Comparison of Genetic Operators for the Multiobjective Pickup and Delivery Problem

The pickup and delivery problem is a pertinent problem in our interconnected world. Being able to move goods and people efficiently can lead to decreases in costs, emissions, and time. In this work, we create a genetic algorithm to solve the multiobjective capacitated pickup and delivery problem, adapting commonly used benchmarks. The objective is to minimize total distance travelled and the number of vehicles utilized. Based on NSGA-II, we explore how different inter-route and intraroute mutations affect the final solution. We introduce 6 inter-route operations and 16 intraroute operations and calculate the hypervolume measured to directly compare their impact. We also introduce two different crossover operators that are specialized for this problem. Our methodology was able to find optimal results in 23% of the instances in the first benchmark and in most other instances, it was able to generate a Pareto front within at most one vehicle and +20% of the best-known distance. With multiple solutions, it allows users to choose the routes that best suit their needs.