Artificial Immune Algorithm for Solving Fixed Charge Transportation Problem

Abstract

Fixed Charge Transportation Problem (FCTP) is considered to be an NP-hard problem. Several genetic algorithms based on spanning tree and Prfer number were presented. Most of such methods do not guarantee the feasibility of all the generated chromosomes and need a repairing procedure for feasibility. Contrary to the findings in previous works, this paper introduces an Artificial Immune System for solving Fixed Charge Transportation Problems (AISFCTP). AISFCTP solves both balanced and unbalanced FCTP without introducing a dummy supplier or a dummy customer. In AISFCTP a coding schema is designed and algorithms are developed for decoding such schema and allocating the transported units. These are used instead of spanning tree and Prfer number. Therefore, a repairing procedure for feasibility is not needed, i.e. all the generated antibodies are feasible. Besides, some mutation functions are developed and used in AISFCTP. Due to the significant role of mutation fun ction on the AISFCTPs quality, its performances are compared to select the best one. For this purpose, various problem sizes are generated at random and then a robust calibration is applied using the relative percentage deviation (RPD) method and paired t-tests. I n addition, two problems with different sizes are solved to evaluate the performance of the AISFCTP and to compare its performance with most recent methods.