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Genetic Algorithm for a Pickup and Delivery Problem with Time Windows

A mathematical model for a multivehicle pickup and delivery problem with time windows is presented, and a genetic algorithm (GA) for solving it is proposed. The mathematical model is formulated as a mixedinteger linear programming problem. The objective of the proposed model is to minimize the total cost, which consists of the fixed cost for the vehicles, the routing cost, and the customer inconvenience cost, which is modeled as a penalty cost for violation of the time windows of each customer. Like other combinatorial problems, solving this pickup and delivery problem is time-consuming, and sometimes it is impossible to find an exact solution. The problem is solved exactly for up to six demands (12 nodes), and GA is used for larger problems with more than six demands. The proposed GA can solve a pickup and delivery problem in an extremely short time compared with the exact solution procedure. It also produces excellent results for small problems. A GA used to solve a 30-demands problem (60 nodes) with 10 vehicles is illustrated.