Solving the Selective Pickup and Delivery Problem Using Max-Min Ant System

The pickup and delivery problem (PDP) is relevant to many real-world problems, e.g., logistic and transportation problems. The problem is to find the shortest route to gain commodities from the pickup nodes and supply them to the delivery nodes. The amount of commodities of pickup nodes and delivery nodes is usually assumed to be in equilibrium; thus, all pickup nodes have to be visited for collecting all commodities required. However, some real-world applications, such as rental bikes and wholesaling business, need only to gain sufficient commodities from certain pickup nodes. A variant of PDP, namely the selective pickup and delivery problem (SPDP), is formulated to address the above scenarios. The major difference of SPDP from PDP lies in the requirement of visiting all pickup nodes. The SPDP relaxes this requirement to achieve more efficient transportation. The goal of the SPDP is to seek the shortest path that satisfies the load constraint to supply the commodities demanded by all delivery nodes with some pickup nodes. This study proposes a max-min ant system (MMAS) to solve the SPDP. The ants aim to construct the shortest route for the SPDP considering the number of selected pickup nodes and all delivery nodes. This study conducts experiments to examine the performance of the proposed MMAS, in comparison with genetic algorithm and memetic algorithm. The experimental results validate the effectiveness and efficiency of the proposed MMAS in route length and convergence speed for the SPDP.