Abstract In recent years, researchers from interdisciplinary teams involving ecologists, economists and operations researchers collaborated to provide decision support tools to address the challenges of preserving biodiversity by optimizing the design of reserves. The goal of this paper is to further advance this area of research and provide new solutions to solve complex Spatial Conservation Planning (SCP) problems under uncertainty that consider risk preferences of decision makers. Our approach employs modern portfolio theory to address uncertainties in SCP problems, and involves two conflicting objectives: maximizing return and minimizing risk. We apply concepts from game theory such as the Nash bargaining solution to directly compute a desirable Pareto-optimal solution for the proposed bi-objective optimization formulation in natural resource management problems. We demonstrate with numerical examples that by directly computing a Nash bargaining solution, a Binary Quadratically Constrained Quadratic Program (BQCQP) can be solved. We show that our approach (implementable with commercial solvers such as CPLEX) can effectively solve the proposed BQCQP for much larger problems than previous approaches published in the ecological literature. Optimal solutions for problems with less than 400 parcels can be computed within a minute. Near optimal solutions (within at most 0.2% gap from an optimal solution) for high-dimensional problems involving up to 800 parcels can be computed within 8 h on a standard computer. We have presented a new approach to solve SCP optimization problems while considering uncertainty and risk tolerance of decision makers. Our new approach expands considerably the applicability of such SCP optimization methods to address real conservation problems.

中文翻译：

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使用现代投资组合理论和纳什讨价还价解决方案的不确定性空间保护规划

摘要 近年来，包括生态学家、经济学家和运筹学研究人员在内的跨学科团队的研究人员合作提供决策支持工具，通过优化保护区设计来应对保护生物多样性的挑战。本文的目标是进一步推进这一研究领域，并提供新的解决方案，以解决考虑决策者风险偏好的不确定性下复杂的空间保护规划 (SCP) 问题。我们的方法采用现代投资组合理论来解决 SCP 问题中的不确定性，并涉及两个相互矛盾的目标：最大化回报和最小化风险。我们应用博弈论中的概念，例如纳什讨价还价解决方案，直接计算自然资源管理问题中提出的双目标优化公式的理想帕累托最优解决方案。我们用数值例子证明，通过直接计算纳什讨价还价解决方案，可以解决二元二次约束二次规划（BQCQP）。我们表明，我们的方法（可通过 CPLEX 等商业求解器实现）可以有效地解决所提出的 BQCQP，其问题比之前在生态文献中发表的方法要大得多。可以在一分钟内计算出少于 400 个包裹的问题的最佳解决方案。接近最优解（最多在 0. 对于涉及多达 800 个包裹的高维问题，可以在标准计算机上在 8 小时内计算出与最优解的 2% 差距）。我们提出了一种新方法来解决 SCP 优化问题，同时考虑决策者的不确定性和风险承受能力。我们的新方法大大扩展了此类 SCP 优化方法的适用性，以解决实际保护问题。