SOLVING A STEP FIXED CHARGE TRANSPORTATION PROBLEM BY A SPANNING TREE-BASED MEMETIC ALGORITHM

Subject Areas : International Journal of Mathematical Modelling & Computations

Saber Molla-Alizadeh-Zavardehi ¹ , Masoud Sanei ² , Reza Soltani ³ , Ali Mahmoodirad ⁴

1 - Department of Industrial Engineering, Masjed Soleyman Branch, Islamic Azad University, Masjed Soleyman, Iran.
2 - Department of Mathematics, Central Tehran Branch, Islamic Azad University, Tehran, Iran. Iran, Islamic Republic of
3 - Department of Industrial Engineering, Masjed Soleyman Branch, Islamic Azad University, Masjed Soleyman, Iran. Iran, Islamic Republic of
4 - Department of Mathematics, Masjed Soleyman Branch, Islamic Azad University, Masjed Soleyman, Iran. Iran, Islamic Republic of

Received: 2016-04-15 Accepted : 2016-04-15 Published : 2014-03-21

Keywords: Genetic Algorithm, Memetic Algorithm, Step Fixed Charge Transportation Problems, Spanning Tree,

Abstract :

In this paper, we consider the step fixed-charge transportation problem (FCTP) in which a step fixed cost, sometimes called a setup cost, is incurred if another related variable assumes a nonzero value. In order to solve the problem, two metaheuristic, a spanning tree-based genetic algorithm (GA) and a spanning tree-based memetic algorithm (MA), are developed for this NP-hard problem. For comparing GA and MA, twenty eight problems with different specifics have been generated at random and then the quality of the proposed algorithms was evaluated using the relative percentage deviation (RPD) method. Finally, based on RPD method, we investigate the impact of increasing the problem size on the performance of our proposed algorithms.