Algorithm For Quadratic Assignment Problem Research Articles

Solving Quadratic Assignment Problem by Using Meta-heuristic Search Method

While analytical solutions to Quadratic Assignment Problems (QAP) have indeed been since a long time, the expanding use of Evolutionary Algorithms (EAs) for similar issues gives a framework for dealing with QAP with an extraordinarily broad scope. The study's key contribution is that it normalizes all of the criteria into a single scale, regardless of their measurement systems or the requirements of minimum or maximum, relieving the researchers of the exhaustively quantifying the quality criteria. A tabu search algorithm for quadratic assignment problems (TSQAP) is proposed, which combines the limitations of tabu search with a discrete assignment problem. The effectiveness of the proposed technique has been compared to well-established alternatives, and its operating principle is illustrated with a numerical example. After repeating the solution of each issue (8) once and recording the algorithm results, it showed its agreement, once from a total (375) repetition of the experiment while the number of times the Artificial Bee Colony (ABC) arrived (2) as for the Firefly (FA) Algorithm giving (117), also Genetic (GA) and Particle Swarm (PSO) gives (120) and the Tabu Search algorithm (174). The proposed technique (TSQAP) is shown to yield a superior solution with low computing complexity. MATLAB was used to generate all of the findings (R2020b).

A discrete artificial bee colony algorithm for quadratic assignment problem

The quadratic assignment problem (QAP) is a well-known challenging combinational optimization problem that has received many researchers’ attention with varied real-world and industrial applications areas. Using the framework of basic artificial bee colony algorithm, frequently used crossover and mutation operators, and combined with an effective local search method, this paper proposes a simple but effective discrete artificial bee colony (DABC) algorithm for solving quadratic assignment problems (QAPs). Typical QAP benchmark instances are selected from QAPLIB in order to conduct the simulation experiment where common performance metrics are used to evaluate the algorithm. The paper also investigates the influence factors of the algorithm’s performance. The results show that the proposed algorithm is a quite effective and practical new approach for handling QAP problems.

A variable neighbourhood search enhanced estimation of distribution algorithm for quadratic assignment problems

Quadratic Assignment Problem (QAP) is one of the most complex combinatorial optimization problems. Many real-world problems such as printed circuit board design, facility location problems, assigning gates to airplanes can be modelled as QAP. Problems of size greater than 35 is not able to solve optimally using conventional optimization methods. This warrants the use of evolutionary optimization methods for obtaining optimal or near optimal solutions for QAPs. This work proposes a hybridization on a univariate Estimation of Distribution Algorithm, namely the Population Based Incremental Learning Algorithm (PBILA), with Variable Neighbourhood Search (VNS) for solving QAPs. The proposed algorithm is employed to solve benchmark instances of QAP and the results are reported. The results of this work reveals that PBILA on its own is not efficient for solving the QAPs. However, when hybridised with VNS, the algorithm performs well providing best known solutions for 95 test instances out of the 101 instances considered. For most of the test instances, the percentage deviation is less than one percentage. The overall average percentage deviation of the obtained solutions from the best-known solutions is 0.037%, which is a significant improvement when compared with state-of-the-art algorithms.

Genetic algorithm for quadratic assignment problems: application of Taguchi method for optimisation

Quadratic assignment problems (QAPs) are the hardest of combinatorial optimisation problems, with some problems of sizes of the order of 30 still remaining unsolved optimally. Solving QAPs with exact optimisation methods is cumbersome and hence, the use of non-conventional optimisation methods is recommended. Genetic algorithm (GA) being one of the most popular evolutionary algorithms is an appropriate choice for solving QAPs. The methods of operations used in GA influence the solution quality and thus, an optimal combination of parameters and operators are required for the efficient implementation of the algorithm. In this paper, the Taguchi's design of experiments method is used to find the best parameter combination and the best performing combination of operations for GA. The GA thus obtained by incorporating the selected parameter values and operators is then used for solving the QAPs taken from the QAP library. For many of the problems, it is found that the results obtained are within one percentage deviation from the best-known solutions.

