This article presents a new approach to the implementation of a quantum-inspired genetic algorithm for numerical optimization to find the global maximum of the objective function based on high-dimensional quantum states by simulating the performance of quantum calculations under the influence of the NISQ-era quantum decoherence process. In order to carry out quantum operations of rotation of states of multilevel quantum systems, a density matrix based on Heisenberg-Weil operators is presented as an analogue of the Bloch sphere for qudits. The simulation of quantum decoherence is considered as the influence of extraneous noise from the environment on the qudit and is presented in the form of the use of a normal random variable with zero mathematical expectation and unit variance in quantum gates. The paper also presents a detailed pseudocode for the functioning of the updated quantum-inspired genetic algorithm for numerical optimization and a description of its individual operations. Testing is carried out by conducting computational experiments with the implementation of an updated algorithm on two-dimensional and multidimensional functions of test optimization problems and when solving a practical problem of increasing the accuracy of prediction based on compact extreme learning machines. The results of the experiments demonstrate the superiority of the new algorithm over the usual quantum-inspired genetic algorithm and classical optimization algorithms in the accuracy of the solution and the execution time of the algorithm.
This article presents a new approach to the implementation of a quantum-inspired genetic algorithm for numerical optimization to find the global maximum of the objective function based on high-dimensional quantum states by simulating the performance of quantum calculations under the influence of the NISQ-era quantum decoherence process. In order to carry out quantum operations of rotation of states of multilevel quantum systems, a density matrix based on Heisenberg-Weil operators is presented as an analogue of the Bloch sphere for qudits. The simulation of quantum decoherence is considered as the influence of extraneous noise from the environment on the qudit and is presented in the form of the use of a normal random variable with zero mathematical expectation and unit variance in quantum gates. The paper also presents a detailed pseudocode for the functioning of the updated quantum-inspired genetic algorithm for numerical optimization and a description of its individual operations. Testing is carried out by conducting computational experiments with the implementation of an updated algorithm on two-dimensional and multidimensional functions of test optimization problems and when solving a practical problem of increasing the accuracy of prediction based on compact extreme learning machines. The results of the experiments demonstrate the superiority of the new algorithm over the usual quantum-inspired genetic algorithm and classical optimization algorithms in the accuracy of the solution and the execution time of the algorithm.
The genetic algorithm for numerical optimization (GA) of the metaheuristic class is a method for finding optimal solutions based on the biological principles of natural selection and variability. GA is characterized by high operating speed, resistance to noise in the data, low probability of hitting the local extremum of the multimodal objective function, as well as the simultaneous application of probabilistic and deterministic rules for generating search space points. An alternative to the classical GA is the quantum-inspired genetic algorithm for numerical optimization (QIGA), which has advantages that are unattainable for GA by using the concepts and principles of quantum computing. The article proposes a new approach to the implementation of a quantum-inspired genetic numerical optimization algorithm for searching for the global maximum of the objective function, based on modeling the functioning of the GA by simulating the execution of quantum calculations based on qudit in the conditions of the existence of quantum decoherence in the era of noisy medium-scale quantum algorithms. For this purpose, to carry out quantum operations of rotating the states of multilevel quantum systems, the paper presents a density matrix based on Heisenberg–Weyl operators as an analogue of the Bloch sphere for qudits. The simulation of quantum decoherence is interpreted from the point of view of the influence of extraneous noise emanating from the environment on the qudit and is presented as the use of a normal random variable with zero mathematical expectation and unit variance in quantum gates. At the same time, the work presents detailed pseudocodes of the functioning of both the most modified quantum-inspired genetic algorithm for numerical optimization and its individual operations. Testing is carried out by conducting computational experiments with the implementation of a modified algorithm on two-dimensional and multidimensional functions of test optimization problems, as well as when solving an applied optimization problem of planning hybrid flow production in the manufacturing industry based on financial costs and solving the problem of increasing forecasting accuracy based on compact extreme learning machines. The experimental results demonstrate the superiority of the new algorithm over QIGA and classical optimization algorithms in the accuracy of the solution, the speed of convergence with the target value of the global maximum and the execution time of the algorithm.
We present a new evolutionary algorithm on the basis of quantum computations technology for solving optimization problems. The algorithm is built using many-valued quantum logic concept, which is more prospective from the computing power’s point of view. We compare the suggested algorithm to the traditional quantum genetic algorithm to demonstrate its high effectiveness on the example of test function global optimization problems. The advantages can be observed in the running time, the convergence speed, and the solution precision. The proposed implementation for the algorithm of quantum gate operator has an adaptive nature and does not require a lookup table. The role and the influence mechanism of the quantum disaster operator on the proposed algorithm effectiveness are also analyzed.
