Abstract
The study focuses on a multiple constrained reliable path problem in which travel time reliability and resource constraints are collectively considered. Nonlinear optimization model is developed to model constrained robust shortest path problem. The dual nature of the proposed problem is deduced based on the Lagrangian duality theory. An efficient algorithm based on Lagrangian dual relaxation is designed to solve constrained robust shortest path problem. An extension problem that considers multiple constraints is discussed. Numerical studies indicate that the proposed algorithm is efficient in terms of obtaining the close-to-optimal solutions within reasonable computational times.
Highlights
The constrained robust shortest path problem is more complex than the constrained shortest path problem due to the addition of the standard deviation in the objective function (8) that completely corresponds to a nonadditive function
The constrained shortest path problem is extended from a deterministic network to a stochastic network
The computational complexity of the model significantly exceeds that of a single model due to the nonlinear and nonadditive nature of the objective function and a few complex constraints
Summary
Handler and Zang [3] first developed a Lagrangian relaxation-based method to solve the constrained shortest path problem and obtained near-optimal solutions. Wang et al [9] examined a stochastic constrained shortest path problem and proposed a mixed algorithm based on Lagrangian relaxation to solve it they only focused on obtaining the least expected travel time path and did not consider travel time reliability. The third problem defines the objective function of path as the sum of mean and standard deviation of stochastic travel time, and they are only constructed based on the stochastic parameter that efficiently reduces the computation cost and memory usage. (1) The study first proposes a multiple constrained robust shortest path problem to obtain the mean-standard deviation shortest path subject to a few resource constraints in stochastic network.
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