A Meta-learning Approach for Algorithm Selection for Capacitated Vehicle Routing Problems

Abstract

Optimization is a must for dealing with scarce resources. Vehicle routing is a major concern in an enormous number of fields involving transportation of goods and services. The vehicle routing problem is a widely studied optimization problem for handling this. A variety of heuristic and meta-heuristic algorithms exist for its solution. For a given instance of an optimization problem, it is challenging to select an algorithm that will perform better out of many existing algorithms. This task of selecting an algorithm to solve a given instance of a problem is known as the algorithm selection problem, which is recognized as a learning task. Learning is done using the performance data of algorithms collected from past experiments, hence it is termed meta-learning. In this chapter, a meta-learning based technique is used for the selection of the best heuristic algorithm for solving the capacitated vehicle routing problem (CVRP). The meta-learning techniques learn a relation between the problem’s features and the algorithm’s performance. Based on the characteristics of the problem, this model can then be used to predict an effective algorithm for a new case. A meta-learning experiment is performed on meta-data prepared for 85 CVRP benchmark instances. Each instance is represented by 23 problem-specific features. The solution cost of two popular heuristic algorithms, namely the Parallel Clarke and Wright (1964) Saving algorithm and the Gillet and Miller (1974) Sweep algorithm, is evaluated for this purpose. A better performing algorithm name is chosen as a meta-label in this instance. Binary classification is taken up to train the meta-learning model. Five classifiers –naive Bayes, multi-layer perceptron, stochastic gradient descent, J48, and random forest – are trained on Weka 3.8.4 software. The accuracy of all classifiers except multi-layer perceptron is observed to be higher than the baseline value. Experimental results show that meta-learning approaches are quite effective for algorithm selection.