A multi-start quantum-inspired evolutionary algorithm for solving combinatorial optimization problems

Quantum-inspired evolutionary algorithm (QEA) has been designed by integrating some quantum mechanical principles in the framework of evolutionary algorithms. They have been successfully employed as a computational technique in solving difficult optimization problems. It is well known that QEAs provide better balance between exploration and exploitation as compared to the conventional evolutionary algorithms. The population in QEA is evolved by variation operators, which move the Q-bit towards an attractor. A modification for improving the performance of QEA was proposed by changing the selection of attractors, namely, versatile QEA. The improvement attained by versatile QEA over QEA indicates the impact of population structure on the performance of QEA and motivates further investigation into employing fine-grained model. The QEA with fine-grained population model (FQEA) is similar to QEA with the exception that every individual is located in a unique position on a two-dimensional toroidal grid and has four neighbors amongst which it selects its attractor. Further, FQEA does not use migrations, which is employed by QEAs. This paper empirically investigates the effect of the three different population structures on the performance of QEA by solving well-known discrete benchmark optimization problems.

An important problem in the study of evolutionary algorithms is how to continuously predict promising solutions while simultaneously escaping from local optima. In this paper, we propose an elitist probability schema (EPS) for the first time, to the best of our knowledge. Our schema is an index of binary strings that expresses the similarity of an elitist population at every string position. EPS expresses the accumulative effect of fitness selection with respect to the coding similarity of the population. For each generation, EPS can quantify the coding similarity of the population objectively and quickly. One of our key innovations is that EPS can continuously predict promising solutions while simultaneously escaping from local optima in most cases. To demonstrate the abilities of the EPS, we designed an elitist probability schema genetic algorithm and an elitist probability schema compact genetic algorithm. These algorithms are estimations of distribution algorithms (EDAs). We provided a fair comparison with the persistent elitist compact genetic algorithm (PeCGA), quantum-inspired evolutionary algorithm (QEA), and particle swarm optimization (PSO) for the 0---1 knapsack problem. The proposed algorithms converged quicker than PeCGA, QEA, and PSO, especially for the large knapsack problem. Furthermore, the computation time of the proposed algorithms was less than some EDAs that are based on building explicit probability models, and was approximately the same as QEA and PSO. This is acceptable for evolutionary algorithms, and satisfactory for EDAs. The proposed algorithms are successful with respect to convergence performance and computation time, which implies that EPS is satisfactory.

In this paper, we propose a novel quantum-inspired evolutionary algorithm, called quantum-inspired Tabu search (QTS). QTS is based on the classical Tabu search and the characteristic of quantum computation such as superposition. We will present how we implement QTS to solve 0/1 knapsack problem. Furthermore, the results of experiments are also compared with other quantum-inspired evolutionary algorithm and other heuristic algorithms' experimental results. The final outcomes show that QTS performs much better than the other heuristic algorithms on 0/1 knapsack problem, without premature convergence and more efficiency.

This study proposes a novel quantum evolutionary algorithm called four‐chain quantum‐inspired evolutionary algorithm (FCQIEA) based on the four gene chains encoding method. In FCQIEA, a chromosome comprises four gene chains to expand the search space effectively and promote the evolutionary rate. Different parameters, including rotational angle and mutation probability, have been analyzed for better optimization. Performance comparison with other quantum‐inspired evolutionary algorithms (QIEAs), evolutionary algorithms, and different chains of QIEA demonstrates the effectiveness and efficiency of FCQIEA.

Quantum rotation gate in quantum-inspired evolutionary algorithm: A review, analysis and comparison study

Based on a quantum-inspired evolutionary algorithm for unit commitment, this paper proposed ways to advance the efficiency and robustness of the algorithm so that its capacity for application in large-scale unit commitment problems can be significantly enhanced. The paper develops an advanced quantum-inspired evolutionary unit commitment algorithm by developing a new initialization method based on unit priority list and a special Q-bit expression for ensuring diversity in the initial search area for improving the efficiency of solution searching. Different techniques such as multi-observation, single-search, and group-search are also proposed for incorporation in the advanced algorithm. The advanced algorithm is tested and compared with the earlier quantum-inspired evolutionary algorithm and a number of known methods through its applications to test systems with up to 100 generator units for a 24-h scheduling horizon.

