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An Efficient Physarum Algorithm for Solving the Bicriteria Traffic Assignment Problem
Xiaoge Zhang

We develop a Physarum-inspired approach to address the bicriteria traffic equilibrium problem, where the path cost function considered has two attributes: travel time and toll. These attributes are combined into a nonlinear generalized cost. The proposed method is implemented using a three-step procedure. First, Physarum model is generalized to solve the shortest path problem in directed networks. Second, we extend it to network optimization problem with multiple sources and sinks. Third, a novel function is proposed to combine the current cost and the cost in the next iteration. This function guarantees Physarum algorithm’s convergence to the optimal traffic flow distribution through the network. Two numerical examples with different link cost functions are conducted to demonstrate the feasibility of the proposed algorithm in this class of traffic equilibrium problems.

Keywords: Traffic equilibrium, shortest path, physarum, network optimization

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