Mathematical and heuristics solution approaches to the multiobjective quadratic assignment problems

Quadratic Assignment Problems (QAP) were firstly defined by Koopmans and Beckmann in 1957. For this problem, the objective is cost minimization of total assignment between locations and facilities. While the constraints of QAP are 0-1 assignment constraints, the objective function is nonlinear because of the quadratic structure. Based on these two reasons, QAP is classified as NP-Hard. And it is almost impossible to find optimal solutions for number of locations are greater than 20. Because of the fact that the multiobjective structure of real life problems, Multiobjective Quadratic Assignment Problems (mQAP) are suggested by Knowles and Corne in 2002. After this, as regards 2005, different researchers have studied about this subject based on different solution approaches. These studies are about heuristics and metaheuristic algorithms. mQAP is also a NP-Hard problem like QAP. In addition, more than one nonlinear objective function have to be considered. In this study, mQAP which is a relatively new subject in the literature will be studied. And we will handle test problems from the literature and seek solutions with conic scalarization method. Conic scalarization method's effectiveness is proved in solution of multiobjective problems with non-linear structure. We also seek solutions with one of the multiobjective evolutionary algorithm NSGA-II. At the end of this study, we propose a hybrid method with evolutionary algorithm and scalarization method. Obtained results were compared with the results from the other methods in the literature and performances were compared.