Multi-objective integer programming for urban relocation decision-making: a satisfaction-aware and cost-efficient optimization approach

This paper addresses a relocation decision optimization problem involving residents unwilling to vacate. We propose a multi-stage computational framework to design compensation-aware, constraint-satisfying relocation schemes. A hybrid satisfaction evaluation model is first established based on area, lighting, psychological pricing, and layout, integrated through an entropy-weighted utility function. Subsequently, a multi-objective 0-1 integer programming model is formulated to maximize courtyard evacuation continuity and economic efficiency under budget constraints. Finally, an economic gain function is introduced to identify turning points in marginal relocation cost-benefit ratios. Experiments demonstrate the model's ability to balance stakeholder interests and reveal a distinct inflection point when the benefit-cost ratio exceeds 52.2. This study offers a transferable framework for data-driven urban relocation and redevelopment planning.