An Hybrid NSGA-II Algorithm for the Bi-objective Mobile Mammography Unit Routing Problem.

This work deals with the Mobile Mammography Unit Routing Problem in Brazil. The problem is a Multi-depot Open Vehicle Routing Problem variant. In this problem, there are a fixed number of depots, each with a limited number of Mobile Mammography Units (MMUs). Each MMU has a known screening capacity and a set of candidate cities it can serve with known demands for screening. The objective is to define the cities visiting order for each MMU, maximizing the served screening demand and minimizing the total travel distance. We introduce a mathematical programming formulation and two algorithms based on Non-dominated Sorting Genetic Algorithm II (NSGA-II). They differ from each other by the use of a local search. One version has a Local Search as a mutation operator, and the other does not. Both algorithms were tested on benchmark based on real data from Minas Gerais state, Brazil. We used the hypervolume metric to analyze the performance of the proposed algorithms considering different scenarios. The results indicate that using multiple crossover operators and adding a local search as a mutation operator to the algorithm brings better results.