A NOVEL DISCRETE RAT SWARM OPTIMIZATION ALGORITHM FOR THE QUADRATIC ASSIGNMENT PROBLEM

-Quadratic assignment problems (QAPs) are NP-hard combinatorial optimization problems often used to compare the performance of meta-heuristics. In this paper, we propose a QAP problem instance generator whose instances can be used as benchmark for meta-heuristics. Our generator aggregates various QAP instances into a larger size QAP instance in order to obtain an large size, additively decomposable QAP. We assume that a QAP instance that is difficult for local search has many local optima from which local search needs to escape from. We call the resulting QAPs the composite QAP instances (cQAPs). We use numerical and empirical techniques for the landscape analysis of generated composite QAPs. The comparison between our QAP instances with the other QAPs from the literature classify cQAPs as difficult. We show that heuristic algorithms that exploit the particularities of the cQAP search space, like iterated local search, can outperform other heuristics that do not consider the structure of this search space, like the multi-restart local search.

Introduction. The quadratic assignment problem is a well-established NP-hard problem in combinatorial optimization with applications in diverse fields like economics, archaeology, and chemistry. Due to its complexity, research on efficient solution methods remains active, including efforts for parallelization on multiprocessor computing systems. However, effective parallel algorithms are crucial to fully leverage these computational resources. In this context, algorithm unions (portfolios and teams) play a significant role in achieving parallel execution for solving such problems. Research objectives. This work investigates the application of portfolios constructed from modifications of the repeated iterated tabu search algorithm to the quadratic assignment problem. The effectiveness of these portfolios was evaluated through experimental computations. Results. The portfolios, derived from modifications of the repeated iterated tabu search algorithm, were applied to the quadratic assignment problem. For the most demanding test instances, the proposed algorithms were evaluated on the SCIT-4 supercomputer, alongside previously published results from the authors, confirming their competitive performance. Additionally, we assessed the parallel efficiency of these portfolios in solving instances of the quadratic assignment problem. The results demonstrate their ability to accelerate the optimization process (with speedup dependent on problem size and utilized processors), enabling the solution of large-scale problems. Conclusions. The conducted studies demonstrate that employing algorithm portfolios significantly accelerates the solution process for the quadratic assignment problem. Analysis of the results reveals a near-linear speedup factor achieved by the portfolio. For the challenging test instance tai100a, a new best solution value of 21040996 was obtained using a portfolio of 16 algorithms. Keywords: quadratic assignment problem, algorithm portfolios, experimental research, algorithm portfolios efficiency.

Quadratic assignment problems (QAPs) is a NP-hard combinatorial optimization problem. QAPs are often used to compare the performance of meta-heuristics. In this paper, we propose a QAP problem instance generator that can be used for benchmarking for heuristic algorithms. Our QAP generator combines small size QAPs with known optimum solution into a larger size QAP instance. We call these instances composite QAPs (cQAPs), and we show that the cost function of cQAPs is additively decomposable. We give mild conditions for which a cQAP instance has known optimum solution. We generate cQAP instances using uniform distributions with different bounds for the component QAPs and for the rest of the cQAP elements. Numerical and analytical techniques that measure the difficulty of the cQAP instances in comparison with other QAPs from the literature are introduced. These methods point out that some cQAP instances are difficult for local search with many local optimum of various values, low epistasis and non-trivial asymptotic behaviour.

The Quadratic Assignment Problem (QAP) is a difficult and important problem studied in the domain of combinatorial optimisation. It is possible to solve QAP instances with 10--20 facilities using exhaustive parallel algorithms within a few days on a cluster machine. However, large QAP instances with more than 100 facilities are not solvable using exhaustive techniques. We have explored a variety of Genetic Algorithm crossover operators for this problem and verified its performance experimentally using well-known instances from the QAPLIB library. By increasing the number of processors, generations and population sizes we have been able to find solutions that are the same as (or very close to) the best reported solutions for large QAP instances in QAPLIB. In order to parallelise the Genetic Algorithm we generate and evolve separate solution pools on each cluster processor, using an island model. This model exchanges 10% of each processor’s solutions at the initial stages of optimisation. We show experimentally that both execution times and solution qualities are improved for large QAP instances by using our Island Parallel Genetic Algorithm.

