Alternate mutation based artificial immune algorithm for step fixed charge transportation problem

Abstract

Step fixed charge transportation problem (SFCTP) is considered as a special version of the fixed-charge transportation problem (FCTP). In SFCTP, the fixed cost is incurred for every route that is used in the solution and is proportional to the amount shipped. This cost structure causes the value of the objective function to behave like a step function. Both FCTP and SFCTP are considered to be NP-hard problems. While a lot of research has been carried out concerning FCTP, not much has been done concerning SFCTP. This paper introduces an alternate Mutation based Artificial Immune (MAI) algorithm for solving SFCTPs. The proposed MAI algorithm solves both balanced and unbalanced SFCTP without introducing a dummy supplier or a dummy customer. In MAI algorithm a coding schema is designed and procedures are developed for decoding such schema and shipping units. MAI algorithm guarantees the feasibility of all the generated solutions. Due to the significant role of mutation function on the MAI algorithm’s quality, 16 mutation functions are presented and their performances are compared to select the best one. For this purpose, forty problems with different sizes have been generated at random and then a robust calibration is applied using the relative percentage deviation (RPD) method. Through two illustrative problems of different sizes the performance of the MAI algorithm has been compared with most recent methods.