<p>Population initialization represents a relevant stage for metaheuristic algorithms because it provides an initial configuration of solutions from which the algorithm lays the foundation for a search strategy to efficiently find high-quality solutions. However, many initialization approaches struggle to find a balance between the proper distribution of the solutions and the initial quality, diminishing the optimization efficacy in complex multidimensional spaces. This paper introduces a new initialization approach integrating Latin Hypercube Sampling (LHS) to obtain a wide exploration of the solution space and a searching mechanism employing a division of space by the Golden Section (GS) to focus on potential locations. The proposed approach divides the space into two sections by the Golden ratio employing three dynamic pivots, and a set of samples is generated by the LHS, keeping only those with the best quality. Considering the position of the best solution, the pivots reduce space, focusing on the search for promising regions. The effectiveness of this method has been incorporated into a traditional Differential Evolution (DE) algorithm and assessed with a set of 30 challenging objective functions, including multimodal, unimodal, hybrid, and shifted functions. The experimental results show a wide distribution of candidate solutions and easy identification of zones with promising quality, facilitating the identification of optimal solutions by metaheuristic algorithms.</p>

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Application of the golden section and the Latin hypercube sampling on metaheuristics: A new population initialization approach

  • Oscar Barba-Toscano,
  • Erik Cuevas,
  • Héctor Escobar-Cuevas,
  • Mario Vásquez,
  • Nahum Aguirre

摘要

Population initialization represents a relevant stage for metaheuristic algorithms because it provides an initial configuration of solutions from which the algorithm lays the foundation for a search strategy to efficiently find high-quality solutions. However, many initialization approaches struggle to find a balance between the proper distribution of the solutions and the initial quality, diminishing the optimization efficacy in complex multidimensional spaces. This paper introduces a new initialization approach integrating Latin Hypercube Sampling (LHS) to obtain a wide exploration of the solution space and a searching mechanism employing a division of space by the Golden Section (GS) to focus on potential locations. The proposed approach divides the space into two sections by the Golden ratio employing three dynamic pivots, and a set of samples is generated by the LHS, keeping only those with the best quality. Considering the position of the best solution, the pivots reduce space, focusing on the search for promising regions. The effectiveness of this method has been incorporated into a traditional Differential Evolution (DE) algorithm and assessed with a set of 30 challenging objective functions, including multimodal, unimodal, hybrid, and shifted functions. The experimental results show a wide distribution of candidate solutions and easy identification of zones with promising quality, facilitating the identification of optimal solutions by metaheuristic algorithms.