Multi objective Quadratic Assignment problem is an NP-Hard complex problem for assigning facilities to locations which significantly influence the transportation cost multitude in real-world applications like facilities location, distributed computing and data analysis. QAP can be solved using metaheuristic algorithm with deterministic and local search by equalising facilities and location. QAP can be applied to decision making framework, economic problems, scheduling to assign and determine services. This work portrays the exhaustive survey of quadratic assignment problem and various methodologies to solve QAP. A comprehensive study has been carried out to solve QAP using optimization algorithms. In this survey many approaches is examined by including multiple objective flow of facilities to locations by using evolutionary algorithm.

A new tool for automated transformation of Quadratic Assignment Problem instances to Quadratic Unconstrained Binary Optimisation models

<p>The main objective of our research is to improve an adaptation of the chicken swarm optimization algorithm (CSO) to solve the quadratic assignment problem, which is a well-known combinatorial optimization problem. The new approach is based on the CSO without using a local search, the CSO-QAP is a stochastic method inspired from the behavior of chickens in swarm while searching for food. The experiments are performed on a set of 56 benchmark QAPLIB instances. To prove the robustness of our algorithm a comparative analysis is done with the known metaheuristic of Genetic algorithm based on SCX. The average percentage of error to get the best Known solution in our proposed work with the results obtained by applying a simple genetic algorithm using sequential constructive crossover for the quadratic assignment problem. The results show the effectiveness of the proposed CSO-QAP to solve the Quadratic assignment problem in term of time and quality of solutions. The proposed adaptation can be further applied by using a local search strategy to solve the same problem or another combinatorial problem.</p>

The quadratic assignment problem (QAP) is one of the NP-hard combinatorial optimization problems, which is very difficult to solve. The tabu search technique, one of the various heuristic methods for the QAP, has been implemented in a neural network form with chaotic dynamics. In order to achieve a high-speed massively parallel solution of the QAP, a mixed analog/digital integrated circuit implementation of the system is mandatory. However, the algorithm in Hasegawa et al. (1997) cannot be implemented with IC technology as it is. Therefore, the algorithm is modified to be suitable for the analog IC implementation in this paper. The performance of the modified algorithm is investigated with numerical simulations. The circuit characteristics obtained from a prototype chip is extensively used in the simulations.

The quadratic assignment problem (QAP) is a well‐known challenging combinatorial optimization problem that has received many researchers' attention with varied real‐world and industrial applications areas. It is noteworthy to mention that a plethora of nature‐inspired optimization algorithms have successfully been used to solve various optimization problems, including several variants of the QAPs. In this article, a comprehensive literature review is presented to show the most relevant nature‐inspired algorithms that have been used in solving the QAP. More so, extensive experiments are conducted and analyzed to show the performance of the well‐known state‐of‐the‐art nature‐inspired meta‐heuristic optimization algorithms in solving the QAP, including the ant colony optimization (ACO), bat algorithm, genetic algorithm (GA), particle swarm optimization (PSO), and tabu search algorithm. Besides, a modified variant of the discrete PSO algorithm is implemented and compared with existing approaches. The six selected algorithms' performances, including the modified PSO, are validated on eight commonly used QAP instances of varying complexity and size, considering the quality of solutions achieved and computational time consumed by the representative algorithms. The numerical results revealed that the most competitive algorithm was ACO, while the GA appeared to be the worst performed algorithm among the six compared meta‐heuristic algorithms. However, based on the extensive analysis conducted on the tested algorithms, further improvements are suggested, including implementing new modified versions of the tested algorithms to tackle the QAP and its variant instances.

