A Preference Biobjective Evolutionary Algorithm for the Payment Scheduling Negotiation Problem

The resource-constrained project scheduling problem (RCPSP) is a basic problem in project management. The net present value (NPV) of discounted cash flow is used as a criterion to evaluate the financial aspects of RCPSP in many studies. But while most existing studies focused on only the contractor’s NPV, this article addresses a practical extension of RCPSP, called the payment scheduling negotiation problem (PSNP), which considers both the interests of the contractor and the client. To maximize NPVs of both sides and achieve a win–win solution, these two participants negotiate together to determine an activity schedule and a payment plan for the project. The challenges arise in three aspects: 1) the client’s NPV and the contractor’s NPV are two conflicting objectives; 2) both participants have special preferences in decision making; and 3) the RCPSP is nondeterministic polynomial-time hard (NP-Hard). To overcome these challenges, this article proposes a new approach with the following features. First, the problem is reformulated as a biobjective optimization problem with preferences. Second, to address the different preferences of the client and the contractor, a strategy of multilevel region interest is presented. Third, this strategy is integrated in the nondominated sorting genetic algorithm II (NSGA-II) to solve the PSNP efficiently. In the experiment, the proposed algorithm is compared with both the double-level optimization approach and the multiobjective optimization approach. The experimental results validate that the proposed method can focus on searching in the region of interest (ROI) and provide more satisfactory solutions.