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 different available trade-offs between objectives for a given section of a route. For this reason, they are increasingly popular in modelling transportation problems with multiple conflicting objectives (e.g., travel time and fuel consumption), such as time-dependent vehicle routing, multi-modal transportation planning, energy-efficient driving, and airport operations. The multigraph MSPP is more complex than the NP-hard simple graph MSPP. Therefore, approximate solution methods are often needed to find a good approximation of the true Pareto front in a given time budget. Evolutionary algorithms have been successfully applied for the simple graph MSPP. However, there has been limited investigation of their applications to the multigraph MSPP. Here, we extend the most popular genetic representations to the multigraph case and compare the achieved solution qualities. Two heuristic initialisation methods are also considered to improve the convergence properties of the algorithms. The comparison is based on a diverse set of problem instances, including both bi-objective and triple objective problems. We found that the metaheuristic approach with heuristic initialisation provides good solutions in shorter running times compared to an exact algorithm. The representations were all found to be competitive. The results are encouraging for future application to the time-constrained multigraph MSPP.
Highlights
There is substantial evidence [1,2,3,4,5] that modelling transportation problems as multigraphs offer benefits with regards to time, cost, environmental impact, and flexibility in multiple practical settings
The multi-objective shortest path problem (MSPP) on multigraphs can be decomposed to two intertwined NPhard problems, the MSPP on simple graphs [7] and the fixed sequence arc selection problem (FSASP) [6]
We introduce a novel heuristic initialisation method based on the idea of discouraging detours, that is applicable to all the representations used
Summary
There is substantial evidence [1,2,3,4,5] that modelling transportation problems as multigraphs offer benefits with regards to time, cost, environmental impact, and flexibility in multiple practical settings. Several different representation methods and genetic operators have been proposed for the simple graph MSPP. The only previous attempts at applying metaheuristics to the multigraph MSPP were in the context of multi-modal transportation [12, 13] Both of these studies used genetic algorithms and extend the direct variable length [14] representation. – Four representations that were originally proposed for simple graph shortest path problems are adapted and extended to the multigraph MSPP. Variants include (1) different crossover operators, (2) direct way of encoding parallel edges for the direct variable length representations, and (3) adapting an existing heuristic initialisation method [9] to priority-based representations. A solution path P1 is said to be Paretooptimal if there is no solution path that is at least as good as P1 according to all k objectives and better according to at least one objective
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
