Robust Optimization Strategy for the Shortest Path Problem under Uncertain Link Travel Cost Distribution

Abstract

This article employs a robust optimization approach for the shortest path problem where travel cost is uncertain and exact information on the distribution function is unavailable. We show that under such conditions the robust shortest path problem can be formulated as a binary nonlinear integer program, which can then be reformulated as a mixed integer conic quadratic program. Based on this reformulation, we present an outer approximation algorithm as a solution algorithm which is shown to be highly efficient for this class of programs. Numerical experiments conducted on small to large networks further compare the robust optimization‐based strategy to the classical deterministic shortest path in terms of the uncertainty in the network.

Parametric search for the bi-attribute concave shortest path problem

“…An important application of the BC-SP model is the mean-standard deviation shortest path (MSD-SP) problem Nie 2011, Khani and, where h is the square root function, ν ij and µ ij represent the variance and mean of the random travel time of a path p. The MSD-SP problem seeks to find a reliable path, which minimizes the sum of the mean and weighted standard deviation of path travel time (Noland and Polak 2002, Zeng et al 2015, Shahabi and Boyles 2015, Zhang et al 2016a).…”

An iterative learning approach for network contraction: Path finding problem in stochastic time‐varying networks

“…Different travelers have distinct decisions in response to travel time uncertainties that may vary by their preferences, risk tolerance, departure time, and trip purpose. Thus, consideration of travelers' preferences is assumed in the path selection procedure through different reliability rules (Duthie, Unnikrishnan, & Waller, 2011;Ng & Waller, 2012;Nie & Wu, 2009;Shahabi, Unnikrishnan, & Boyles, 2015). However, the fast heuristic algorithms in the literature are not applicable to stochastic time-dependent networks.…”

Meta‐heuristic multi‐ and many‐objective optimization techniques for solution of machine learning problems

“…Optimization techniques have been used widely for the solution of many engineering and real‐life problems such as the allocation of resources (Kyriklidis & Dounias, ), product design and development (Lostado, Fernandez, Mac Donald, & Villanueva, ; Paz, Pei, Monzón, Ortega, & Suárez, ), process planning and scheduling (X. X. Li, Li, Cai, & He, ), wind farm distribution network optimization (Cerveira, Baptista, & Solteiro Pires, ), vertical transportation optimization in skyscrapers (Koo, Hong, Yoon, & Jeong, ), railway line design and timetable optimization (Castillo, Grande, Moraga, & Sánchez‐Vizcaíno, ), freeway travel cost optimization (Shahabi, Unnikrishnan, & Boyles, ), sustainable road network design (Y. Wang & Szeto, ), bridge design optimization (Bisadi & Padgett, ), construction scheduling (Karim & Adeli, ), mountain railway alignment optimization (W. Li et al, ), road weather information system network optimization (Kwon, Fu, & Melles, ), cost optimization of concrete (Sirca & Adeli, ) and steel building structures (Tashakori & Adeli, ) and composite floors (Adeli & Kim, ), free‐form steel space‐frame roof design optimization (Kociecki & Adeli, ), freeway work zone traffic delay and cost optimization (Jiang & Adeli, ), optimal control of bridges (Adeli & Saleh, ) and buildings (Saleh & Adeli, ), and among others.…”