Genetic algorithm for quadratic assignment problems: application of Taguchi method for optimisation

Quadratic assignment problems (QAPs) are the hardest of combinatorial optimisation problems, with some problems of sizes of the order of 30 still remaining unsolved optimally. Solving QAPs with exact optimisation methods is cumbersome and hence, the use of non-conventional optimisation methods is recommended. Genetic algorithm (GA) being one of the most popular evolutionary algorithms is an appropriate choice for solving QAPs. The methods of operations used in GA influence the solution quality and thus, an optimal combination of parameters and operators are required for the efficient implementation of the algorithm. In this paper, the Taguchi's design of experiments method is used to find the best parameter combination and the best performing combination of operations for GA. The GA thus obtained by incorporating the selected parameter values and operators is then used for solving the QAPs taken from the QAP library. For many of the problems, it is found that the results obtained are within one percentage deviation from the best-known solutions.

Tournament selection based antlion optimization algorithm for solving quadratic assignment problem

We propose and develop an improved version of antlion optimizer (ALO), namely tournament selection based antlion optimization algorithm for quadratic assignment problem (QAP). ALO algorithm has some handicaps, such as long run time, local optima stagnation and premature convergence for some problems. The literature describes different methods that improve the performance of antlion optimizer, but most of these are about specific optimization problems. In this paper, we introduce the tournament selection method instead of the roulette wheel method on random walking mechanism of ALO and we update some equations used in ALO algorithm. To compare the proposed tournament selection based ALO (TALO) algorithm with classic ALO, we deal with ten benchmark functions from literature. The comparison results are evaluated according to the different metrics, such as mean best, standard deviation, optimality, accuracy, CPU time, number of function evaluations (NFE). The detailed analyzes of the proposed TALO algorithm are performed. These are the convergence analysis, statistical analysis, search history analysis, trajectory analysis, average distance analysis, computational complexity analysis. The proposed TALO algorithm is compared with the other ALO versions (binary ALO and chaotic ALO variants) for same ten benchmark functions. As last, TALO algorithm has been also implemented for the quadratic assignment problem (QAP). The QAP results has been compared with several well-known meta-heuristic algorithms. TALO’s performance has been evaluated with those of binary ALO and chaotic ALO variants for same QAP instance. Finally, the solution quality of proposed TALO algorithm has been analyzed for solving QAP using some instances presented in QAPLIB site. The results provide the proposed TALO algorithm has the best performance in comparison with those of the other meta-heuristic algorithms. Due to the performance of TALO algorithm, we expect this version to be applied for different optimization problems.

A cooperative GPU-based Parallel Multistart Simulated Annealing algorithm for Quadratic Assignment Problem

GPU hardware and CUDA architecture provide a powerful platform to develop parallel algorithms. Implementation of heuristic and metaheuristic algorithms on GPUs are limited in literature. Nowadays developing parallel algorithms on GPU becomes very important. In this paper, NP-Hard Quadratic Assignment Problem (QAP) that is one of the combinatorial optimization problems is discussed. Parallel Multistart Simulated Annealing (PMSA) method is developed with CUDA architecture to solve QAP. An efficient method is developed by providing multistart technique and cooperation between threads. The cooperation is occurred with threads in both the same and different blocks. This paper focuses on both acceleration and quality of solutions. Computational experiments conducted on many Quadratic Assignment Problem Library (QAPLIB) instances. The experimental results show that PMSA runs up to 29x faster than a single-core CPU and acquires best known solution in a short time in many benchmark datasets.

