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The recent emergence of novel computational devices, such as quantum computers, coherent Ising machines, and digital annealers presents new opportunities for hardware-accelerated hybrid optimization algorithms. Unfortunately, demonstrations of unquestionable performance gains leveraging novel hardware platforms have faced significant obstacles. One key challenge is understanding the algorithmic properties that distinguish such devices from established optimization approaches. Through the careful design of contrived optimization tasks, this work provides new insights into the computation properties of quantum annealing and suggests that this model has the potential to quickly identify the structure of high-quality solutions. This result provides new insights into the time scales and types of optimization problems where quantum annealing has the potential to provide notable performance gains over established optimization algorithms and suggests the development of hybrid algorithms that combine the best features of quantum annealing and state-of-the-art classical approaches. Quantum Population Based Meta Heuristic

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In computer science and mathematical optimization , a metaheuristic is a higher-level procedure or heuristic designed to find, generate, or select a heuristic partial search algorithm that MAY provide a sufficiently good solution to an optimization problem , especially with incomplete or imperfect information or limited computation capacity. Metaheuristics may make relatively few assumptions about the optimization problem being solved and so may be usable for a variety of problems. Compared to optimization algorithms and iterative methods , metaheuristics do not guarantee that a globally optimal solution can be found on some class of problems. Most literature on metaheuristics is experimental in nature, describing empirical results based on computer experiments with the algorithms. But some formal theoretical results are also available, often on convergence and the possibility of finding the global optimum. While the field also features high-quality research, many of the publications have been of poor quality; flaws include vagueness, lack of conceptual elaboration, poor experiments, and ignorance of previous literature. These are properties that characterize most metaheuristics: [3].

Either your web browser doesn't support Javascript or it is currently turned off. In the latter case, please turn on Javascript support in your web browser and reload this page. The paper focuses on the opportunity of the application of the quantum-inspired evolutionary algorithm for determining minimal costs of the assignment in the quadratic assignment problem.

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The idea behind the paper is to present how the algorithm has to be adapted to this problem, including crossover and mutation operators https://amazonia.fiocruz.br/scdp/blog/woman-in-black-character-quotes/marketing-plan-for-a-delivery-service.php introducing quantum principles in particular procedures. The results have shown that the performance of our approach in terms of converging to the best solutions is satisfactory.

Moreover, we have presented the results of the selected parameters of the approach on the quality of the obtained solutions. The quadratic assignment problem QAP is one of the most interesting and difficult combinatorial optimization problem. Due to its popularity, many publications have focused on the QAP problem to search for methods that are sufficient for Quantum Population Based Meta Heuristic applications.

Some studies have focused on the applicability of the QAP to the solution of many various problems. There exist several problems which are specializations of this problem, like: graph partitioning and maximum clique problem, travelling salesman problem, graph isomorphism and graph packing problem [ 1 ].

Intensive studies on quadratic assignment problems produced many algorithms over the last few decades. For a survey on these methods, see [ 34 ]. It should be mentioned that the link of the methods for solving the quadratic assignment problems depends on the complexity of the problems. Therefore, to obtain near-optimal solutions, various Quantum Population Based Meta Heuristic and metaheuristic approaches have been developed, such as tabu search [ 567 ], simulated annealing [ 89 ], scatter search or swarm algorithms including ant colony optimization [ 10 ], particle swarm optimization [ 1112 ] and bees algorithm [ 1314 ].

One of the initiatives followed by many researchers is using evolutionary algorithms for solving quadratic assignment problems [ 315161718 ]. Although these algorithms do not ensure obtaining optimum solutions, they produce good results in a reasonable computation time. In this paper we focus on the quantum-inspired evolutionary algorithm QIEA that draws inspiration from evolutionary computing and quantum computing.

It is worth mentioning that the harnessing of quantum computing to the study of various problems can take two forms.

Introduction

One may choose to adapt some principles of quantum computing in the classical existing approaches. Alternatively, a quantum mechanical hardware may be sought via the studies. In recent years quantum-inspired algorithms have received growing attention. Many researchers have presented various quantum-inspired evolutionary algorithms to solve many optimization problems with success, including image processing [ 19 ], network design problems [ 2021 ], scheduling problems [ 222324 Quantum Population Based Meta Heuristic, 25 ], real and reactive power dispatch [ 26 ], parameter estimation of chaotic systems [ 27 ], parameter selection for support vector machines [ 28 ], community detection on CUDA-enabled GPUs [ 29 ] etc.

Below we provide a brief summary of different methods for solving QAP.

1. Introduction

In many cases, evolutionary algorithms and their hybridizations solved different combinatorial optimization problems quite successfully. In [ 3031 ] a hybrid genetic algorithm and its variants for solving the quadratic assignment problem QAP are studied. Benlic et al. Lalla-Ruiz et al. It should be mentioned that extensive research was carried out on developing various specific modifications of particular components of evolutionary algorithms to increase the EA efficiency, including crossover schemes [ 163637 ] or replacement strategies of the population [ 25 ].]