Robust Solutions to Least-Squares Problems with Uncertain Data
SIAM Journal on Matrix Analysis and Applications
On the robust shortest path problem
Computers and Operations Research
Lectures on modern convex optimization: analysis, algorithms, and engineering applications
Lectures on modern convex optimization: analysis, algorithms, and engineering applications
Interval data minmax regret network optimization problems
Discrete Applied Mathematics
An exact algorithm for the robust shortest path problem with interval data
Computers and Operations Research
Information Sciences: an International Journal
Taylor series approach to fuzzy multiobjective linear fractional programming
Information Sciences: an International Journal
Information Sciences: an International Journal
Shortest paths in stochastic networks with correlated link costs
Computers & Mathematics with Applications
Building confidence-interval-based fuzzy random regression models
IEEE Transactions on Fuzzy Systems
Distance formula and shortest paths for the (n,k)-star graphs
Information Sciences: an International Journal
A method to evaluate routing policy through p minimal paths for stochastic case
Information Sciences: an International Journal
Interactive multiobjective fuzzy random programming through the level set-based probability model
Information Sciences: an International Journal
Computers and Operations Research
Solving shortest path problems with a weight constraint and replenishment arcs
Computers and Operations Research
Expert Systems with Applications: An International Journal
Fuzzy goal programming - A parametric approach
Information Sciences: an International Journal
Confidence regional method of stochastic spanning tree problem
Mathematical and Computer Modelling: An International Journal
Robust solutions of uncertain linear programs
Operations Research Letters
Quality-of-service routing for supporting multimedia applications
IEEE Journal on Selected Areas in Communications
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This paper proposes a model for a robust shortest path problem with random edge costs. The proposed model is formulated as a bicriteria optimization problem to minimize the total cost of the path from a start node to an end node as well as to maximize the range of the confidence interval satisfying the condition that the total cost of any path in the region is less than a target value in terms of robustness. It is not always the case that a solution that simultaneously optimizes all of the objectives exists when the objectives conflict with each other. In this paper, fuzzy goals for both objectives and the aggregation function are introduced in a solution approach that considers the decision maker's preference and the subjectivity of her or his judgment in multicriteria decision making. The fuzzy bicriteria problem is transformed into a constrained shortest path problem. Furthermore, an exact algorithm based on Dijkstra's algorithm and a heuristic algorithm based on the Lagrange relaxation-based algorithm are developed for the constrained shortest path problem.