Equilibrium Decomposed Optimization: A Heuristic for the Continuous Equilibrium Network Design Problem

Abstract

For applications of realistic size, both the discrete and continuous versions of the equilibrium network design problem are too computationally intensive to be solved exactly with the algorithms proposed to date. This intractibility owes to Braess' paradox which makes it necessary to constrain the flow pattern to be a noncooperative Nash or user equilibrium. This paper suggests a new heuristic for finding an approximate solution to the continuous equilibrium network design problem. Numerical tests are reported which indicate that, for networks with significant congestion, the heuristic is markedly more efficient than the Hooke-Jeeves algorithm which has been employed previously. The efficiency of the heuristic results from decomposition of the original problem into a set of interacting optimization subproblems. This decomposition is such that, at each iteration of the algorithm, only one user equilibrium needs to be calculated in order to update the improvement variables of all arcs of the network. This contrasts sharply with the Hooke-Jeeves algorithm which can require that a new user equilibrium be calculated each time an individual arc improvement variable is updated.

An MPCC Formulation and Its Smooth Solution Algorithm for Continuous Network Design Problem

“…It is obvious that the objective function values increase with the increase of d. From Table 4, it can be seen that the links y 6 and y 16 are the most necessary ones, whose link capacity should be enhanced. And, y 6 reaches the largest link capacity expansion when d=25, 30,35,40,45,50.…”

“…The network has been extensively tested in the CNDP literatures such as Ref. [6,8,12,13,14,20,21]. As shown in Figure 1, the 16-link network consists of two OD pairs, six nodes and links.…”

“…As shown in Figure 1, the 16-link network consists of two OD pairs, six nodes and links. All input information by Suwansirikul et al [6] for the test network is presented in Table 2. The travel demand of (1,6) is assumed to be d, which is half of that for (6,1).…”

“…A subset containing 10 links (16,17,19,20,25,26,29,39,48,74) was chosen for capacity improvement. The link cost function with the corresponding parameters and the OD demand are presented in Tables 6 and 7 [6]. The experimental environment and the parameters are adopted as the same as those in Subsection 4.1.…”

Statistical metamodeling of dynamic network loading

“…For example, the heuristic network design based on sensitivity analysis from Suwansirikul et al (1987) can be adapted to treat dynamic traffic networks.…”