Loo Hay Lee

Heuristic methods for vehicle routing problem with time windows

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 Glovers TS, strict Tabu, is evaluated and first used for VRPTW, with the help of both recency and frequency measures. Our GA implementation, unlike Thangiahs 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 Solomons 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.

Stochastic Simulation Optimization: An Optimal Computing Budget Allocation

With the advance of new computing technology, simulation is becoming very popular for designing large, complex and stochastic engineering systems, since closed-form analytical solutions generally do not exist for such problems. However, the added flexibility of simulation often creates models that are computationally intractable. Moreover, to obtain a sound statistical estimate at a specified level of confidence, a large number of simulation runs (or replications) is usually required for each design alternative. If the number of design alternatives is large, the total simulation cost can be very expensive. Stochastic Simulation Optimization addresses the pertinent efficiency issue via smart allocation of computing resource in the simulation experiments for optimization, and aims to provide academic researchers and industrial practitioners with a comprehensive coverage of OCBA approach for stochastic simulation optimization. Starting with an intuitive explanation of computing budget allocation and a discussion of its impact on optimization performance, a series of OCBA approaches developed for various problems are then presented, from the selection of the best design to optimization with multiple objectives. Finally, this book discusses the potential extension of OCBA notion to different applications such as data envelopment analysis, experiments of design and rare-event simulation.

A multiobjective evolutionary algorithm for solving vehicle routing problem with time windows

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 Paretos 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 Solomons 56 VRPTW 100-customer instances, which yields 20 routing solutions better than or competitive as compared to the best solutions published in literature.

Efficient Simulation Budget Allocation for Selecting an Optimal Subset

We consider a class of the subset selection problem in ranking and selection. The objective is to identify the top m out of k designs based on simulated output. Traditional procedures are conservative and inefficient. Using the optimal computing budget allocation framework, we formulate the problem as that of maximizing the probability of correctly selecting all of the top-m designs subject to a constraint on the total number of samples available. For an approximation of this correct selection probability, we derive an asymptotically optimal allocation and propose an easy-to-implement heuristic sequential allocation procedure. Numerical experiments indicate that the resulting allocations are superior to other methods in the literature that we tested, and the relative efficiency increases for larger problems. In addition, preliminary numerical results indicate that the proposed new procedure has the potential to enhance computational efficiency for simulation optimization.

A hybrid multi-objective evolutionary algorithm for solving truck and trailer vehicle routing problems

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.

An optimization model for storage yard management in transshipment hubs

This paper studies a yard storage allocation problem in a transshipment hub where there is a great number of loading and unloading activities. The primary challenge is to efficiently shift containers between the vessels and the storage area so that reshuffling and traffic congestion is minimized. In particular, to reduce reshuffling, a consignment strategy is used. This strategy groups unloaded containers according to their destination vessel. To reduce traffic congestion, a new workload balancing protocol is proposed. A mixed integer-programming model is then formulated to determine the minimum number of yard cranes to deploy and the location where unloaded containers should be stored. The model is solved using CPLEX. Due to the size and complexity of this model two heuristics are also developed. The first is a sequential method while the second is a column generation method. A bound is developed that allows the quality of the solution to be judged. Lastly, a numerical investigation is provided and demonstrates that the algorithms perform adequately on most cases considered.

A decision model for berth allocation under uncertainty

This paper studies the berth allocation problem (BAP) under uncertain arrival time or operation time of vessels. It does not only concern the proactive strategy to develop an initial schedule that incorporates a degree of anticipation of uncertainty during the schedules execution, but also studies the reactive recovery strategy which adjusts the initial schedule to handle realistic scenarios with minimum penalty cost of deviating from the initial schedule. A two-stage decision model is developed for the BAP under uncertainties. Moreover, a meta-heuristic approach is proposed for solving the above problem in large-scale realistic environments. Numerical experiments are conducted to validate the effectiveness and efficiency of the proposed method.

A yard storage strategy for minimizing traffic congestion in a marine container transshipment hub

This paper studies a storage yard management problem in a transshipment hub where the loading and unloading activities are both heavy and concentrated. In order to reduce the number of reshuffles, which helps to reduce the vessel turnaround time, the port operator uses the consignment strategy to group export and transshipment containers according to their destination vessel. To reduce the potential traffic congestion of prime movers, a high–low workload balancing protocol is used. A mixed integer programming model is formulated to determine the storage locations of incoming containers, the number of incoming containers and the smallest number of yard cranes to deploy in each shift. An iterative improvement method is developed to solve the problem, in which a tabu search based heuristic algorithm is used to generate an initial yard template, and then the generated yard template is improved by an improvement algorithm iteratively until an optimal or a satisfactory solution is obtained. Experiment results show that the proposed method can generate excellent results within a reasonable time, even for the extreme cases.

Artificial intelligence heuristics in solving vehicle routing problems with time window constraints

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 Solomons 56 VRPTW with 100-customer instances, and yield 23 solutions competitive to the best solutions published in literature according to the authors’ best knowledge.

Multi-objective simulation-based evolutionary algorithm for an aircraft spare parts allocation problem

Simulation optimization has received considerable attention from both simulation researchers and practitioners. In this study, we develop a solution framework which integrates multi-objective evolutionary algorithm (MOEA) with multi-objective computing budget allocation (MOCBA) method for the multi-objective simulation optimization problem. We apply it on a multi-objective aircraft spare parts allocation problem to find a set of non-dominated solutions. The problem has three features: huge search space, multi-objective, and high variability. To address these difficulties, the solution framework employs simulation to estimate the performance, MOEA to search for the more promising designs, and MOCBA algorithm to identify the non-dominated designs and efficiently allocate the simulation budget. Some computational experiments are carried out to test the effectiveness and performance of the proposed solution framework.