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<p>The rapid proliferation of metaphor-based optimization algorithms has faced criticism from researchers regarding their novelty and contribution. Many of these pseudo-novel metaheuristics suffer from performance inefficiencies, biased verification systems, and excessive similarities in their modelling as they imitate the foraging behaviors of animals and other living beings. This study introduces a population-based and metaphor-free optimization algorithm using the well-known and efficient Lagrange interpolation formula to address these concerns. The proposed algorithm, called Lagrange interpolation-based optimization (LIBO), is designed for numerical optimization and solving real-world optimization problems. The second-order Lagrange interpolation formula is considered to construct the algorithm where the polynomial passes through three given random points, thereby demonstrating a parabolic structure. While updating the algorithm, every trial solution considers three randomly chosen solutions and obtains the minimal point. To strike a suitable balance between exploration and exploitation and avoid local optima trapping, the proposed LIBO algorithm incorporates specific measures in its search mechanism. Its effectiveness is evaluated by IEEE CEC 2017 and IEEE CEC 2019 benchmark functions, three practical engineering problems, and the highly non-linear multiple gravity assist spacecraft trajectory problem. Comparative analyses were conducted, and it was found that in CEC 2017 functions, the proposed LIBO is better on 100% occasions than the basic algorithms and more than 85% efficient than differential evolution variants. Also, it is better than the competitors in more than 80% of instances, as in the case of the CEC 2019 suite. Statistical analysis, exploration–exploitation analysis, and computational complexity assessments confirm the promising and competitive performance of the LIBO algorithm. Concerning performance metrics, exploration–exploitation inclinations, and avoiding local optima, it exhibits higher performance. The metaphor-free LIBO algorithm showcases its dominance in optimizing engineering problems and multiple gravity assist spacecraft trajectory problems.</p>

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A Lagrange interpolation-based optimization algorithm for numerical optimization and spacecraft trajectory problems

  • 期刊论文

  • 发表日期：

    2026年6月27日

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  • Apu Kumar Saha,
  • Sanjoy Chakraborty,
  • Ratul Chakraborty,
  • Absalom E. Ezugwu,
  • Vladimir Simic,
  • Sushmita Sharma

摘要

The rapid proliferation of metaphor-based optimization algorithms has faced criticism from researchers regarding their novelty and contribution. Many of these pseudo-novel metaheuristics suffer from performance inefficiencies, biased verification systems, and excessive similarities in their modelling as they imitate the foraging behaviors of animals and other living beings. This study introduces a population-based and metaphor-free optimization algorithm using the well-known and efficient Lagrange interpolation formula to address these concerns. The proposed algorithm, called Lagrange interpolation-based optimization (LIBO), is designed for numerical optimization and solving real-world optimization problems. The second-order Lagrange interpolation formula is considered to construct the algorithm where the polynomial passes through three given random points, thereby demonstrating a parabolic structure. While updating the algorithm, every trial solution considers three randomly chosen solutions and obtains the minimal point. To strike a suitable balance between exploration and exploitation and avoid local optima trapping, the proposed LIBO algorithm incorporates specific measures in its search mechanism. Its effectiveness is evaluated by IEEE CEC 2017 and IEEE CEC 2019 benchmark functions, three practical engineering problems, and the highly non-linear multiple gravity assist spacecraft trajectory problem. Comparative analyses were conducted, and it was found that in CEC 2017 functions, the proposed LIBO is better on 100% occasions than the basic algorithms and more than 85% efficient than differential evolution variants. Also, it is better than the competitors in more than 80% of instances, as in the case of the CEC 2019 suite. Statistical analysis, exploration–exploitation analysis, and computational complexity assessments confirm the promising and competitive performance of the LIBO algorithm. Concerning performance metrics, exploration–exploitation inclinations, and avoiding local optima, it exhibits higher performance. The metaphor-free LIBO algorithm showcases its dominance in optimizing engineering problems and multiple gravity assist spacecraft trajectory problems.