This paper presents two strategies for solving multicriteria shortest path problems with more than two criteria. Given an undirected graph within vertices, medges, and a set of K weights associated with each edge, we define a path as a sequence of edges from vertex s to vertex t. We want to find the Pareto-optimal set of paths from s to t. The solutions proposed herein are based on cluster computing using the Message-Passing Interface (MPI) extensions to the C programming language. We solve problems with 3 and 4 criteria, using up to 8 processors in parallel and using solutions based on two strategies. The first strategy obtains an approximation of the Pareto-optimal set by solving for supported solutions in bi--criteria sub-problems using a weighted-sum approach, then merging the solutions. The second strategy applies the weighted-sum algorithm directly to the tri-criteria and quad-criteria problems to find the Pareto-optimal set of supported solutions, with each processor using a range of weights.
Sonnier, David L.
"Parallel Algorithms for Multicriteria Shortest Path Problems,"
Journal of the Arkansas Academy of Science: Vol. 60
, Article 20.
Available at: http://scholarworks.uark.edu/jaas/vol60/iss1/20