Xiao, Yiyong, Zuo, Xiaorong, Huang, Jiaoying, Konak, Abdullah and Xu, Yuchun (2020). The continuous pollution routing problem. Applied Mathematics and Computation, 387 ,
Abstract
In this paper, we presented an ε-accurate approach to conduct a continuous optimization on the pollution routing problem (PRP). First, we developed an ε-accurate inner polyhedral approximation method for the nonlinear relation between the travel time and travel speed. The approximation error was controlled within the limit of a given parameter ε, which could be as low as 0.01% in our experiments. Second, we developed two ε-accurate methods for the nonlinear fuel consumption rate (FCR) function of a fossil fuel-powered vehicle while ensuring the approximation error to be within the same parameter ε. Based on these linearization methods, we proposed an ε-accurate mathematical linear programming model for the continuous PRP (ε-CPRP for short), in which decision variables such as driving speeds, travel times, arrival/departure/waiting times, vehicle loads, and FCRs were all optimized concurrently on their continuous domains. A theoretical analysis is provided to confirm that the solutions of ε-CPRP are feasible and controlled within the predefined limit. The proposed ε-CPRP model is rigorously tested on well-known benchmark PRP instances in the literature, and has solved PRP instances optimally with up to 25 customers within reasonable CPU times. New optimal solutions of many PRP instances were reported for the first time in the experiments.
Publication DOI: | https://doi.org/10.1016/j.amc.2020.125072 |
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Divisions: | College of Engineering & Physical Sciences > School of Engineering and Technology > Mechanical, Biomedical & Design |
Funding Information: | This work is partly supported by the National Natural Science Foundation of China under Grant Nos. 71871003 , 71871003 , 71971009 , and 71971013 . |
Additional Information: | © 2020, Elsevier. Licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International http://creativecommons.org/licenses/by-nc-nd/4.0/ |
Uncontrolled Keywords: | Continuous optimization,Convex programming,Emission reduction,Vehicle routing problem,Computational Mathematics,Applied Mathematics |
Publication ISSN: | 1873-5649 |
Last Modified: | 15 Aug 2024 07:36 |
Date Deposited: | 17 Feb 2020 16:14 |
Full Text Link: | |
Related URLs: |
http://www.scop ... tnerID=8YFLogxK
(Scopus URL) https://www.sci ... 0412?via%3Dihub (Publisher URL) |
PURE Output Type: | Article |
Published Date: | 2020-12-15 |
Published Online Date: | 2020-02-05 |
Accepted Date: | 2020-01-19 |
Authors: |
Xiao, Yiyong
Zuo, Xiaorong Huang, Jiaoying Konak, Abdullah Xu, Yuchun ( ![]() |
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