Graph matching problem that incorporates pair-wise constraints can be formulated as Quadratic Assignment Problem(QAP). The optimal solution of QAP is discrete and combinational, which makes QAP problem NP-hard. Thus, many algorithms have been proposed to find approximate solutions. In this paper, we propose a new algorithm, called Nonnegative Orthogonal Graph Matching (NOGM), for QAP matching problem. NOGM is motivated by our new observation that the discrete mapping constraint of QAP can be equivalently encoded by a nonnegative orthogonal constraint which is much easier to implement computationally. Based on this observation, we develop an effective multiplicative update algorithm to solve NOGM and thus can find an effective approximate solution for QAP problem. Comparing with many traditional continuous methods which usually obtain continuous solutions and should be further discretized, NOGM can obtain a sparse solution and thus incorporates the desirable discrete constraint naturally in its optimization. Promising experimental results demonstrate benefits of NOGM algorithm.

This paper presents two meta-heuristic algorithms to solve the quadratic assignment problem. The iterated greedy algorithm has two main components, which are destruction and construction procedures. The algorithm starts from an initial solution and then iterates through a main loop, where first a partial candidate solution is obtained by removing a number of solution components from a complete candidate solution. Then a complete solution is reconstructed by inserting the partial solution components in the destructed solution. These simple steps are iterated until some predetermined termination criterion is met. We also present our previous discrete differential evolution algorithm modified for the quadratic assignment problem. The quadratic assignment problem is a classical NP-hard problem and its applications in real life are still considered challenging. The proposed algorithms were evaluated on quadratic assignment problem instances arising from real life problems as well as on a number of benchmark instances from the QAPLIB. The computational results show that the proposed algorithms are superior to the migrating birds optimization algorithm which appeared very recently in the literature. Ultimately, 7 out of 8 printed circuit boards (PCB) instances are further improved.

A branch-and-bound algorithm for the quadratic assignment problem based on the Hungarian method

Presently, most tabu search designers devise their applications without considering the potential of design and code reuse, which consequently prolong the development of subsequent applications. In this paper, we propose a software solution known as Tabu Search Framework (TSF), which is a generic C++ software framework for tabu search implementation. The framework excels in code recycling through the use of a well- designed set of generic abstract classes that clearly define their collaborative roles in the algorithm. Additionally, the framework incorporates a centralized process and control mechanism that enhances the search with intelligence. This results in a generic framework that is capable of solving a wide range of combinatorial optimization problems using various tabu search techniques and adaptive strategies. The applications of TSF are demonstrated on the implementation of two NP-hard problems, the Vehicle Routing Problem with Time Windows (VRPTW) and Quadratic Assignment Problem (QAP). We show that TSF is able to obtain quality solutions within reasonable implementation as well as computation time.Key wordsTabu Searchsoftware frameworkreusabilitycombinatorial optimization

Quadratic Assignment Problem (QAP) is one of the most difficult combinatorial problems in the literature and has a diverse field of applications. This paper presents the results of experiments on the impact of parallelization of a sequential GA using island model. Both of the genetic algorithms are applied to the QAP. For the island model parallel GA, we systematically change the number of islands and investigate the effects of dividing the same global population into a number of subpopulations. The number of islands is gradually increased to observe the effects on solution quality and speedup in total execution time using different problem instances. The results clearly indicate that, while parallelized version outperforms sequential counterpart in both solution quality and total execution time, an increasing number of subpopulations also positively effects the results until a critical point where every subpopulation has a certain number of individuals to be able to evolve independently. Beyond that point, the performance of the algorithm begins to decrease.

The generalized quadratic assignment problem (GQAP) is a generalization of the NP-hard quadratic assignment problem (QAP) that allows multiple facilities to be assigned to a single location as long as the capacity of the location allows. The GQAP has numerous applications, including facility design, scheduling, and network design. In this paper, we propose several GRASP with path-relinking heuristics for the GQAP using different construction, local search, and path-relinking procedures. We introduce a novel approximate local search scheme, as well as a new variant of path-relinking that deals with infeasibilities. Extensive experiments on a large set of test instances show that the best of the proposed variants is both effective and efficient.