Markov and Markov-regenerative PERT networks
Operations Research
A computational study of efficient shortest path algorithms
Computers and Operations Research
ARC reduction and path preference in stochastic acyclic networks
Management Science
Shortest path algorithms: a computational study with the C programming language
Computers and Operations Research
Network flows: theory, algorithms, and applications
Network flows: theory, algorithms, and applications
Optimal paths in graphs with stochastic or multidimensional weights
Communications of the ACM
Multi-objective and multi-constrained non-additive shortest path problems
Computers and Operations Research
Algebraic methods for stochastic minimum cut and maximum flow problems
INOC'11 Proceedings of the 5th international conference on Network optimization
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In the context of stochastic networks, we study the problem of finding a path P that combines in a reasonable way the mean m(P) and variance v(P) of its length. Specifically we study a separable objective function that combines these two path measures: namely, z(P)=f(m(P))+g(v(P)), where f is an increasing convex function and g is an increasing concave function. A new type of dominance (e-dominance), stronger than the standard form of dominance, is then introduced, and it is shown to satisfy a certain form of Bellman's optimality principle. This means that it is possible to modify existing label-setting and label-correcting methods by using e-dominance, and without sacrificing optimality. Computational experience with these enhanced labeling algorithms has been promising. Test results for a variety of sample problems show that the e-dominance criterion can often significantly reduce the number of nondominated path vectors, compared to the standard dominance criterion. We observe a consequent reduction in both computation time and storage requirements.