A transportation network model with intelligent probabilistic travel times and two hybrid algorithms

Abstract

A main component of a transportation network is travel time or distance. Due to stochastic events such as accidents and failures in roads, a deterministic estimation of the travel time between two cities or regions is impossible. Also, on special occasions like holidays, with increase in the traveling population in the transportation network, probabilities of occurrence of these events increase. The increase in traveling population has a direct effect on the estimation of travel times and subsequently on the decision-making process. Therefore, provision of an appropriate model for the intelligent probabilistic travel times to distribute the population in a transportation network is a practical necessity. Here, we study a capacitated location-multi allocation-routing problem with intelligent probabilistic travel times. In our study, the concept of intelligent probabilistic travel times incurs two issues: (1) consideration of some random factors in computing the travel times and (2) impact of the traveling population on these random factors simultaneously. Here, we consider three random factors of the time spent in traffic, the number of accidents and the number of road failures. It is assumed that server nodes and arcs have limited capacities for accepting the population. After proposing a function for computing the intelligent probabilistic travel time, we first formulate the problem as a mixed-integer nonlinear programming model, and then suitably transform it into a mixed-integer linear programming one. Our aim is to determine appropriate server locations among the candidate locations, allocate the existing population in each demand node to server locations, and find the movement path of each member to reach its corresponding server with respect to the simultaneous change of the probabilistic travel times so that the expected total transportation time is minimized. For small problems, the model is efficiently solvable by the CPLEX software package. For large problems, two solution approaches, a heuristic algorithm incorporating genetic algorithm and local search, and an evolutionary simulated annealing algorithm, are proposed. Comparative numerical results demonstrate the effectiveness of the proposed probabilistic model and the proposed algorithms.