bi-level programming

In this paper, we consider the problem of hazardous material distribution where the distributer chooses the routes on the network, and a regulatory agency controls the behavior of the distributer to traverse the specified routes. In these circumstances, the distributer wants to select some routes to minimize the total distributing costs. Most of the time, this occurs due to selecting risky arcs in which more individuals are exposed to risk. To prevent this and increase the capability to deal with the risk of hazardous material transportation through roads, the regulatory agency obliges carriers to traverse through the most secure arcs, though imposing more distribution costs.
In reality, two decision makers may have different perceptions or asymmetric information about the network. To apply network interdiction models for real situations, we introduce the information asymmetry for these types of vehicle routing network interdiction problems and investigate its benefits and risks. For this purpose, a bi-level programming model is proposed and two bi-level meta-heuristics are suggested to solve this Stachelberg interdictor-evader game. The computational results showed that the developed co-evolutionary meta-heuristic algorithm could be more effective and more rational than the developed Bi-GA for these problems.

In this paper, is proposed a method for study the strategies of passenger transport pricing with bi-level programming and value of travel time. many studies about transportation is consist of bi-level programming and value of travel time, but few studies have included both of them. In this paper, the passengers are divided into some groups according to income level. As well as, a variable of comfort levels is introduced to calculate the generalized value of travel time. A pricing model which is based on the value of travel time and Bi-level programming is put forward to maximize the benefit of the railway agencies and the passenger s’ utility, which considers the passenger’s mode choice behavior with different income levels. At the end, validity of the model is evaluated by some test problems. The study results show that the model is appropriate and practical for problems of passenger transport pricing.

Origin-Destination demand information, namely the O-D matrix, is one of the essential inputs for many studies of operational analysis of transportation networks. Obtaining such a matrix by conventional surveying methods needs a considerable amount of time and consumes a significant portion of studies' budget. Instead, many researchers have tried to develop some methods to solve the OD matrix adjustment problem (ODMAP), that is, how to adjust an outdated (initial) O-D matrix using easily available traffic counts. These methods are known as low-cost surrogates to the conventional methods and some of them have been shown to cope well with the ODMAP. The problem is formulated as a bi-level programming model where the upper level problem resembles an O-D matrix which can reproduce the counts as close as possible, and the lower level problem performs an equilibrium traffic assignment for any given solution. The gradient algorithm is the most used solution method to the ODMAP, but its efficiency for large-scale problems is not well determined. The method requires significant computational effort to calculate the derivatives of the objective function of the upper level problem when the size of the matrix is large. Moreover, the solution of the gradient is shown to be highly sensitive to the percentage of the links of the network that are counted. Our study also shows that the solution of the gradient method could not remain close enough to the structure of the initial matrix. In this paper, the meta-heuristic intelligence of the Particle Swarm Optimization (PSO) is used to develop an alternative solution method for the ODMAP. The proposed method is applied to solve the problem for Tehran metropolis, and the results are compared against those of the gradient one. The results reveal that the gradient is slightly superior to the PSO in the sense of reduction the objective function value, but the PSO obviously outperforms the gradient method when considering the structure of the adjusted matrix and the sum of its elements. Regarding the CPU times, the PSO can solve the problem in shorter time, due to its simplicity, while both methods use the same algorithm for the lower level problem. The results are promising and encourage further investigation to use the PSO for updating old matrices in transportation studies.