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<p>This paper addresses the Generalized Quadratic Assignment Problem (GQAP) under uncertainty, where installation and transportation costs are represented as grey numbers due to limited information. A novel grey variant, termed GGQAP, is formulated and solved using two hybrid metaheuristic approaches: OHNN-PSO and OHNN-SA. Both methods integrate an Optimized Hopfield Neural Network (OHNN) with its parameters fine-tuned by Particle Swarm Optimization (PSO), followed by global refinement using either PSO or Simulated Annealing (SA). Extensive experiments on 23 classical benchmark functions, 21 GQAP instances, and 28 generated GGQAP instances show that OHNN-PSO achieves the best average rank across all datasets: 1.71 (among 10 algorithms), 1.33 (among 3), and 1.32 (among 4). OHNN-PSO significantly outperforms PSO and standard OHNN on all 28 GGQAP instances (<InlineEquation ID="IEq1"><EquationSource Format="TEX">\(p &lt; 0.001\)</EquationSource></InlineEquation>) and outperforms OHNN-SA on 24 out of 28 instances (<InlineEquation ID="IEq2"><EquationSource Format="TEX">\(p &lt; 0.05\)</EquationSource></InlineEquation>). The proposed framework offers a practical and statistically validated solution for complex assignment problems under grey uncertainty.</p>

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Hybrid metaheuristic approaches for grey generalized quadratic assignment problem

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年7月8日

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  • Malihe Niksirat,
  • Mostafa Sabzekar,
  • Javad Tayyebi,
  • Mostafa Hajiaghaei-Keshteli

摘要

This paper addresses the Generalized Quadratic Assignment Problem (GQAP) under uncertainty, where installation and transportation costs are represented as grey numbers due to limited information. A novel grey variant, termed GGQAP, is formulated and solved using two hybrid metaheuristic approaches: OHNN-PSO and OHNN-SA. Both methods integrate an Optimized Hopfield Neural Network (OHNN) with its parameters fine-tuned by Particle Swarm Optimization (PSO), followed by global refinement using either PSO or Simulated Annealing (SA). Extensive experiments on 23 classical benchmark functions, 21 GQAP instances, and 28 generated GGQAP instances show that OHNN-PSO achieves the best average rank across all datasets: 1.71 (among 10 algorithms), 1.33 (among 3), and 1.32 (among 4). OHNN-PSO significantly outperforms PSO and standard OHNN on all 28 GGQAP instances (\(p < 0.001\)) and outperforms OHNN-SA on 24 out of 28 instances (\(p < 0.05\)). The proposed framework offers a practical and statistically validated solution for complex assignment problems under grey uncertainty.