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.