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.
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.
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 paper explores the application of a quantum-inspired genetic algorithm (QIGA) for solving complex optimization problems. Traditional genetic algorithms (GAs) can struggle with the intricacies of high-dimensional and non-linear problems, often encountering issues with premature convergence and local optima. This research proposes a novel approach where a standard GA is modified to incorporate principles inspired by quantum mechanics, specifically utilizing quantum-inspired concepts such as superposition and interference, to enhance the exploration and exploitation phases. The core claim is that QIGA can effectively tackle complex optimization scenarios. The mechanism involves mapping the original problem into the fitness function of the GA, and subsequently using the QIGA to perform the optimization. The results demonstrate the potential of this hybrid approach to improve solution quality and speed, particularly in problems with challenging characteristics. The research highlights a promising direction for combining classical optimization techniques with quantum-inspired ideas, offering a new tool for tackling computationally intensive optimization tasks. ---
This research explores the application of a Quantum-Inspired Genetic Algorithm (QIGA) to optimize complex systems, utilizing a numerical experiment with a focus on the objective function... The QIGA integrates quantum-inspired principles, including crossover, entanglement, and evolution, to strike a balance between exploration and exploitation within the solution space. A 100-generation experiment with a population size of 50 reveals the algorithm's adaptability and gradual convergence towards optimal solutions. The linear combination crossover, guided by quantum principles, enhances diversity, while entanglement and evolution operations introduce correlations between quantum states. The results underscore the algorithm's potential, prompting discussions on parameter tuning, comparisons with classical algorithms, and considerations for transitioning to real quantum hardware. The findings contribute to the understanding of quantum-inspired optimization and pave the way for further research in quantum computing applications for complex system optimization.
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.
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.
The development in the field of quantum computing gives us a significant edge over classical computing in terms of time and efficiency.This is particularly useful for NP-hard problems such as graph layout problems.Since many real world problems are effectively solved by genetic algorithm (GA) and the performance of GA highly depends upon the setting of its parameters, therefore this paper focuses on a Quantum Inspired Genetic Algorithm (QIGA) and develops and evaluates adaptive strategies for the same.QIGA adapts ideas of Q-bits, superposition of Q-bits from quantum computing.The effectiveness and the applicability of adaptive QIGA is demonstrated by experimental results on the benchmark Knapsack, Maxcut and Onemax combinatorial optimization problems.The results show that adaptive QIGA is superior to QIGAs.