Abstract
A stochastic algorithm for obtaining feasible initial populations to the Vehicle Routing Problem with Time Windows is presented. The theoretical formulation for the Vehicle Routing Problem with Time Windows is explained. The proposed method is primarily divided into a clustering algorithm and a two-phase algorithm. The first step is the application of a modifiedk-means clustering algorithm which is proposed in this paper. The two-phase algorithm evaluates a partial solution to transform it into a feasible individual. The two-phase algorithm consists of a hybridization of four kinds of insertions which interact randomly to obtain feasible individuals. It has been proven that different kinds of insertions impact the diversity among individuals in initial populations, which is crucial for population-based algorithm behavior. A modification to the Hamming distance method is applied to the populations generated for the Vehicle Routing Problem with Time Windows to evaluate their diversity. Experimental tests were performed based on the Solomon benchmarking. Experimental results show that the proposed method facilitates generation of highly diverse populations, which vary according to the type and distribution of the instances.
Highlights
The Routing Problem is one of the most important and widely studied combinatorial problems focused on distribution, logistics, and transportation systems
Experimental testing was performed by evaluating each of the five chosen insertion heuristics separately
A modified k-means algorithm was applied to the Vehicle Routing Problem with Time Windows (VRPTW), where only the capacity constraints were taken into account
Summary
The Routing Problem is one of the most important and widely studied combinatorial problems focused on distribution, logistics, and transportation systems. It is important to note that there is great variation in real problems. Each company has a different problem with specific features that makes it unique. According to its importance and hardness, several variants of the Routing Problem have been proposed to provide approaches for more realistic problems. Variants of the Routing Problem are defined by theoretical mathematical models that focus on general problems with specific features. Due to its high complexity and similarities with real problems, the Vehicle Routing Problem with Time Windows (VRPTW) is one of the most studied models
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