The application of the self organizing map to the vehicle routing problem

The Vehicle Routing Problem (VRP) is an NP-hard, combinatorial optimization problem. For NP-hard problems, there is no known polynomial time algorithm to solve these problems. Therefore, for many moderately sized problems, these problems cannot be reliably solved to optimality. This is the case with the VRP, where problem instances with over 100 cities are not easily solved using exact methods. Therefore, the majority of VRP research focuses on heuristics. Artificial Neural Networks (ANNs) are inspired by the functions in the human brain. Researchers have applied ANNs across a wide range of problems with great success. Since solving the VRP relies heavily on heuristics, and ANNs have shown to be effective heuristics for numerous applications, this research seeks to determine the effectiveness of applying ANNs to the VRP The first part of this work investigates the effectiveness of the existing application of ANNs for solving the VRP. An updated Self Organizing Map (SOM) algorithm is proposed for solving the VRP. The proposed SOM incorporates fuzzy logic in order to overcome the need for parameter tuning for each new problem. Experiments are conducted, and the results indicate that the performances of the proposed algorithm exceeds previous results. Further, a comparison is made to other constructive heuristics which makes it clear that the proposed algorithm is a competitive constructive heuristic for solving the VRP. The second part of this research investigates the VRP in the context of the algorithm selection problem. This work utilizes the SOM as a tool for both exploratory data analysis of the diversity of the existing VRP benchmark problem sets, as well as a prediction tool for algorithm selection. 23 VRP problem characteristics are examined across 102 VRP benchmark problems, and a method for automatic extraction of these problem characteristics is proposed. Finally, both an unsupervised and supervised SOM are trained and tested for prediction of algorithm performance. The results indicate that the SOM is capable of distinguishing between algorithm performance based on the 23 problem characteristics extracted from each VRP instance.

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