Optimizing the cost and benefit allocation among multiple players in a public-private partnership (PPP) project is recognized to be a multi-objective optimization problem (MOP). When the least present value of revenue (LPVR) mechanism is adopted in the competitive procurement of PPPs, the MOP presents asymmetry in objective levels, control variables and action orders. This paper characterizes this asymmetrical MOP in Stackelberg theory and builds a bi-level programing model to solve it in order to support the decision-making activities of both the public and private sectors in negotiation. An intuitive algorithm based on the non-dominated sorting genetic algorithm III (NSGA III) framework is designed to generate Pareto solutions that allow decision-makers to choose optimal strategies from their own criteria. The effectiveness of the model and algorithm is validated via a real case of a highway PPP project. The results reveal that the PPP project will be financially infeasible without the transfer of certain amounts of exterior benefits into supplementary income for the private sector. Besides, the strategy of transferring minimum exterior benefits is more beneficial to the public sector than to users.

中文翻译：

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双层规划求解LPVR机制下PPP的非对称多目标优化问题

在公私合作 (PPP) 项目中优化多个参与者之间的成本和收益分配被认为是一个多目标优化问题 (MOP)。当PPPs的竞争性采购采用收入最小现值(LPVR)机制时，MOP在客观水平、控制变量和行动顺序上呈现出不对称性。本文在 Stackelberg 理论中刻画了这种不对称的 MOP，并构建了一个双层规划模型来解决它，以支持公共和私营部门在谈判中的决策活动。基于非支配排序遗传算法 III (NSGA III) 框架的直观算法旨在生成帕累托解决方案，允许决策者根据自己的标准选择最佳策略。通过高速公路PPP项目的真实案例验证了模型和算法的有效性。结果表明，如果不将一定数量的外部收益转化为私营部门的补充收入，PPP 项目在财务上是不可行的。此外，转移最小外部利益的策略对公共部门比对用户更有利。