The capacity constraint physarum solver

Abstract

Physarum polycephalum inspired algorithm (PPA) has attracted immense attention recently. By modeling real-world problems into a graph and adopting proper adaption equation, PPA could solve system optimization or user equilibrium problems. However, few PPA-based algorithms can tackle problems with capacity constraints, lacking the ability to control link flows in the PPA. To tackle this problem, a novel framework, the capacitated PPA (CPPA), is proposed to allow capacity constraints toward link flow in the PPA. To demonstrate the validity of the CPPA, we have developed three applications of the CPPA, i.e., the CPPA for the maximum-flow problem (CPPA-MF), the CPPA for the minimum-cost–maximum-flow problem (CPPA-MCMF), and the CPPA for the link-capacitated traffic assignment problem (CPPA-CTAP). In the experiments, the CPPA-MF shows competitive performance among four baseline algorithms; the CPPA-MCMF is approximately 50% faster than the baseline algorithms; the CPPA-CTAP reduce the oversaturated degree from approximately 40% to 1.5% compared to the original algorithm. The experimental results prove the validation of the CPPA framework. The CPPA is also robust since it have been successfully applied in three different scenarios. The proposed CPPA extends the PPA’s application to capacity-constrain problems and might shed some lights on its future applications in complex real-world problems.