An efficient two-phase exact algorithm for the automated truck freight transportation problem

https://doi.org/10.1016/j.cie.2017.04.030Get rights and content

Highlights

  • An automated truck freight transportation planning problem via lane reservation is studied.

  • Improved formulation is provided and several special cases of the problem are investigated.

  • An efficient two-phase exact algorithm based on problem properties is developed.

  • Computational results confirm the efficiency of the proposed model and algorithm.

Abstract

A recent study has developed an integer linear program and an exact algorithm for the automated truck transportation freight problem with lane reservation. However, due to its NP-hard nature, their proposed method becomes difficult to solve large-size problems within acceptable time. In this paper, we firstly present an improved integer linear program by adding valid inequalities and identify that its several special cases are classical combinatorial optimization problems. Based on analyzed properties, a new efficient two-phase exact algorithm is developed. Computational results on benchmark and new larger-size instances with up to 700 nodes and 55 tasks show that the new algorithm outperforms very favorably the state-of-the-art one.

Introduction

Efficient shipments of cargos has attracted much attention and considerable freight transportation planning problems have been investigated extensively over the past decades (Goksal et al., 2013, Prins, 2004, Shaabani and Kamalabadi, 2016). However, increasing travel demand results in increasingly severe congestion, which causes many problems in transportation, such as low efficiency, unpredictable transport time, traffic accidents, and fuel waste. These problems increasingly prevent the freight transportation from being operated in an efficient, reliable and safe fashion (Fang, Chu, Mammar, & Che, 2013). Introducing automated driving for trucks would be a promising solution to cope with such challenge, as automated trucks could provide remarkable advantages such as high safety and efficiency, and lower fuel consumption.

Unlike manually driven trucks, automated ones must have the ability of detecting possible dangers and responding to them correctly and promptly. Dedicated truck lanes would be ideal in this sense. Since constructing new network dedicated to automated trucks may be infeasible due to the high costs and limited geographic space, converting existing general-purpose (GP) lanes in the existing network to dedicated ones is an effective alternative. But due to the exclusive use of reserved lanes by automated trucks, the available lanes in the network for GP vehicles are reduced, and negative impact, such as the increase in travel time of GP vehicles, will be generated on the adjacent lanes. It is necessary to well decide appropriate lanes to be reserved to achieve the safe and time-guaranteed automated truck transportation, while minimizing the negative traffic impact. Such an optimization problem is called the automated truck transportation problem with lane reservation (ATP) (Fang et al., 2013). We note that there have also been studies investigating lane reservation for other applications, such as large sport events, hazardous material transportation, bus transit (Che et al., 2015, Fang et al., 2014, Fang et al., 2015, Fang et al., 2012, Wu et al., 2013, Wu et al., 2016, Wu et al., 2015, Wu et al., 2009, Zhou et al., 2013).

Fang et al. (2013) have formulated an integer linear program (ILP) and developed an exact cut-and-solve algorithm for the ATP. However, due to the NP-hardness of the ATP, their proposed methods become difficult to solve large-size problems within acceptable computational time. In this paper, we first provide an improved ILP by adding valid inequalities. Then, we identify that several special cases of the ATP are classical combinatorial optimization problems. Based on the analyzed properties, a new efficient two-phase exact algorithm is developed. Computational results on 120 benchmark and 210 new larger-size instances with up to 700 nodes and 55 tasks confirm the effectiveness of the proposed algorithm.

The remainder of the paper is organized as follows. Section 2, recalls the problem description and provides the improved ILP. In Section 3, we derive several optimal properties of the ATP. Based on them, a new efficient exact algorithm is presented in Section 4. Section 5 reports the computational results. Section 6 concludes this study.

Section snippets

Problem description and formulation

The ATP considered in this study has been addressed by Fang et al. (2013). For the sake of self-consistency, the problem description is first recalled as follows.

The ATP can be defined on a transportation network that can be represented by a directed graph G(N,A) with a node set N and an arc set A. A node (resp. an arc) represents a road intersection (resp. a road segment). Given a set of automated truck transportation tasks to be accomplished and their corresponding origin-destination (OD)

Property analysis for the ATP

In this section, we first investigate several special cases for the ATP. Note that these special cases correspond to classical combinatorial optimization problems and can be tackled using existing techniques. The potential benefits are that if an instance is recognized as one special case of them, then it can be efficiently solved accordingly. Then, the ATP in the general case is analyzed.

Two-phase exact algorithm for the ATP

For an ATP in general case, Fang et al. (2013) proposed a cut-and-solve algorithm, which can solve problem instances with up to 150 nodes in the network and 30 tasks within 18,000 CPU seconds. In this paper, a new efficient two-phase exact algorithm is developed to efficiently solve the larger-size ATP. The algorithm is composed of two major phases. In the first phase, all feasible paths respecting the travel deadline constraint are enumerated for each task kK. An optimal lane reservation

Computational experiments

In this section, we conduct numerical computational experiments to show the performance of the proposed algorithm. Our algorithm is coded in C++ language and combined with Yen’s K-shortest loopless path algorithm (Yen, 1971) and CPLEX (12.6) IP solver with default settings. All the experiments are done on a PC with 2.5 GHz and 2.95 GB RAM with windows 7 system.

The performance of the proposed model and algorithm is evaluated on 74 groups of instances with five instances each group, including 160

Conclusion

In this paper, we have revisited the automated truck transportation problem with lane reservation proposed by Fang et al. (2013). For the problem, we first propose valid inequalities for the integer linear program proposed by Fang et al. (2013). Computational comparison results indicate that these valid inequalities are effective in saving computational time. Furthermore, we have investigated several special cases of the considered problem, which can be identified to be classical combinatorial

Acknowledgements

This work was supported in part by the National Natural Science Foundation of China under Grants 71571061 and 71471145, in part by the Natural Science Foundation of Fujian Province, China under Grant 2015J05137 and by the Scientific Research Foundation of Fuzhou University under Grants GXRC201709, 14SKQ05.

References (20)

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