. The study highlights the potential of socio-cognitive learning principles in evolutionary computation and suggests directions for further refinement.

Paper Structure

This paper contains 15 sections, 10 equations, 2 figures, 2 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. State of the Art
  3. Socio-cognitively inspired hybrid mutation operators
  4. TOPSIS-like mutation in evolutionary algorithm
  5. Baseline evolutionary algorithm
  6. Best Solution Selection
  7. Single-Point Crossover
  8. Bit-Flip Mutation
  9. Socio-cognitive mutation inspired by TOPSIS
  10. Follow Best
  11. Follow Best Distinct
  12. Repel Worst Gravity
  13. Repel Worst Gravity Multistep
  14. Experiments
  15. Conclusions

Figures (2)

  • Figure 1: A standard boxplot with whiskers of the energy function values of the best individual at the end of each run for each algorithm that obtains significantly different results from the base algorithm.
  • Figure 2: Comparison of mean energy function values for different algorithm variants. (a) Includes all algorithms. (b) Focuses on significantly different results.