L.H. Lee

National University of Singapore, Singapore, Singapore

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Publications (7)5.28 Total impact

  • Source
    K. C. Tan, Y. H. Chew, L. H. Lee
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    ABSTRACT: Vehicle routing problem with time windows (VRPTW) involves the routing of a set of vehicles with limited capacity from a central depot to a set of geographically dispersed customers with known demands and predefined time windows. The problem is solved by optimizing routes for the vehicles so as to meet all given constraints as well as to minimize the objectives of traveling distance and number of vehicles. This paper proposes a hybrid multiobjective evolutionary algorithm (HMOEA) that incorporates various heuristics for local exploitation in the evolutionary search and the concept of Pareto's optimality for solving multiobjective optimization in VRPTW. The proposed HMOEA is featured with specialized genetic operators and variable-length chromosome representation to accommodate the sequence-oriented optimization in VRPTW. Unlike existing VRPTW approaches that often aggregate multiple criteria and constraints into a compromise function, the proposed HMOEA optimizes all routing constraints and objectives simultaneously, which improves the routing solutions in many aspects, such as lower routing cost, wider scattering area and better convergence trace. The HMOEA is applied to solve the benchmark Solomon's 56 VRPTW 100-customer instances, which yields 20 routing solutions better than or competitive as compared to the best solutions published in literature.
    Computational Optimization and Applications 05/2006; 34(1):115-151. · 1.28 Impact Factor
  • Source
    K.C. Tan, Y.H. Chew, L.H. Lee
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    ABSTRACT: This paper considers a transportation problem for moving empty or laden containers for a logistic company. Owing to the limited resource of its vehicles (trucks and trailers), the company often needs to sub-contract certain job orders to outsourced companies. A model for this truck and trailer vehicle routing problem (TTVRP) is first constructed in the paper. The solution to the TTVRP consists of finding a complete routing schedule for serving the jobs with minimum routing distance and number of trucks, subject to a number of constraints such as time windows and availability of trailers. To solve such a multi-objective and multi-modal combinatorial optimization problem, a hybrid multi-objective evolutionary algorithm (HMOEA) featured with specialized genetic operators, variable-length representation and local search heuristic is applied to find the Pareto optimal routing solutions for the TTVRP. Detailed analysis is performed to extract useful decision-making information from the multi-objective optimization results as well as to examine the correlations among different variables, such as the number of trucks and trailers, the trailer exchange points, and the utilization of trucks in the routing solutions. It has been shown that the HMOEA is effective in solving multi-objective combinatorial optimization problems, such as finding useful trade-off solutions for the TTVRP routing problem.
    European Journal of Operational Research 01/2006; · 2.04 Impact Factor
  • Source
    K C Tan, T H Lee, Y.H. Chew, L.H. Lee
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    ABSTRACT: This paper considers a transportation problem for moving empty or laden containers for a logistic company. A model for this truck and trailer vehicle routing problem (TTVRP) is first constructed in the paper. The solution to the TTVRP consists of finding a complete routing schedule for serving the jobs with minimum routing distance and number of trucks, subject to a number of constraints such as time windows and availability and multimodal combinatorial optimization problem, a hybrid multiobjective evolutionary algorithm (HMOEA) is applied to find the Pareto optimal routing solutions for the TTVRP. Detailed analysis is performed to extract useful decision-making information from the multiobjective optimization results. The computational results have shown that the HMOEA is effective for solving multiobjective combinatorial problems, such as finding useful trade-off solutions for the TTVRP.
    Evolutionary Computation, 2003. CEC '03. The 2003 Congress on; 01/2004
  • [Show abstract] [Hide abstract]
