Quantum-Inspired Algorithms for Optimization Problems: A Research-Oriented Computational Study

Motivated by concepts in quantum mechanics and particle swarm optimization (PSO), quantum-behaved particle swarm optimization (QPSO) was proposed as a variant of PSO with better global search ability. In this paper, a QPSO with weighted mean personal best position and adaptive local attractor (ALA-QPSO) is proposed to simultaneously enhance the search performance of QPSO and acquire good global optimal ability. In ALA-QPSO, the weighted mean personal best position is obtained by distinguishing the difference of the effect of the particles with different fitness, and the adaptive local attractor is calculated using the sum of squares of deviations of the particles’ fitness values as the coefficient of the linear combination of the particle best known position and the entire swarm’s best known position. The proposed ALA-QPSO algorithm is tested on twelve benchmark functions, and compared with the basic Artificial Bee Colony and the other four QPSO variants. Experimental results show that ALA-QPSO performs better than those compared method in all of the benchmark functions in terms of better global search capability and faster convergence rate.

The quantum-behaved particle swarm optimization (QPSO) has better global search capability and is regarded as an extremely effective improvement to the particle swarm optimization (PSO), however, there is still a population diversity decay in its operation. To promote the global search capability of QPSO, based on the weighted quantum-behaved particle swarm optimization (WQPSO) with the concept of weighted average optimal position, an improved QPSO based on particle aggregation-driven bias-average weighting is proposed, which analyses the action mechanism and parameter control law of bias-average weighting from the dimension of Euclidean distance, derives the judgment condition to avoid excessive aggregation of particle population, adopts average distance of particle population as the particle aggregation metric parameter to adjust the weighted bias centre, thus effectively increasing the traversal of the algorithm search space and avoiding premature convergence of the algorithm. The effectiveness of the improved algorithm proposed in this paper is demonstrated by applying several conventional test functions and comparing the analysis with PSO, QPSO and WQPSO.

This paper proposes a new parallel evolutionary algorithm called parallel quantum-inspired genetic algorithm (PQGA). Quantum-inspired genetic algorithm (QGA) is based on the concept and principles of quantum computing such as qubits and superposition of states. Instead of binary, numeric, or symbolic representation, by adopting the qubit chromosome as a representation, QGA can represent a linear superposition of solutions due to its probabilistic representation. QGA is suitable for parallel structures because of rapid convergence and good global search capability. That is, QGA is able to possess the two characteristics of exploration and exploitation simultaneously. The effectiveness and the applicability of PQGA are demonstrated by experimental results on the knapsack problem, which is a well-known combinatorial optimization problem. The results show that PQGA is superior to QGA as well as other conventional genetic algorithms.

Estimation of parameters of chaotic systems is a subject of substantial and well-developed research issue in nonlinear science. From the viewpoint of optimization, parameter estimation can be formulated as a multi-modal constrained optimization problem with multiple decision variables. This investigation makes a systematic examination of the feasibility of applying a newly proposed population-based optimization method labeled here as teaching---learning-based optimization (TLBO) to identify the unknown parameters for a class of chaotic system. The preliminary test demonstrates that despite its global fast coarse search capability, teaching---learning-based optimization often risks getting prematurely stuck in local optima. To enhance its fine (local) searching performance of TLBO, Nelder---Mead simplex algorithm-based local improvement is incorporated into TLBO so as to continually search for the global optima through the reflection, expansion, contraction, and shrink operators. Working with the well-established Lorenz system, we assess the effectiveness and efficiency of the proposed improved TLBO strategy. The empirical results indicate the success of the proposed hybrid approach in which the global exploration and the local exploitation are well balanced, providing the best solutions for all instances used over other state-of-the-art metaheuristics for chaotic identification in literature, including particle swarm optimization, genetic algorithm, and quantum-inspired evolutionary algorithm.

Due to the nonlinear of the Black-Scholes option pricing model, r and σ were not easy to be solved by analytic method. Quantum-behaved Particle Swarm Optimization (QPSO) algorithm was proposed to estimate the parameters because of its global search ability and robustness. In the process of optimization, Black-Scholes option pricing formula was used as the research object to establish the algorithm model of parameter estimation and weighted sum of squared errors between experimental values and predicted values was used as the objective optimization function. Experimental results show that QPSO algorithm is more effectively than Particle Swarm Optimization (PSO) algorithm and Deferential Evolution (DE) algorithm.

