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<p>Exploitation and exploration operators are the fundamental building blocks in Evolutionary and Metaheuristic optimization algorithms. Specifically, crossover or recombination operators are used for exploitation, combining two or more candidate solutions to generate new ones, seeking improvements in the near search space. In continuous optimization, Simulated Binary Crossover (SBX) and DE/rand/1/bin from the Differential Evolution (DE) algorithm are the first-choice recombination operators for optimizing real-coded problems in single- and multi-objective optimization. This paper proposes a new bi-parental recombination based on three key ideas: the combinatorial recombination used in SBX, the <i>CR</i> and <i>F</i> control parameters from DE, and the requirement for only two parent solutions. The proposal is called Synthetic Differences Crossover (SDX) because, unlike DE strategies, which require at least three parent solutions, SDX only requires two and uses synthetic points. The experimental results favor SDX on larger-dimension benchmarks. For the 20-variable version of CEC2022, in comparison with three crossovers, SDX achieves a Friedman of 1.86, followed by BLX-<InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\alpha \)</EquationSource> </InlineEquation> 2.42, SBX 2.68, and DE/rand/1/bin 3.05. For the 100-variable version of CEC2017, compared with four CEC competition winners, SDX achieves a Friedman rank of 2.53, followed by RDEx 2.60, L-SRTDE 3.10, NL-SHADE-LBC 3.30, and NL-SHADE-RSP 3.47.</p>

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A synthetic differences crossover operator for real-coded evolutionary algorithms

  • 期刊论文

  • 发表日期：

    2026年7月9日

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  • Alejandro Santiago

摘要

Exploitation and exploration operators are the fundamental building blocks in Evolutionary and Metaheuristic optimization algorithms. Specifically, crossover or recombination operators are used for exploitation, combining two or more candidate solutions to generate new ones, seeking improvements in the near search space. In continuous optimization, Simulated Binary Crossover (SBX) and DE/rand/1/bin from the Differential Evolution (DE) algorithm are the first-choice recombination operators for optimizing real-coded problems in single- and multi-objective optimization. This paper proposes a new bi-parental recombination based on three key ideas: the combinatorial recombination used in SBX, the CR and F control parameters from DE, and the requirement for only two parent solutions. The proposal is called Synthetic Differences Crossover (SDX) because, unlike DE strategies, which require at least three parent solutions, SDX only requires two and uses synthetic points. The experimental results favor SDX on larger-dimension benchmarks. For the 20-variable version of CEC2022, in comparison with three crossovers, SDX achieves a Friedman of 1.86, followed by BLX- \(\alpha \) 2.42, SBX 2.68, and DE/rand/1/bin 3.05. For the 100-variable version of CEC2017, compared with four CEC competition winners, SDX achieves a Friedman rank of 2.53, followed by RDEx 2.60, L-SRTDE 3.10, NL-SHADE-LBC 3.30, and NL-SHADE-RSP 3.47.