Simulated Annealing Approach for the Constrained Shortest Path with Fuzzy Arc and Node Weights

The constrained shortest path problem in a network with fuzzy arc and node weights, abbreviated as the CSP problem, has important applications in modern logistics and supply-chain management, which is known to be NP-hard. In this paper, a fuzzy integer optimization model is established for the CSP problem with the improved decision variables, which will reduce the space complexity. Then the fuzzy objective weight of a directed path is introduced in the objective function, and the penalty function method is adopted to deal with the constraints. Hence, an unconstrained programming is proposed for the CSP problem, which is solved by a simulated annealing algorithm. Finally, the computational results demonstrate the efficiency and feasibility of the algorithm.