Quantum genetic algorithms(QGA) typically construct traditional quantum chromosomes as independent quantum bit systems, which has facilitated the enhancement of search speed and precision in genetic algorithms, demonstrating powerful problem-solving capabilities in optimization issues. Although traditional QGA have enriched population diversity, they still tend to fall into local optima, and the evolutionary update operations require rotation directions to be determined by lookup tables, a process involving multiple conditional judgments that affect algorithm efficiency. To address these issues, an improved method has been proposed to further enhance the performance of QGA. In the initial population selection, a population grouping evolution method based on microhabitat coevolution strategy is used to prevent the algorithm from getting trapped in local optima when solving complex function problems. Additionally, quantum entanglement is introduced on top of quantum super-position by implementing quantum entanglement using quantum registers, and higher-order quantum rotation gates are employed that do not involve multiple conditional judgments of lookup tables, thus improving the efficiency of quantum chromosome measurement and evolutionary updates. Finally, traditional QGA and higher-order quantum genetic algorithms were applied to test functions in multiple experiments. The results indicate that, compared to traditional QGA, the higher-order quantum genetic algorithms have achieved an increase in convergence speed, an approximate 14.3% improvement in convergence precision, and possess enhanced global search capabilities.
Large-scale optimization (LSO) problems—those with hundreds to thousands of decision variables—are prevalent in engineering design, logistics, telecommunications, and machine learning hyperparameter search. Classical evolutionary algorithms often struggle in this regime due to premature convergence and prohibitive search costs. This manuscript presents a Quantum-Inspired Genetic Algorithm (QIGA) that transfers three ideas from quantum computation into a purely classical algorithm: (i) Q-bit angle encoding that maintains a compact, uncertainty-aware distribution over decision values, (ii) rotation-gate adaptation that updates search probabilities toward promising regions while preserving exploration, and (iii) quantum observation that draws diverse candidate solutions from the encoded amplitudes at each generation. We further couple the core QIGA with (a) an island-model decomposition for ultra-high dimensionality, (b) surrogate-assisted local refinement for exploitation at low cost, and (c) a feasibility-aware penalty for constraints. We evaluate the approach on five canonical continuous benchmarks in 1,000 dimensions (Sphere, Rosenbrock, Rastrigin, Ackley, Griewank) under a fixed computational budget. Across 30 independent runs per function, QIGA achieves lower final objective values and higher success rates than classical GA, PSO, and DE baselines. A non-parametric Wilcoxon signed-rank test indicates statistically significant improvements for QIGA (adjusted p < 0.01) on all functions. We analyze the algorithm’s scaling behavior, the role of angle-space step control, and the contribution of island-level diversity. The results suggest that quantum-inspired probability evolution provides a robust inductive bias for LSO by decoupling representation capacity from point estimates and by enabling distribution-aware search moves. We conclude with practical guidelines for tuning and discuss extensions to constrained and mixed-variable problems.
Genetic algorithms are heuristic optimization techniques inspired by Darwinian evolution. Quantum computation is a new computational paradigm which exploits quantum resources to speed up information processing tasks. Therefore, it is sensible to explore the potential enhancement in the performance of genetic algorithms by introducing quantum degrees of freedom. Along this line, a modular quantum genetic algorithm has recently been proposed, with individuals encoded in independent registers comprising exchangeable quantum subroutines [1], which leads to different variants. Here, we address the numerical benchmarking of these algorithms against classical genetic algorithms, a comparison missing from previous literature. To overcome the severe limitations of simulating quantum algorithms, our approach focuses on measuring the effect of quantum resources on the performance. In order to isolate the effect of the quantum resources on the performance, we selected the classical variants to resemble the fundamental characteristics of the quantum genetic algorithms. Under these conditions, we encode an optimization problem in a two-qubit Hamiltonian and face the problem of finding its ground state. A numerical analysis based on a sample of 200 random cases shows that some quantum variants outperform all classical ones in convergence speed towards a near-optimal result. Additionally, we have considered a diagonal Hamiltonian and the Hamiltonian of the hydrogen molecule to complete the analysis with two relevant use-cases. If this advantage holds for larger systems, quantum genetic algorithms would provide a new tool to address optimization problems with quantum computers.
In this paper, we present a novel quantum-inspired genetic algorithm with expanded solution space. Based on the double chains quantum genetic algorithm (DCQGA), we have expanded the solution space by increasing the number of solution space transformation functions. And we propose a novel method for quantum rotation gate's update by using the sign function and the gradient of objective function. With this method we can automatically determine the direction of quantum rotation gate and adaptively adjust the magnitude of quantum rotation gate. Through experimenting on 2 benchmark problem in the optimization literature: Rosenbrock function and Schaffer's F6 function, we demonstrate that our expanded solution space quantum genetic algorithm (ESSQGA) has achieved more satisfactory results than DCQGA and common genetic algorithm.