Universal Journal of Applied Mathematics 6(3): 79-93, 2018 DOI: 10.13189/ujam.2018.060302 http://www.hrpub.org A Comparison between two Modified NSGA-II Algorithms for Solving the Multi-objective Flexible Job Shop Scheduling Problem Aydin Teymourifar 1,2,∗ , Gurkan Ozturk 1,2 , Ozan Bahadir 1,2 1 Faculty of Engineering, Anadolu University, 26555, Eskisehir, Turkey 2 Computational Intelligence and Optimization Laboratory (CIOL), Anadolu University, 26555, Eskisehir, Turkey Copyright c 2018 by authors, all rights reserved. Authors agree that this article remains permanently open access under the terms of the Creative Commons Attribution License 4.0 International License Abstract Many evolutionary algorithms have been used to solve multi-objective scheduling problems. NSGA-II is one of them that is based on the Pareto optimality concept and generally obtains good results. However, it is possible to improve its performance with some modifications. In this paper, two modified NSGA-II algorithms have been suggested for solving the multi-objective flexible job shop scheduling problem. The neighborhood structures defined for the problem are integrated into the algorithms to create better generations during the iterations. Also, their initial populations are created with an effective heu- ristic. In the first modified NSGA-II, after the creation of the offspring population, a neighbor of each individual in the parent population is constructed, and then one of them is selected according to the domination state of the solutions. Then the popula- tions are merged to create a new population. In the second modified NSGA-II, only the solutions on the first and second fronts of the parent population and also their neighbors are merged with the offspring population. Other operators of the algorithms like the non-dominated sorting and calculating the crowding distances are as the classic NSGA-II. A comparison is done with a classic NSGA-II based on two metrics. The results show that as it is in the first modified NSGA-II, including neighbors of more individuals of the population provides better results because it increases diversity and intensity of the search. The performance of the second modified NSGA-II is almost similar to the NSGA-II. So, it can be concluded that although integrating the neighbor- hood structures can improve the performance of search, it is better to define that the structures should be applied to how many and which solutions, in otherwise the quality of search may not increase. Keywords Flexible Job Shop Scheduling, Multi-objective Optimization, NSGA-II, Neighborhood Structures, Hybrid Algo- rithms 1 Introduction Flexible job shop scheduling problem (FJSSP) is an NP-hard problem that has been investigated by many researchers in the recent decades. Many of the scheduling problems in the manufacturing and computer science can be modelled based on this problem. For example, Ho et al. have defined the production process of the printed circuit board (PCB) in the electronic manu- facturing service (EMS) as a FJSSP [19]. Because of the complex structure of this combinatorial problem, it is difficult to solve it with the non-hybrid and exact methods [45]. So, several hybrid methods, which integrate the population-based meta-heuristics (P-metaheuristics), single-based meta-heuristics (S-metaheuristics), heuristics, mathematical programming, constraint program- ming, machine learning and graph-based methods are suggested for solving this problem [1][36][39][41][42][43][44][47][50]. Also, in many real scheduling problems of the manufacturing systems, it is necessary to deal with more than one objective. Therefore, the algorithms for the multi-objective optimization are widely researched in the scheduling literature. Generally, in these algorithms, the diversity and intensity of the search are increased to create better generations. There are many approaches for this aim. For example, Knowles and Corne have proposed the Pareto archived evolution strategy, in which a child is generated from each parent. If the child dominates the parent, it is selected. If the parent dominates the child, a new child is created by the