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Outline

Title
Abstract
Figures
Introduction
Literature Review
First Stage of the Proposed Solution Method
Shaking Method
Computational Results
Computational Analysis on PTSPR Instances
Sensitivity Analysis
Conclusions
References
All Topics
Computer Science
Algorithms and Data Structures

The Pollution Traveling Salesman Problem with Refueling

Profile image of Angelo SifalerasAngelo SifalerasProfile image of Panagiotis KarakostasPanagiotis Karakostas

2024, Computers & Operations Research

https://doi.org/10.1016/J.COR.2024.106661
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Abstract

This study presents the Pollution Traveling Salesman Problem with Refueling, a novel optimization problem which integrates two recently proposed variants of the Traveling Salesman Problem: the Pollution Traveling Salesman Problem and the Traveling Salesman Problem with Refueling. The proposed problem captures the operational dynamics of a real-world routing scenario involving a single vehicle originating from a central depot and delivering products to end customers. When considering the vehicle’s fuel tank capacity and fuel consumption during the routing process, the need to visit fuel stations for refueling arises. To address this complex problem, a new mixed integer linear programming model was developed, and the Gurobi solver was employed to solve smaller instances. For the effective resolution of larger practical problem cases, a two-stage double adaptive general variable neighborhood search method was proposed. The proposed methodology exhibits comparable efficiency to a commercial solver, demonstrating notably low execution time requirements. To further assess its performance, a comparative study was conducted on TSPLib instances. In comparison to various solution approaches documented in the open literature, encompassing both VNS-based and alternative methods, our proposed approach consistently yields highly competitive results within low execution times.

Figures (24)
Table 2: Vehicle-based parameters
Table 2: Vehicle-based parameters
Table 3: Remaining model parameters
Table 3: Remaining model parameters
ere, we provide the necessary mathematical expressions to simplify the function which
ere, we provide the necessary mathematical expressions to simplify the function which
Figure 1: Proposed solution approach algorithmic approach is illustrated in Figure 1. che optimization of the route, while the second focuses on fuel-based decisions. The overal. The Nearest-Neighbor Heuristic (NNH) (Flood, 1956) is used to build an initial feasible
Figure 1: Proposed solution approach algorithmic approach is illustrated in Figure 1. che optimization of the route, while the second focuses on fuel-based decisions. The overal. The Nearest-Neighbor Heuristic (NNH) (Flood, 1956) is used to build an initial feasible
To provide clarity, a PTSPR solution is denoted as S = {RP, RS,SL}, where RP represents the speed levels for traversing the nodes within the integrated route. Specifically, with r
To provide clarity, a PTSPR solution is denoted as S = {RP, RS,SL}, where RP represents the speed levels for traversing the nodes within the integrated route. Specifically, with r
Figure 9: Contribution of local search operators und those derived from each operator or combination, considering all generated problen
Figure 9: Contribution of local search operators und those derived from each operator or combination, considering all generated problen
Table 5: TSP objective values due to different iteration limits of DB operator the improvement phase in this work is differentiated from the one considered in the work
Table 5: TSP objective values due to different iteration limits of DB operator the improvement phase in this work is differentiated from the one considered in the work
Table 6: Best found objective values using different shaking and search strategies the most efficient combinations of search and shaking strategies.
Table 6: Best found objective values using different shaking and search strategies the most efficient combinations of search and shaking strategies.
Table 7: PTSPR objective values method required 40.05s for the solution of the largest instance, while the second required it a valuable tool in addressing the computational complexities of the optimization problem
Table 7: PTSPR objective values method required 40.05s for the solution of the largest instance, while the second required it a valuable tool in addressing the computational complexities of the optimization problem
Table 8: Impact of execution time adjustments Table 9 provides the total and individual costs of the best-found solution for each PTSPR.
Table 8: Impact of execution time adjustments Table 9 provides the total and individual costs of the best-found solution for each PTSPR.
Table 9: Total and individual costs of the best-found solution 5.5. Sensitivity analysis The dimensions of the fuel tank and the refueling policy are recognized as two pivotal pa-
Table 9: Total and individual costs of the best-found solution 5.5. Sensitivity analysis The dimensions of the fuel tank and the refueling policy are recognized as two pivotal pa-
Table 10: Average values of the best-found total costs (€) for all PTSPR instances Table 11: Average values of the best-found refueling costs (€) for all PTSPR instances different combinations of fuel tank sizes and refueling policies.
Table 10: Average values of the best-found total costs (€) for all PTSPR instances Table 11: Average values of the best-found refueling costs (€) for all PTSPR instances different combinations of fuel tank sizes and refueling policies.
Table 12: Average values of the best-found emissions taxation costs (€) for all PTSPR instances
Table 12: Average values of the best-found emissions taxation costs (€) for all PTSPR instances
Table 13: Average values of the best-found driver wages costs (€) for all PTSPR instances Initially, it is noteworthy that the cost of refueling significantly contributes to the overall
Table 13: Average values of the best-found driver wages costs (€) for all PTSPR instances Initially, it is noteworthy that the cost of refueling significantly contributes to the overall
Table 14: Number of intermediate refueling stops for each problem case
Table 14: Number of intermediate refueling stops for each problem case
Table 15: Total refueling quantities for each problem case (in liters) tive scenarios. By investigating the impact of different fuel tank sizes and refueling policies
Table 15: Total refueling quantities for each problem case (in liters) tive scenarios. By investigating the impact of different fuel tank sizes and refueling policies
Table 16: Comparison between the proposed method and other solution approaches correspond to the best-found values.
Table 16: Comparison between the proposed method and other solution approaches correspond to the best-found values.
Table 16 — continued from previous page
Table 16 — continued from previous page

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