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Table 2. Model decision variables.

Table 2 Model decision variables.

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Table 1. Model sets. For the readers clarity sake, the mathematical formulation of the problem is presented in this section. Model notations are summarized in Tables 1, 2 and 3.
Table 1. Model sets. For the readers clarity sake, the mathematical formulation of the problem is presented in this section. Model notations are summarized in Tables 1, 2 and 3.
Table 3. Model parameters. The following utilization of formulas simplifies the fuel consumption compo- nents of the objective function: \ = ai Vk = [mV TER? a=T+gCRsin d+ gCRcos@ and 8, = 0.5CADpFSA,.
Table 3. Model parameters. The following utilization of formulas simplifies the fuel consumption compo- nents of the objective function: \ = ai Vk = [mV TER? a=T+gCRsin d+ gCRcos@ and 8, = 0.5CADpFSA,.
Adaptive GVNS methods for pollution location inventory routing problems According to the neighborhood change step, there are different VND schemes. Two of the most well-known VND schemes are the cyclic VND (cVND) and the pipe V hood in the expl occurred be ment number the se ioned of the D (pVND). In the first one, the search continuous in the next neighbor- t independently of the improvement criterion, while in the pVND oration continuous in the same neighborhood while an improvement is [5]. In this work both cVND and pVND are used. Moreover, it should that the parameter [j,¢, in both VND pseudo-codes denotes the used neighborhood structures. The pseudo-codes of the proposed VND schemes are given in Algorithms 2 and 3.
Adaptive GVNS methods for pollution location inventory routing problems According to the neighborhood change step, there are different VND schemes. Two of the most well-known VND schemes are the cyclic VND (cVND) and the pipe V hood in the expl occurred be ment number the se ioned of the D (pVND). In the first one, the search continuous in the next neighbor- t independently of the improvement criterion, while in the pVND oration continuous in the same neighborhood while an improvement is [5]. In this work both cVND and pVND are used. Moreover, it should that the parameter [j,¢, in both VND pseudo-codes denotes the used neighborhood structures. The pseudo-codes of the proposed VND schemes are given in Algorithms 2 and 3.
The local search operators are applied with an adaptive search strategy, which combines the first and best improvement search strategies [8]. More specifically, if the number of customers in a problem instance is more than 90, the fist improvement search strategy is applied, otherwise the algorithm explores the neighborhoods with the best improvement strategy.
The local search operators are applied with an adaptive search strategy, which combines the first and best improvement search strategies [8]. More specifically, if the number of customers in a problem instance is more than 90, the fist improvement search strategy is applied, otherwise the algorithm explores the neighborhoods with the best improvement strategy.
provement step [5,10]. Based on the two proposed VND methods, two GVNS schemes are shaped and provided in the following pseudo-codes.
provement step [5,10]. Based on the two proposed VND methods, two GVNS schemes are shaped and provided in the following pseudo-codes.
Adaptive mechanism. The order of the neighborhood structures is a cru- cial component for the successful performance of a VNS-based algorithm (4, 6]. Consequently, it is important to employ an intelligent mechanism for the re-ordering of the neighborhood structures. According to the literature, some adaptive variants of the VNS have been proposed for that case. Todosijevic et al. [12] proposed an Adaptive GVNS in which a re-ordering of the neighborhoods
Adaptive mechanism. The order of the neighborhood structures is a cru- cial component for the successful performance of a VNS-based algorithm (4, 6]. Consequently, it is important to employ an intelligent mechanism for the re-ordering of the neighborhood structures. According to the literature, some adaptive variants of the VNS have been proposed for that case. Todosijevic et al. [12] proposed an Adaptive GVNS in which a re-ordering of the neighborhoods
Table 4. Computational results of the proposed methods
Table 4. Computational results of the proposed methods
Fig.1. AGVNS1,vnp vs BVNS on 20 PLIRP instances
Fig.1. AGVNS1,vnp vs BVNS on 20 PLIRP instances
Table 5. Best found values of the proposed methods
Table 5. Best found values of the proposed methods
Table 6. BKS vs Best found values of the proposed methods
Table 6. BKS vs Best found values of the proposed methods
Related topics:
Vehicle Routing ProblemsVariable Neighborhood SearchIntelligent Optimization
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