RT - Journal Article
T1 - The Lagrangian Relaxation Method for the Shortest Path Problem Considering Transportation Plans and Budgetary Constraint
JF - JAMLU
YR - 2019
JO - JAMLU
VO - 16
IS - 2
UR - http://jamlu.liau.ac.ir/article-1-1631-en.html
SP - 39
EP - 57
K1 - Transportation Network
K1 - Constrained Shortest Path Problem
K1 - Lagrangian Dual Method
K1 - Sub-gradient Method.
AB - In this paper, a constrained shortest path problem (CSP) in a network is investigated, in which some special plans for each link with corresponding pre-determined costs as well as reduction values in the link travel time are considered. The purpose is to find a path and selecting the best plans on its links, to improve the travel time as most as possible, while the costs of conducting plans do not exceed the available budget. Using the Lagrangian relaxation approach, some constraints of the problem are relaxed and the Lagrangian dual problem is decomposed into two smaller sub-problems. Then, by applying the sub-gradient algorithm, a near optimal solution is determined for the original problem. Finally, by considering the proposed model on a small-sized network and on Khorasan state network, solutions for different origin-destination pairs with different parameters are determined.
LA eng
UL http://jamlu.liau.ac.ir/article-1-1631-en.html
M3
ER -