A Cross Entropy Based Multi-Agent Approach to Traffic Assignment Problems

In this paper, we propose a Cross Entropy (CE) [1] based multiagent approach for solving static/dynamic traffic assignment problems (TAP). This algorithm utilizes a family of probability distributions in order to guide travelers (agents) to network equilibrium. The route choice probability distribution depends on the average network performance experienced by agents on previous days. Based on the minimization of cross entropy concept, optimal probability distributions are derived iteratively such that high quality routes are more attractive to agents. The advantage of the CE method is that it is based on a mathematical framework and sampling theory, in order to derive the optimal probability distributions guiding agents to the dynamic system equilibrium. Interestingly, we demonstrate that the proposed approach based on CE method coincides with dynamic system approaches. Numerical studies illustrate both nonlinear and bimodal static traffic assignment problems. A comparative study of the proposed method and the dynamic system approach is provided to justify the efficiency of proposed method.