Abstract
We consider the pickup and delivery problem (PDP) as a general model of practical transportation problems in the automated guided vehicle (AGV) transportation systems, elevator systems and so on. In this paper, we focus on the single-vehicle PDP (1-PDP). This 1-PDP is regarded as an extension of traveling salesman problems (TSP), and is more complex due to the presence of the constraints both on precedence and vehicle capacity. We formulate the 1-PDP into a mathematical programming model by introducing decision variables which represent the precedence relations of locations. Based on this model, we propose two approaches based on genetic algorithms (called as GA1 and GA2, respectively). GA1 uses a sequence of customer indices as a genetic representation such that genetic operators designed for TSP can be applied. As for GA2, a sequence of location indices is used as a genetic representation, and a new crossover operator is applied, which can inherit precedence relations in generating new individuals. Several computational experiments show the effectiveness of the proposed approaches. GA2 shows an advantage especially for the 1-PDP with harder capacity constraints.
