VRPTWVehicle Routing Problem with Time Windows
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The VRPTW can be formally described as a directed graph G = (V, E) with a set V = {0,1,2, .
According to this description, the integer linear programming model of the VRPTW [2] can be formulated as shown below.
This algorithm is applied specifically to the VRPTW.
Algorithm 1: Clustering algorithm applied to VRPTW.
The input for this algorithm is a semifeasible solution, where capacity constraints of the VRPTW are met.
The time constraints are known for being the hardest constraints in the VRPTW, because each customer has a different and well-defined time window during which it must be served by a single vehicle.
Once all the customers have been inserted, it is said that a feasible solution to the VRPTW has been obtained.
Methodology for Hamming Distance Calculation for the VRPTW
The procedure explained in Section 5 was modified in this research, according to the solution structure for the VRPTW of the model shown in (1)-(11).
Based on the features of individuals, a methodology for applying the Hamming distance to VRPTW was developed.
The experimental tests were performed to prove the efficacy of the clustering algorithm and the proposed two-phase algorithm to obtain feasible solutions to VRPTW.
In this paper, a methodology to calculate the Hamming distance for solutions to the model of VRPTW was described and is shown in (1)-(11).