Multi-swarm particle swarm optimization for payment scheduling

The payment scheduling negotiation problem with multi-mode and resource constraints (MRCPSNP) is a practical extension to the resource-constrained project scheduling problem (RCPSP). It considers the interests of both the client and the contractor, who negotiate with each other to maximize their own benefits. Since the interests of the client and contractor are conflicting and the two roles have special scheduling requirements, it is difficult to solve this problem. This paper addresses MRCPSNP and adopts the net present value (NPV) of discounted cash flows to measure the potential value. To simulate the negotiation process, we adopt a co-evolution strategy and make the two parts negotiate with each other to maximize their own NPV. To specify special requirements of the two roles, a multi-level region of interest strategy is proposed. The co-evolution strategy and the multi-level region of interest strategy are integrated into a particle swarm optimization (PSO) algorithm, forming a multi-swarm particle swarm optimization (MPSO) approach. Experimental comparisons with the other two methods on 30 project instances demonstrate that the proposed approach is very effective and promising.