The continuous pollution routing problem
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 con...
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| Vydáno v: | Applied mathematics and computation Ročník 387; s. 125072 |
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| Hlavní autoři: | , , , , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
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Elsevier Inc
15.12.2020
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| ISSN: | 0096-3003 |
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| 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. |
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| AbstractList | 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. |
| ArticleNumber | 125072 |
| Author | Zuo, Xiaorong Huang, Jiaoying Xiao, Yiyong Konak, Abdullah Xu, Yuchun |
| Author_xml | – sequence: 1 givenname: Yiyong surname: Xiao fullname: Xiao, Yiyong email: xiaoyiyong@buaa.edu.cn organization: School of Reliability and System Engineering, Beihang University, Beijing 100191, China – sequence: 2 givenname: Xiaorong surname: Zuo fullname: Zuo, Xiaorong email: zuoxiaorong710@163.com organization: School of Reliability and System Engineering, Beihang University, Beijing 100191, China – sequence: 3 givenname: Jiaoying surname: Huang fullname: Huang, Jiaoying email: huangjy@buaa.edu.cn organization: School of Reliability and System Engineering, Beihang University, Beijing 100191, China – sequence: 4 givenname: Abdullah surname: Konak fullname: Konak, Abdullah email: auk3@psu.edu organization: Information Sciences and Technology, Penn State Berks, Tulpehocken Road, P.O. Box 7009, Reading, PA 19610-6009, United States – sequence: 5 givenname: Yuchun surname: Xu fullname: Xu, Yuchun email: y.xu16@Aston.ac.uk organization: School of Engineering & Applied Science, Aston University, Birmingham B4 7ET, United Kingdom |
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