Hybrid meta-heuristics for Vehicle Routing Problem with Time Window Constraints

Abstract

This paper proposes a hybrid meta-heuristic, Tabu Threshold Algorithm (TTA), to efficiently and effectively solve Vehicle Routing Problem with Time Window Constraints (VRPTW). TTA integrates Tabu Search (TS) and Threshold Accepting (TA). TS is one of the most popular generic heuristics in solving VRPTW in recent years, and TA is a combinatorial optimization meta-heuristic. The first objective is to determine the route that minimizes the total vehicle travel distances. This leads to a quick response to satisfy customer demands. The second objective is to find the minimum required number of vehicles. This can reduce the transportation cost. TTA consists of three major phases: initial solution construction, local search improvement, and Tabu Threshold improvement. The initial solution construction phase uses nearest neighbour algorithm to generate initial solution, and this solution is improved by both inter-route and intra-route improvement algorithms in local search improvement phase. In Tabu Threshold improvement phase, a hybrid algorithm of TS and TA is used to improve the current solution and finds the best solution. TTA results in good solution quality by the evaluation of Solomon's benchmark instances. Comparing with the best known solutions of Solomon's 56 benchmark instances, the average deviation of distance is about 3.5% and the average deviation of number of vehicles is about 9.6%. Furthermore, TTA is compared with the optimal solution of the partial instances, the average deviation of distance is about 1.9% and the average deviation of number of vehicles is about 2.4%. TTA is implemented in part by a distribution center delivering equipment spare parts to factories manufacturing semiconductors and Thin Film Transistor Liquid Crystal Display (TFT-LCD) in Science-Based Industrial Park in Hsinchu, Taiwan.