Solving non-linear fixed-charge transportation problems using nature inspired non-linear particle swarm optimization algorithm

Abstract

The main objective of this study is to formulate and solve the model of non-linear fixed-charge transportation problem (NFCTP), which is one of the NP-hard problems. This type of problem is challenging to solve using conventional methods because these methods are usually inefficient, costly to compute, and may stuck at the local optimum solution. To overcome this issue, a non-linear particle swarm optimization (NPSO) algorithm with new non-linear acceleration parameters is proposed in this study. Also, to preserve the feasibility condition (non-negative integer solution) of the transportation problem, two novel negative repair and fraction repair strategies have been incorporated into the proposed NPSO. The efficiency of the NPSO algorithm is tested on both the small-scale and large-scale NFCTPs. The dataset are considered from the existing studies. The obtained results are compared with those obtained by the spanning tree-based genetic algorithm (st-GA), priority-based genetic algorithm (pb-GA), and minimum cost flow-based genetic algorithm. The comparative study reveals that for all the considered problems, the proposed NPSO provides better feasible solutions in lesser computational time. Furthermore, the effectiveness of the NPSO algorithm is shown by comparing it to other seven existing variants of PSO and is found to outperformed these variants for the small scale as well as large scale NFCTPs.