Quantum-inspired evolutionary algorithms, one of the three main research areas related to the complex interaction between quantum computing and evolutionary algorithms, are receiving renewed attention. A quantum-inspired evolutionary algorithm is a new evolutionary algorithm for a classical computer rather than for quantum mechanical hardware. This paper provides a unified framework and a comprehensive survey of recent work in this rapidly growing field. After introducing of the main concepts behind quantum-inspired evolutionary algorithms, we present the key ideas related to the multitude of quantum-inspired evolutionary algorithms, sketch the differences between them, survey theoretical developments and applications that range from combinatorial optimizations to numerical optimizations, and compare the advantages and limitations of these various methods. Finally, a small comparative study is conducted to evaluate the performances of different types of quantum-inspired evolutionary algorithms and conclusions are drawn about some of the most promising future research developments in this area.

The quantum-inspired evolutionary algorithm (QEA) uses several quantum computing principles to optimize problems on a classical computer. QEA possesses a number of quantum individuals, which are all probability vectors. They work well for linear problems but fail on problems with strong interactions among variables. Moreover, many optimization problems have multiple global optima. And because of the genetic drift, these problems are difficult for evolutionary algorithms to find all global optima. Local and global migration that QEA uses to synchronize different individuals prevent QEA from finding multiple optima. To overcome these difficulties, we proposed a quantum-inspired evolutionary algorithm with linkage learning (QEALL). QEALL uses a modified concept-guide operator based on low order statistics to learn linkage. We also replaced the migration procedure by a niching technology to prevent genetic drift, accordingly to find all global optima and to expedite convergence speed. The performance of QEALL was tested on a number of benchmarks including both unimodal and multimodal problems. Empirical evaluation suggests that the proposed algorithm is effective and efficient.

Autoimmune hepatitis (AIH) is an inflammatory liver disease with an undiscovered cause that is attributed to the promiscuous humoral as well as cellular immune response against homologous self-antigens. If AIH is not diagnosed and treated in its early stages, it can result in cirrhosis or liver failure. In this regard, we propose a novel algorithm based on fuzzy cognitive maps (FCM) for paving the way for accurate diagnosis of it. For doing so, major and innate characteristics of AIH which play a significant role in diagnosing it, in addition to the data of 216 samples-suffering from AIH-have been gathered by the help of three pathologists. Then, we have applied our developed FCM solution on obtained data in order to classify them in one the definite AIH or improbable AIH classes. Our devised algorithm utilizes quantum inspired evolutionary algorithm (QEA) as a link reduction tool as well as particle swarm optimization algorithm as a link tuning mean. In the QEA, instead of coding the presence and absence of links between concepts with 1 and 0, respectively, the probability of their existence or inexistence is modeled with a Q-bit (the smallest information unit in the QEA) and, depending on the outcome of objective function, the quantum state of these Q-bits are updated. Using a probabilistic representation instead of 0 and 1, in addition to creating diversity in the solution space, can lead to escapes from many local optima; which is an issue of concern in the optimization of FCM structure. Experimental results show that not only does our developed algorithm make accurate diagnosis, but it outperforms other conventional methods as well.

This paper investigates the problem of minimizing the network coding resources while achieving the desired throughput in a multicast scenario. Since quantum-inspired evolutionary algorithm (QEA), a combination of quantum computing and evolutionary algorithm, can address NP-hard problem and is considered powerful in terms of global optimization, we propose an attempt to adapt QEA to avoid the computational complexity that makes the above problem NP-hard. The effectiveness and the applicability of QEA are demonstrated by carrying out simulation over a number of network topologies.