An improved quantum-inspired evolutionary algorithm for coding resource optimization based network coding multicast scheme

In this paper, we propose a novel Urban Heat Island detection method in which a Quantum-Inspired Genetic Algorithm is executed to determine the optimal initialization of the cluster centres in Fuzzy C-Means. Our method aims to overcome limitations related to sensitivity to initial cluster centres in traditional FCM improving the accuracy of the urban heat islands detected. The method is implemented in a GIS-based framework and was tested using Landsat 8-derived Land Surface Temperature and Normalized Difference Vegetation Index data for the city of Naples, Italy. Experimental results show that the proposed method leads to higher clustering accuracy and better identification of critical urban heat zones compared to classical approaches. The results highlight the potential of Quantum Inspired algorithms as practical tools for enhancing environmental data analysis and supporting urban climate resilience strategies.

Feature selection (FS) has garnered significant attention because of its pivotal role in enhancing the efficiency and effectiveness of various machine learning and data mining algorithms. Concurrently, multiobjective feature selection (MOFS) algorithms strive to balance the complexity of multiple optimization objectives during the FS process. These include minimizing the number of selected features while maximizing classification performance. Nonetheless, managing the complexity of feature combinations presents a formidable challenge, particularly in high-dimensional datasets. Evolutionary algorithms (EAs) are increasingly adopted in MOFS owing to their exceptional global search capabilities and robustness. Despite their strengths, EAs face difficulties in navigating expansive solution spaces and achieving a balance between exploration and exploitation. To address these challenges, this study introduces a novel information gain-based EA for MOFS, designated as IGEA. This approach utilizes a clustering method for selecting a diverse parent population, thereby enhancing individual variability and maintaining a high-quality population. Considerably, IGEA employs information gain as a metric to evaluate the contribution of features to classification tasks. This metric informs crucial operations such as crossover and mutation. Moreover, the study extensively examines the actual solutions derived from IGEA, focusing on feature correlation and redundancy. This analysis illuminates IGEA's adept handling of these aspects to refine MOFS. Experimental results on 23 widely used classification datasets confirm IGEA's superiority over five other state-of-the-art algorithms, demonstrating its enhanced effectiveness and efficiency in complex MOFS scenarios.

State of health prediction of lithium-ion batteries under early partial data based on IWOA-BiLSTM with single feature

The optimization of beer recipe is a powerful approach to improve the efficiency of beer company. But for recipe optimization problems, the traditional mathematical optimization methods achieve more complex and lack the robust search for the optimal solution. Ant colony algorithm (ACA) is fit to solve the combinatorial optimization problems, but it has disadvantage of slow convergence and time-consuming in the process of evolution. Therefore, the variable scale ant colony algorithm was presented and the scope of search is shorted constantly in the iterative process to improve the efficiency of optimization in the paper. Then the study of new ACA of the optimization of beer recipe is also presented, which meet production targets, and achieve the lowest total cost of the raw materials. Simulation results show that comparing with the traditional ACA, the improved ACA has more global search capability and better robustness, and it also has practical value because of its easy implementation.

Quantum machine learning (QML) has emerged as a promising domain to leverage the computational capabilities of quantum systems to solve complex classification tasks. In this work, we present the first comprehensive QML study by benchmarking the MedMNIST-a diverse collection of medical imaging datasets on a 127-qubit real IBM quantum hardware, to evaluate the feasibility and performance of quantum models (without any classical neural networks) in practical applications. This study explores recent advancements in quantum computing such as device-aware quantum circuits, error suppression, and mitigation for medical image classification. The proposed methodology is comprised of three stages: preprocessing, generation of noise-resilient and hardware-efficient quantum circuits, optimizing/training of quantum circuits on classical hardware, and inference on real IBM quantum hardware. Firstly, we process all input images in the preprocessing stage to reduce the spatial dimension due to quantum hardware limitations. We generate hardware-efficient quantum circuits using backend properties expressible to learn complex patterns for medical image classification. After classical optimization of QML models, we perform inference on real quantum hardware. We also incorporate advanced error suppression and mitigation techniques in our QML workflow, including dynamical decoupling (DD), gate twirling (Twir), and matrix-free measurement mitigation (M3) to mitigate the effects of noise and improve classification performance. The experimental results showcase the potential of quantum computing for medical imaging and establish a benchmark for future advancements in QML applied to healthcare.