Development of modified discrete particle swarm optimization algorithm for quadratic assignment problems

Development of modified discrete particle swarm optimization algorithm for quadratic assignment problems

Elite opposition-flower pollination algorithm for quadratic assignment problem

Elite opposition-flower pollination algorithm for quadratic assignment problem

On the performance of parallel hybrid algorithms for the solution of the quadratic assignment problem

The quadratic assignment problem (QAP) is a combinatorial optimization problem, which is computationally demanding, and considered to be NP-hard. Therefore, the problem cannot be solved in polynomial time. The known sequential algorithms can solve small problem instances within long computational times; moreover, parallelization may provide only a linear speed-up. Near-optimal solutions can be obtained in feasible times using heuristics like genetic algorithms and tabu search. The QAP algorithms can be modified to solve various problems like the travelling salesman problem, the data allocation problem, and the file allocation problem. In this paper, a parallel hybrid algorithm (PHA) with three stages was proposed. In the first stage, a genetic algorithm was used to obtain a high quality seed. Later, a diversification phase was run on the initial seed. Finally, a robust tabu search was run on the intermediate solution to find a near-optimal result. Parallel computing was used to increase the seed quality, and a considerable speed-up was obtained in the diversification phase of the tabu search. The QAPLIB benchmark instances were used to conduct the experiments. The PHA is quite competitive with respect to the best-performing algorithms in the literature in terms of solution quality and execution time. It achieves results on average within 0.05% of the best solutions given in the QAPLIB. The PHA was able to solve even the largest problem instance size of 256 within 11h, and with a higher accuracy than the best-known solutions. It was also observed that the solution quality improved considerably especially for larger instances, when the degree of parallelism increased.

A Hybrid Ant Colony Algorithm for Quadratic Assignment Problem

Quadratic assignment problem (QAP) is one of fundamental combinatorial optimization problems in many fields. Many real world applications such as backboard wiring, typewriter keyboard design and scheduling can be formulated as QAPs. Ant colony algorithm is a multi-agent system inspired by behaviors of real ant colonies to solve optimization problems. Ant colony optimization (ACO) is one of new bionic optimization algorithms and it has some characteristics such as parallel, positive feedback and better performances. ACO has achieved in solving quadratic assignment problems. However, its solution quality and its computation performance need be improved for a large scale QAP. In this paper, a hybrid ant colony optimization (HACO) has been proposed based on ACO and particle swarm optimization (PSO) for a large scale QAP. PSO algorithm is combined with ACO algorithm to improve the quality of optimal solutions. Simulation experiments on QAP standard test data show that optimal solutions of HACO are better than those of ACO for QAP.

Breakout local search for the quadratic assignment problem

The quadratic assignment problem (QAP) is one of the most studied combinatorial optimization problems with various practical applications. In this paper, we present breakout local search (BLS) for solving QAP. BLS explores the search space by a joint use of local search and adaptive perturbation strategies. Experimental evaluations on the set of QAPLIB benchmark instances show that the proposed approach is able to attain current best-known results for all but two instances with an average computing time of less than 4.5hours. Comparisons are also provided to show the competitiveness of the proposed approach with respect to the best-performing QAP algorithms from the literature.

A comment on “Biological computation of the solution to the quadratic assignment problem”

This note provides one counterexample to illustrate that DNA algorithm for quadratic assignment problem (QAP), especially DNA checking procedure which is proposed by Yang, Lu, Li, Liao in the above referenced paper is incorrect. We give the revised algorithm.

Path Relinking with Multi-Start Tabu Search for the Quadratic Assignment Problem

This paper introduces a new path relinking algorithm for the well-known quadratic assignment problem (QAP) in combinatorial optimization. The QAP has attracted considerable attention in research because of its complexity and its applicability to many domains. The algorithm presented in this study employs path relinking as a solution combination method incorporating a multistart tabu search algorithm as an improvement method. The resulting algorithm has interesting similarities and contrasts with particle swarm optimization methods. Computational testing indicates that this algorithm produces results that rival the best QAP algorithms. The authors additionally conduct an analysis disclosing how different strategies prove more or less effective depending on the landscapes of the problems to which they are applied. This analysis lays a foundation for developing more effective future QAP algorithms, both for methods based on path relinking and tabu search, and for hybrids of such methods with related processes found in particle swarm optimization.

