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<p>This paper introduces a novel extension of the raw material model (RMM) by incorporating parallel line segment barriers, addressing a gap in location theory where supply and demand interactions are often assumed to occur in unobstructed space. The presence of barriers creates a non-convex optimization landscape with non-differentiable objective functions, rendering standard gradient-based methods ineffective. To solve this, we develop a graph-based visibility approach to compute barrier-respecting distances and propose a comparative algorithmic framework. We implement and adapt the deterministic Big Square Small Square (BSSS) algorithm specifically for the barrier environment to guarantee global optimality, and benchmark it against four metaheuristics: Particle Swarm Optimization (PSO), Grey Wolf Optimizer (GWO), Covariance Matrix Adaptation Evolution Strategy (CMA-ES), and Differential Evolution (DE). The experimental results, validated by Wilcoxon signed-rank tests, demonstrate that while the deterministic BSSS provides a theoretical baseline, it is computationally prohibitive for complex instances. Crucially, the study identifies that the CMA-ES significantly outperforms other methods.</p>

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A raw material model with parallel barriers: comparing global optimization approach and metaheuristics

  • 期刊论文

  • 发表日期：

    2026年4月7日

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  • Nguyen Ngoc Dang Duy,
  • Nguyen Thanh Hung,
  • Kien Trung Nguyen

摘要

This paper introduces a novel extension of the raw material model (RMM) by incorporating parallel line segment barriers, addressing a gap in location theory where supply and demand interactions are often assumed to occur in unobstructed space. The presence of barriers creates a non-convex optimization landscape with non-differentiable objective functions, rendering standard gradient-based methods ineffective. To solve this, we develop a graph-based visibility approach to compute barrier-respecting distances and propose a comparative algorithmic framework. We implement and adapt the deterministic Big Square Small Square (BSSS) algorithm specifically for the barrier environment to guarantee global optimality, and benchmark it against four metaheuristics: Particle Swarm Optimization (PSO), Grey Wolf Optimizer (GWO), Covariance Matrix Adaptation Evolution Strategy (CMA-ES), and Differential Evolution (DE). The experimental results, validated by Wilcoxon signed-rank tests, demonstrate that while the deterministic BSSS provides a theoretical baseline, it is computationally prohibitive for complex instances. Crucially, the study identifies that the CMA-ES significantly outperforms other methods.