Optimization is one of the most important problems in engineering applications. Substantial algorithms have been proposed to tackle these problems, such as differential evolution(DE), which has excellent global search capability and robustness. However, like most metaheuristics, differential evolution is computationally expensive and difficult to converge to the exact global optimum. The modified Powell(MP) method is a derivative-free local optimization algorithm with fast convergence speed but is prone to fall into the local optimum trap. Combining the advantages of these two algorithms, we propose a hybrid optimization algorithm, which is called the DEMP algorithm. The DEMP algorithm is compared to other three well-known optimization algorithms by a set of benchmark functions. The results show that DEMP is not only notably better than the traditional DE Algorithm, but also highly competitive for other metaheuristic algorithms.

To address issues of local optimization, slow convergence, and poor accuracy, this work introduces a time-optimal trajectory planning method using the Adaptive Gold Search algorithm (AGS). The method enhances algorithm diversity and escapes local optima through elite reverse strategy population initialization. It employs an adaptive nonlinear decreasing factor for a balance between linearity and nonlinearity, improving accuracy and convergence speed. The golden sinusoidal variation technique enhances global search capabilities and robustness in robot arm trajectory planning. Experimental results show that the AGS algorithm produces smooth joint angular displacement, acceleration, velocity, and jerk curves. It outperforms the GA, PSO, GOOSE, and GWO algorithms in time optimization by 13.31%, 13.61%, 5.34%, and 4.73%, respectively, effectively reducing trajectory planning time.

To achieve rapid and accurate identification of genetically modified (GM) and non-GM rapeseed oils, a support vector machine (SVM) model based on an improved mayfly optimization algorithm and coupled with the terahertz time-domain spectroscopy, is proposed. Two types of GM rapeseed oils and two types of non-GM rapeseed oils are selected as research subjects. Their spectral information is acquired by using the terahertz time-domain spectroscopy. The observations show that GM rapeseed oils exhibit stronger terahertz absorption characteristics than non-GM rapeseed oils. However, their absorption spectra are highly similar, making direct differentiation difficult through visual inspection alone. Therefore, SVM is used for spectral recognition. Considering that the classification performance of SVM is significantly affected by its parameters, the mayfly optimization algorithm is combined to optimize these parameters. Furthermore, adaptive inertia weight and Lévy flight strategies are introduced to enhance the global search capability and robustness of the mayfly optimization algorithm, thus addressing the issue of easily becoming trapped in local optima in the optimization process. Moreover, principal component analysis is used to reduce the dimensionality of the absorbance data in a 0.3–1.8 THz range, aiming to extract critical features, thereby enhancing modeling efficiency and reducing redundancy in spectral data. Experimental results demonstrate that the improved mayfly optimization algorithm effectively identifies the optimal parameter combination for SVM, thereby enhancing the overall performance of the identification model. The proposed SVM model, in which the improved mayfly optimization algorithm is used, can achieve a recognition accuracy of 100% for the four types of rapeseed oils, surpassing the 98.15% accuracy achieved by the SVM model with the original mayfly optimization algorithm. Thus, this study presents a rapid and effective new approach for identifying GM rapeseed oils and offers a valuable reference for identifying other genetically modified substances.

This study develops a novel Q-learning-based hyperheuristic (QHH) to effectively solve the distributed flowshop group scheduling problem (DFGSP). A modified NEH-based initialization method is introduced to accelerate the early-stage search. A diverse collection of low-level heuristics, designed under the principles of critical factories and critical jobs, is then employed to strengthen the algorithm's exploration capacity. Subsequently, Q-learning is utilized as the high-level strategy to autonomously identify and execute optimal actions. To avoid premature convergence, simulated annealing is embedded into the framework, improving global search capability and robustness. Moreover, an enhanced local search is incorporated to refine solutions and reinforce exploitation. Extensive computational experiments conducted on 810 benchmark instances demonstrate that the proposed QHH significantly outperforms existing advanced algorithms.