An efficient continuation method for quadratic assignment problems

In this article, we propose a Lagrangian smoothing algorithm for quadratic assignment problems, where the continuation subproblems are solved by the truncated Frank–Wolfe algorithm. We establish practical stopping criteria and show the algorithm finitely terminates at a KKT point of a continuation subproblem. The quality of the returned solution is studied in detail. Finally, limited numerical results are provided.

The single-finger keyboard layout problem

The problem of designing new keyboard layouts able to improve the typing speed of an average message has been widely considered in the literature of the Ergonomics domain. Empirical tests with users and simple optimization criteria have been used to propose new solutions. On the contrary, very few papers in Operations Research have addressed this optimization problem. In this paper we firstly resume the most relevant problems in keyboard design, enlightening the related Ergonomics aspects. Then we concentrate on keyboards that must be used with a single finger or stylus, like that of portable data assistant, smartphones and other small devices. We show that the underlying optimization problem is a generalization of the well-known quadratic assignment problem (QAP). We recall some of the most effective metaheuristic algorithms for QAP and we propose some non-trivial extensions to the keyboard design problem. We compare the new algorithms through computational experiments with instances obtained from word lists of the English, French, Italian and Spanish languages. We provide on the web benchmark instances for each language and the best solutions we obtained.

A population-based hybrid ant system for quadratic assignment formulations in facility layout design

The facility layout design problem is an extensively studied research problem and belongs to nonpolynomial hard (NP-hard) combinatorial optimization problem. Quadratic assignment problem (QAP) is one of the formulations that is investigated for facility layout design because of its wide applicability. Ant colony optimization (ACO), a biologically inspired heuristic has centered on solving the QAP by achieving approximation as good as possible. This paper presents a population-based hybrid ant system (PHAS), which is an extension of the hybrid ant system (HAS) in which the size of the ant colony has been fixed. The performance of the proposed ant algorithm for QAP is compared with the existing metaheuristic implementations such as tabu search, reactive tabu search, simulated annealing, genetic hybrid method, HAS, and max–min ant system. The experimental results show that the proposed PHAS perform significantly better than the other existing algorithms of QAP.

A branch-and-cut algorithm for quadratic assignment problems based on linearizations

The quadratic assignment problem (QAP) is one of the hardest combinatorial optimization problems known. Exact solution attempts proposed for instances of size larger than 15 have been generally unsuccessful even though successful implementations have been reported on some test problems from the QAPLIB up to size 36. In this study, we focus on the Koopmans–Beckmann formulation and exploit the structure of the flow and distance matrices based on a flow-based linearization technique that we propose. We present two new IP formulations based on the flow-based linearization technique that require fewer variables and yield stronger lower bounds than existing formulations. We strengthen the formulations with valid inequalities and report computational experience with a branch-and-cut algorithm. The proposed method performs quite well on QAPLIB instances for which certain metrics (indices) that we proposed that are related to the degree of difficulty of solving the problem are relatively high ( ⩾ 0.3 ). Many of the well-known instances up to size 25 from the QAPLIB (e.g. nug24, chr25a) are in this class and solved in a matter of days on a single PC using the proposed algorithm.

An extreme point algorithm for a local minimum solution to the quadratic assignment problem

In this paper the network structure of basic solutions to the quadratic assignment problem (QAP) is revisited. The concept of a relative local star minimum is introduced. Results characterizing a relative local star minimum are obtained. Then an extreme point algorithm for QAP is proposed.

Quadratic Assignment Problems and M/G/C/C/ State Dependent Network Flows

One of the most notorious network design problems is the Quadratic Assignment Problem (QAP). We develop an heuristic algorithm for QAPs along with an M/G/C/C state dependent queueing model for capturing congestion in the traffic system interconnecting the nodes in the network. Computational results are also presented.