The Quadratic Assignment Problem (QAP) is one of the classical combinatorial optimization problems and is known for its diverse applications. The QAP is an NP-hard optimization problem which attracts the use of heuristic or metaheuristic algorithms that can find quality solutions in an acceptable computation time. On the other hand, there is quite a broad spectrum of mathematical programming techniques that were developed for finding the lower bounds for the QAP. This paper presents a fusion of the two approaches whereby the solutions from the computations of the lower bounds are used as the starting points for a metaheuristic, called HC12, which is implemented on a GPU CUDA platform. We perform extensive computational experiments that demonstrate that the use of these lower bounding techniques for the construction of the starting points has a significant impact on the quality of the resulting solutions.

The Combinatorial Optimization Problem (COPs) is one of the branches of applied mathematics and computer sciences, which is accompanied by many problems such as Facility Layout Problem (FLP), Vehicle Routing Problem (VRP), etc. Even though the use of several mathematical formulations is employed for FLP, Quadratic Assignment Problem (QAP) is one of the most commonly used. One of the major problems of Combinatorial NP-hard Optimization Problem is QAP mathematical model. Consequently, many approaches have been introduced to solve this problem, and these approaches are classified as Approximate and Exact methods. With QAP, each facility is allocated to just one location, thereby reducing cost in terms of aggregate distances weighted by flow values. The primary aim of this study is to propose a hybrid approach which combines Discrete Differential Evolution (DDE) algorithm and Tabu Search (TS) algorithm to enhance solutions of QAP model, to reduce the distances between the locations by finding the best distribution of N facilities to N locations, and to implement hybrid approach based on discrete differential evolution (HDDETS) on many instances of QAP from the benchmark. The performance of the proposed approach has been tested on several sets of instances from the data set of QAP and the results obtained have shown the effective performance of the proposed algorithm in improving several solutions of QAP in reasonable time. Afterwards, the proposed approach is compared with other recent methods in the literature review. Based on the computation results, the proposed hybrid approach outperforms the other methods.

Particle swarm optimization has been established to be one of the efficient algorithms for finding solutions for continuous optimization problems. The discretized form of particle swarm optimization, known as the discrete particle swarm optimization is an efficient tool for solving combinatorial optimization problems and other problems involving discrete variables. In this paper, a revised version of the discrete particle swarm optimization algorithm is proposed for solving Quadratic Assignment Problems (QAP). Instead of using the general velocity and position update procedures in particle swarm optimization algorithms, four different possible positions are found out for each particle and the best among them is accepted as the updated position. The algorithm is applied to solve some benchmark instances of QAP taken from QAP Library and the results show minute deviations from best-known solutions.

Assembly lines and cellular manufacturing systems (CMSs) design have been widely used in the literature. However the integration of these manufacturing concepts is neglected in an environment where parts need to be assembled after production in different shops. In this paper, a comprehensive quadratic assignment problem is developed for the assignment of machines of each part manufacturing cell, sub-assembly tasks of each sub-assembly cell as well as the assignment of different cells and final assembly tasks within the shop floor in their relevant predetermined locations. A genetic algorithm (GA) as well as a memetic algorithm (MA) consisting of the proposed GA and Tabu search (TS) algorithm are proposed and implemented on different size numerical examples. The obtained results show the efficiency of both algorithms to reach near optimal solutions compared to the optimal solution of small-sized problems.

In this paper, an integrated layout model has been considered to incorporate intra and inter-department layout. In the proposed model, the arrangement of facilities within the departments is obtained through the QAP and from the other side the continuous layout problem is implemented to find the position and orientation of rectangular shape departments on the planar area. First, a modified version of QAP with fewer binary variables is presented. Afterward the integrated model is formulated based on the developed QAP. In order to evaluate material handling cost precisely, the actual position of machines within the departments (instead of center of departments) is considered. Moreover, other design factors such as aisle distance, single or multi row intra-department layout and orientation of departments have been considered. The mathematical model is formulated as mixed-integer programming (MIP) to minimize total material handling cost. Also due to the complexity of integrated model a heuristic method has been developed to solve large scale problems in a reasonable computational time. Finally, several illustrative numerical examples are selected from the literature to test the model and evaluate the heuristic.

Quadratic assignment problem (QAP) has been considered as one of the most complicated problems. The problem is NP-Hard and the optimal solutions are not available for large-scale problems. This paper presents a hybrid method using tabu search and simulated annealing technique to solve QAP called TABUSA. Using some well-known problems from QAPLIB generated by Burkard et al. (1997) [Burkard, R. E., Karisch, S. E., & Rendl, F. (1997). QAPLIB–a quadratic assignment problem library. Journal of Global Optimization, 10(4), 391-403.], two methods of TABUSA and TS are both coded on MATLAB and they are compared in terms of relative percentage deviation (RPD) for all instances. The performance of the proposed method is examined against Tabu search and the preliminary results indicate that the hybrid method is capable of solving real-world problems, efficiently.

In this paper, we consider job shop scheduling and machine location problem, simultaneously. Processing, transportation, and setup times are defined as deterministic parameters. The purpose of this paper is to determine machine location and job scheduling such that the make span and transportation cost is minimized. Therefore, the proposed model is a multi-objective problem one, where the first objective function minimizes make span and another minimizes the transportation cost. To solve the multi-objective problem, two methods are evaluated. Considering combination of job shop scheduling problem and machine location problem makes the proposed model more complex than job shop scheduling problem, which is an NP-hard problem. Therefore, to solve the proposed model, genetic algorithm as a meta-heuristic algorithm is implemented. To show the efficiency of the proposed genetic algorithm, 6×6 job shop scheduling problems are considered.