Objective Variation Network Simplex Algorithm for Concave Continuous Piecewise Linear Network Flow Problems

Abstract

In this work, an efficient algorithm is developed for the local optimization of Concave Continuous Piecewise Linear Network Flow Problems (CCPLNFP) with network constraints. Inspired by the piecewise linearity and concavity of the cost functions in CCPLNFP, we propose an Objective Variation Network Simplex Algorithm (OVNSA) based on a network simplex method (NSM), which derives a locally optimal solution. For large-scale problems, OVNSA fails to obtain a local minimum within acceptable computation time. Hence, we propose a Modified Objective Variation Network Simplex Algorithm (MOVNSA), which provides a sub-optimal solution within reasonable computation time. Numerical experiments show high efficiency of the proposed algorithms compared with two relevant algorithms on random test problems.