A Comparison of Genetic Representations and Initialisation Methods for the Multi-objective Shortest Path Problem on Multigraphs

Abstract This paper compares different solution approaches for the multi-objective shortest path problem (MSPP) on multigraphs. Multigraphs as a modelling tool are able to capture available trade-offs between objectives given section of route. For this reason, they increasingly popular in transportation problems with multiple conflicting (e.g., travel time and fuel consumption), such time-dependent vehicle routing, multi-modal planning, energy-efficient driving, airport operations. The multigraph MSPP is more complex than NP-hard simple graph MSPP. Therefore, approximate methods often needed find good approximation true Pareto front budget. Evolutionary algorithms have been successfully applied However, there has limited investigation their applications Here, we extend most genetic representations case compare achieved qualities. Two heuristic initialisation also considered improve convergence properties algorithms. comparison based diverse set instances, including both bi-objective triple objective problems. We found that metaheuristic approach provides solutions shorter running times compared an exact algorithm. were all be competitive. results encouraging future application time-constrained