Constrained Metropolitan Service Placement: Integrating Bayesian Optimization with Spatial Heuristics

Abstract

Highlights: What are the main findings? Under a strict budget of 50 function evaluations, the two-stage optimization framework rapidly attains near-optimal solutions, delivering up to 1.3× higher service provision scores than NSGA-II/CMA-ES. The framework scales to metropolitan land-use planning under complex regulatory constraints, maintaining sample-efficient exploration and fast convergence. What is the implication of the main findings? Surrogate-assisted, gradient-free optimization is a practical, deployable method on standard computing hardware for simultaneous urban service placement in large cities, quantifying city-wide system effects (load redistribution, accessibility changes, etc.) and maximizing a composite provision metric aligned with equitable distribution. The modular, open-source implementation enables evidence-based decision making and reproducible evaluation of proposed plans, establishing a validated base for dynamic/stochastic extensions. Metropolitan service-placement optimization is computationally challenging under strict evaluation budgets and regulatory constraints. Existing approaches either neglect capacity constraints, producing infeasible solutions, or employ population-based metaheuristics requiring hundreds of evaluations—beyond typical municipal planning resources. We introduce a two-stage optimization framework combining Bayesian optimization with domain-informed heuristics to address this constrained, mixed discrete–continuous problem. Stage 1 optimizes continuous service area allocations via the Tree-structured Parzen Estimator with empirical gradient prioritization, reducing effective dimensionality from 81 services to 10–15 per iteration. Stage 2 converts allocations into discrete unit placements via efficiency-ranked bin packing, ensuring regulatory compliance. Evaluation across 35 benchmarks on Saint Petersburg, Russia (117–3060 decision variables), demonstrates that our method achieves 99.4% of the global optimum under a 50-evaluation budget, outperforming BIPOP-CMA-ES (98.4%), PURE-TPE (97.1%), and NSGA-II (96.5%). Optimized configurations improve equity (Gini coefficient of 0.318 → 0.241) while maintaining computational feasibility (2.7 h for 109-block districts). Open-source implementation supports reproducibility and facilitates adoption in metropolitan planning practice.