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Technical Brief

Computation of Lower Bounds for a Multiple Depot, Multiple Vehicle Routing Problem With Motion Constraints

[+] Author and Article Information
Satyanarayana G. Manyam

Department of Mechanical Engineering,
Texas A&M University,
College Station, TX 77843
e-mail: msngupta@gmail.com

Sivakumar Rathinam

Assistant Professor
Department of Mechanical Engineering,
Texas A&M University,
College Station, TX 77843
e-mail: srathinam@tamu.edu

Swaroop Darbha

Professor
Department of Mechanical Engineering,
Texas A&M University,
College Station, TX 77843
e-mail: dswaroop@tamu.edu

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received March 6, 2014; final manuscript received April 5, 2015; published online May 28, 2015. Assoc. Editor: Junmin Wang.

J. Dyn. Sys., Meas., Control 137(9), 094501 (Sep 01, 2015) (5 pages) Paper No: DS-14-1101; doi: 10.1115/1.4030354 History: Received March 06, 2014; Revised April 05, 2015; Online May 28, 2015

This paper considers the problem of planning paths for a collection of identical vehicles visiting a given set of targets, such that the total lengths of their paths are minimum. Each vehicle starts at a specified location (called a depot) and it is required that each target to be on the path of at least one vehicle. The path of every vehicle must satisfy the motion constraints of every vehicle. In this paper, we develop a method to compute lower bound to the minimum total path lengths by relaxing some of the constraints and posing it as a standard multiple traveling salesmen problem (MTSP). A lower bound is often important to ascertain suboptimality bounds for heuristics and for developing stopping criterion for algorithms computing an optimal solution. Simulation results are presented to show that the proposed method can be used to improve the lower bounds of instances with four vehicles and 40 targets by approximately 39%.

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Copyright © 2015 by ASME
Topics: Vehicles , Computation
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References

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Figures

Grahic Jump Location
Fig. 1

Dual solution versus heuristic solution with 12 targets

Grahic Jump Location
Fig. 2

Dual solution versus heuristic solution with 20 targets

Grahic Jump Location
Fig. 3

Dual solution versus heuristic solution with 20 targets

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