Performance of a Genetic Algorithm for Solving the Multi-Objective, Multimodal Transportation Network Design Problem

The optimization of infrastructure planning in a multimodal network is defined as a multiobjective network design problem, with accessibility, use of urban space by parking, operating deficit and climate impact as objectives. Decision variables are the location of park and ride facilities, train stations and the frequency of public transport lines. For a case study the Pareto set is estimated by the Non-dominated Sorting Genetic Algorithm (NSGA-II). Such a Pareto set is one specific outcome of the optimization process, for a specific value of the parameters generation size, number of generations and mutation rate and for a specific outcome of the Monte Carlo simulation within NSGA-II. Similar issues exist for many other metaheuristics. However, when applied in practice, a policy maker desires a result that is robust for these unknown aspects of the method. In this paper Pareto sets from various runs of the NSGA-II algorithm are analyzed and compared. To compare the values of the decision variables in the Pareto sets, new methods are necessary, so these are defined and applied. The results show that the differences concerning decision variables are considerably larger than the differences concerning objectives. This indicates that the randomness of the algorithm may be a problem when determining the decisions to be made. Furthermore, it is concluded that variations caused by different parameters are comparable with the variations caused by randomness within the algorithm.