    ABSTRACT: Vehicle routing problem with time windows (VRPTW) involves the routing of a set of vehicles with limited capacity from a central depot to a set of geographically dispersed customers with known demands and predefined time windows. This paper proposes a hybrid multiobjective evolutionary algorithm (HMOEA) that incorporates various heuristics for local exploitation in the evolutionary search and the concept of Pareto's optimality for solving multiobjective optimization in VRPTW problems. The proposed HMOEA optimizes all routing constraints and objectives simultaneously, which improves the routing solutions in many aspects, such as lower routing cost, wider scattering area and better convergence trace.
    Systems, Man and Cybernetics, 2003. IEEE International Conference on; 11/2003
  • K.C. Tan, T.H. Lee, K. Ou, L.H. Lee
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    ABSTRACT: In vehicle routing problems with time window constraints (VRPTW), a set of vehicles with limited capacity, are to be routed from a central depot to a set of geographically dispersed customers with known demands and predefined time windows. To solve the problem, the optimized assignment of vehicles to each customer is needed as to achieve the minimal total cost without violating the capacity and time window constraints. Combinatorial optimization problems of this kind are NP-hard and are best solved to the near optimum by heuristics. The authors describe their research on a rare class of genetic algorithms, known as the messy genetic algorithms (mGA) in solving the VRPTW problem. The mGA has the merit of directly realizing the relational search needed in VRPTW representation, which cannot be easily realized using simple heuristic methods. The mGA was applied to solve the benchmark Solomon's 56 VRPTW 100-customer instances, and yielded 23 solutions better than or equivalent to the best solutions ever published in literature
    Evolutionary Computation, 2001. Proceedings of the 2001 Congress on; 02/2001
  • K.C. Tan, L.H. Lee, K. Ou
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    ABSTRACT: This paper describes the authors’ research on various heuristics in solving vehicle routing problem with time window constraints (VRPTW) to near optimal solutions. VRPTW is NP-hard problem and best solved to near optimum by heuristics. In the vehicle routing problem, a set of geographically dispersed customers with known demands and predefined time windows are to be served by a fleet of vehicles with limited capacity. The optimized routines for each vehicle are scheduled as to achieve the minimal total cost without violating the capacity and time window constraints. In this paper, we explore different hybridizations of artificial intelligence based techniques including simulated annealing, tabu search and genetic algorithm for better performance in VRPTW. All the implemented hybrid heuristics are applied to solve the Solomon's 56 VRPTW with 100-customer instances, and yield 23 solutions competitive to the best solutions published in literature according to the authors’ best knowledge.
    Engineering Applications of Artificial Intelligence 01/2001; · 1.96 Impact Factor
  • Source
    K.C Tan, L.H Lee, Q.L Zhu, K Ou
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    ABSTRACT: This paper documents our investigation into various heuristic methods to solve the vehicle routing problem with time windows (VRPTW) to near optimal solutions. The objective of the VRPTW is to serve a number of customers within predefined time windows at minimum cost (in terms of distance travelled), without violating the capacity and total trip time constraints for each vehicle. Combinatorial optimisation problems of this kind are non-polynomial-hard (NP-hard) and are best solved by heuristics. The heuristics we are exploring here are mainly third-generation artificial intelligent (AI) algorithms, namely simulated annealing (SA), Tabu search (TS) and genetic algorithm (GA). Based on the original SA theory proposed by Kirkpatrick and the work by Thangiah, we update the cooling scheme and develop a fast and efficient SA heuristic. One of the variants of Glover's TS, strict Tabu, is evaluated and first used for VRPTW, with the help of both recency and frequency measures. Our GA implementation, unlike Thangiah's genetic sectoring heuristic, uses intuitive integer string representation and incorporates several new crossover operations and other advanced techniques such as hybrid hill-climbing and adaptive mutation scheme. We applied each of the heuristics developed to Solomon's 56 VRPTW 100-customer instances, and yielded 18 solutions better than or equivalent to the best solution ever published for these problems. This paper is also among the first to document the implementation of all the three advanced AI methods for VRPTW, together with their comprehensive results.
    Artificial Intelligence in Engineering 02/2000;