摘要

Ant colony optimization (ACO) can be used to find approximate solutions to difficult optimization problems. Many implementations of ACO have been presented for a variety of combinatorial optimization problems. In this paper, we propose assignment-preference ant colony optimization (AP-ACO) to deal with the two-echelon vehicle routing problem (2E-VRP). 2E-VRP is a combinatorial optimization problem, where the delivery from a depot to the customers is managed by routing and consolidating the freight through satellites, and the objective is to minimize the total cost. Due to the uncertainty of satellite-to-customer assignment, it might be difficult for ACO to search for different routing subproblems. We introduce assignment preferences to ACO to provide solutions for 2E-VRP. A multi-player game is used to analyze the mutual relationships among routing subproblems to obtain assignment preferences for satellites and customers. Assignment preferences estimation, the pheromone updating rule, and solution construction are exploited to improve the search efficiency of the proposed algorithm. The computational results from three test sets with sizes ranging from 20 to 50 customers indicate the effectiveness and usefulness of the proposed algorithm for solving 2E-VRPs.

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