For describing nonlinear system accurately and improving adaptive neuro-fuzzy inference system model, a quantum-inspired evolutionary algorithm is presented for optimizing parameters of adaptive neuro-fuzzy inference system. In this paper, an allele real-coded quantum evolutionary algorithm is introduced to optimize the premise and consequent parameters of adaptive neuro-fuzzy inference system. The real-coding method based on allele is adopted, and variable-scale updating strategy of parameter is employed. As a result, the parameter falling into local minimum is avoided. The model accuracy of adaptive neuro-fuzzy inference system is improved. The simulation examples show the effectiveness of proposed method. The proposed improved algorithm is compared with the standard adaptive neuro-fuzzy inference system. Finally, the proposed adaptive neuro-fuzzy inference system model is applied to predict the quality index in textile slashing process.

In ordinary statistical methods, multiple outliers in least-squares regression model are detected sequentially one after another, where smearing and masking effects give misleading results. If the potential multiple outliers can be detected simultaneously, smearing and masking effects can be avoided. Such multiple-case outlier detection is of combinatorial nature and 2 N – 1 sets of possible outliers need to be tested, where N is the number of data points. This exhaustive search is practically impossible. Like other combinatorial applications, evolutionary algorithms may play a vital role in multiple-case outlier detection problem. In this paper, we have used Quantum-inspired Evolutionary Algorithm (QEA) for multiple-case outlier detection in least-squares regression model. An information-criterion-based fitness function incorporating extra penalty for number of potential outliers has been used for identifying the most appropriate set of potential outliers. Experimental results with four data sets from statistical literature show that the QEA effectively detects the most appropriate set of outliers.

Quantum-Inspired Evolutionary Algorithmにおける量子ビット表現に基づく整数型遺伝子表現法の基礎検討

Machine learning techniques have achieved remarkable development in recent years. However, the performance of many machine learning models usually involves careful tuning of hyperparameters. The hyperparameter optimization (HPO) is usually a high-dimensional black box optimization problem and often faces expensive function evaluations. Besides, the task of HPO has gained great attention in academy and industry. In this paper, a novel method for hyperparameter optimization is proposed, referred to as surrogate model assisted quantum-inspired evolutionary algorithm (SA-QEA), which incorporates the principles of quantum-inspired evolutionary algorithm (QEA) and an efficient search framework based on a surrogate model. In the proposed algorithm, we adopt a single individual QEA with neighborhood exploration as the evolution scheme to generate the candidate solutions, and multivariate adaptive regression splines (MARS) is used as a surrogate to approximate the objective function around the individuals. Through conducting comprehensive experimental evaluations on two benchmark problems and three machine learning models, we test our proposed algorithm and compare it with other widely used methods. The results achieve competitive performance and demonstrate the effectiveness of SA-QEA for hyperparameter optimization.

Quantum-inspired algorithms (QIAs) are computationally efficient algorithms that generate a quantum model in classical hardware as an alternative to the use of quantum models. In this research paper, the researchers carried out an experimental appraisal of four quantum-inspired algorithms in quantum-inspired Evolutionary Algorithm (QEA), quantum-behaved Particle Swarm Optimization (QPSO), quantum-inspired Genetic Algorithm (QIGA) and quantum Simulated Annealing (QSA) on benchmark optimization functions. The introduction of a simulation-based methodology was done in Python to test the convergence speed, global search capability, accuracy and robustness. According to the experimental findings, QPSO always performs well compared with other methods in the achievement of faster convergence and enhanced global optimality, but QEA is highly successful in cases of discrete combinatorial problems. The paper concludes that quantum-inspired models are effective in modeling the key quantum concepts like probabilistic superposition and tunneling to attain high quality optimization results with conventional computing platforms. Such results demonstrate the opportunities of QIAs as scalable pre-quantum tools of designing, AI, and industrial optimization.