scholarly journals Multi-objective and multi-constrained non-additive shortest path problems

2011 ◽  
Vol 38 (3) ◽  
pp. 605-616 ◽  
Author(s):  
Line Blander Reinhardt ◽  
David Pisinger
Keyword(s):  
Shortest Path ◽  
Shortest Path Problems ◽  
Multi Objective

scholarly journals Extensions of labeling algorithms for multi-objective uncertain shortest path problems

Networks ◽  
2018 ◽  
Vol 72 (1) ◽  
pp. 84-127 ◽  
Author(s):  
Andrea Raith ◽  
Marie Schmidt ◽  
Anita Schöbel ◽  
Lisa Thom
Keyword(s):  
Shortest Path ◽  
Shortest Path Problems ◽  
Multi Objective ◽  
Labeling Algorithms

Martins' algorithm revisited for multi-objective shortest path problems with a MaxMin cost function

4OR ◽  
2006 ◽  
Vol 4 (1) ◽  
pp. 47-59 ◽  
Author(s):  
Xavier Gandibleux ◽  
Frédéric Beugnies ◽  
Sabine Randriamasy
Keyword(s):  
Cost Function ◽  
Shortest Path ◽  
Shortest Path Problems ◽  
Multi Objective

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

2021 ◽  
Vol 2 (3) ◽  
Author(s):  
Lilla Beke ◽  
Michal Weiszer ◽  
Jun Chen
Keyword(s):  
Shortest Path ◽  
Time Budget ◽  
Exact Algorithm ◽  
Simple Graph ◽  
Shortest Path Problem ◽  
Future Application ◽  
Multi Objective ◽  
Trade Offs ◽  
Conflicting Objectives ◽  
Problem Instances

AbstractThis 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.

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