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<p>Optimizing age-friendly community facilities has become crucial for enhancing elderly well-being. This study proposes a distributionally robust optimization (DRO) framework for public seating facility planning, addressing the limitations of conventional models in handling multidimensional uncertainties. We construct Wasserstein metric-based ambiguity sets to characterize stochastic interactions among individual physiological traits (e.g., balance capacity), environmental factors (e.g., terrain irregularity), and fatigue-induced risk accumulation. A dual-layer constraint system synergizes safety assurance (fall probability control) and functional adequacy (demand-responsive coverage) under budget limits. To address computational challenges in large-scale networks, we develop a Two-stage Greedy-deterministic (TSGD) algorithm with dynamic candidate screening and dual-variable correction, achieving high computational efficiency and scalability for large-scale networks. For small-scale validation, we further propose a Distributionally Robust Simulated Annealing (DRSA) algorithm. Numerical experiments demonstrate the following facts: 1) TSGD reduces computation time by 66% compared to Gurobi in 200-node scenarios with &lt; 3% optimality gap; 2) The Wasserstein-DRO formulation ensures 89.3% risk compliance under worst-case uncertainty. Theoretically, this work integrates safety-functionality synergy into stochastic facility location models. Practically, it provides a decision-making paradigm for spatial optimization in aging communities, with algorithmic innovations enabling scalable implementation.</p>

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Robust Optimization for Age-friendly Facility Location Problem

  • 期刊论文

  • 发表日期：

    2026年4月27日

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  • Bin Lei,
  • Xia Wu,
  • Tunan Wang,
  • Weili Xue

摘要

Optimizing age-friendly community facilities has become crucial for enhancing elderly well-being. This study proposes a distributionally robust optimization (DRO) framework for public seating facility planning, addressing the limitations of conventional models in handling multidimensional uncertainties. We construct Wasserstein metric-based ambiguity sets to characterize stochastic interactions among individual physiological traits (e.g., balance capacity), environmental factors (e.g., terrain irregularity), and fatigue-induced risk accumulation. A dual-layer constraint system synergizes safety assurance (fall probability control) and functional adequacy (demand-responsive coverage) under budget limits. To address computational challenges in large-scale networks, we develop a Two-stage Greedy-deterministic (TSGD) algorithm with dynamic candidate screening and dual-variable correction, achieving high computational efficiency and scalability for large-scale networks. For small-scale validation, we further propose a Distributionally Robust Simulated Annealing (DRSA) algorithm. Numerical experiments demonstrate the following facts: 1) TSGD reduces computation time by 66% compared to Gurobi in 200-node scenarios with < 3% optimality gap; 2) The Wasserstein-DRO formulation ensures 89.3% risk compliance under worst-case uncertainty. Theoretically, this work integrates safety-functionality synergy into stochastic facility location models. Practically, it provides a decision-making paradigm for spatial optimization in aging communities, with algorithmic innovations enabling scalable implementation.