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This study introduces a Hadamard matrix-based local search (HLS) to enhance differential evolution (DE) algorithms. HLS significantly improves DE

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Area of Science:

  • Computational Intelligence
  • Optimization Algorithms
  • Numerical Analysis

Background:

  • Differential evolution (DE) is a powerful global optimization technique.
  • Standard DE algorithms exhibit limitations in local search effectiveness, hindering performance on complex problems.
  • Binomial crossover in DE inadequately explores local search space.

Purpose of the Study:

  • To introduce a novel local search scheme, Hadamard matrix-based local search (HLS), to improve DE performance.
  • To enhance the local search capability of DE algorithms.
  • To address the inefficiency of DE in local research for complex optimization tasks.

Main Methods:

  • Implementation of a new local search scheme (HLS) utilizing Hadamard matrices.
  • Integration of HLS into four classical DE algorithms and the jDE variant.
  • Experimental evaluation on a suite of widely used benchmark functions.

Main Results:

  • DE algorithms augmented with HLS demonstrated superior performance across 20 benchmark problems.
  • HLS-based DE schemes achieved improvements in 80%, 75%, 65%, and 65% of tested problems.
  • The jDE algorithm with HLS outperformed the standard jDE in 50% of the test cases.

Conclusions:

  • The Hadamard matrix-based local search (HLS) effectively enhances the overall performance of differential evolution (DE) algorithms.
  • HLS provides a robust method for improving local search capabilities in optimization.
  • Experimental results confirm HLS as a valuable addition to DE for complex optimization problems.