Nonlinear fixed charge transportation problem by minimum cost flow-based genetic algorithm

Nonlinear Fixed Charge Transportation Problem (NFCTP) is a variant of fixed charge transportation problem, which is to ship available amounts of goods to satisfy the demands at minimal total cost, on condition that any route has a fixed cost irrelative to its shipping amount if it is used, and a variable cost directly proportional to the quadratic of its shipping amount as a nonlinear term. This paper aims at developing an efficient method to solve NFCTP. In this paper, NFCTP is formulated using a mixed integer programming model. Based on steady-state genetic algorithm as framework, and minimum cost flow algorithm as decoder, a hybrid genetic algorithm named NFCTP-HGA is proposed as a solution method of the model. Taking advantage of nonlinear structure and special network structure of NFCTP, the NFCTP-HGA algorithm has good performance in the sense of being implemented on computer, computational time, required memory for computation, and ability to search global optimum. The application of the NFCTP-HGA algorithm is illustrated with examples. Numerical experiments demonstrate that the NFCTP-HGA algorithm is an efficient and robust method to solve NFCTP, especially applicable to large scale problems.