Quantum-Inspired Genetic Algorithms for Large-Scale Optimization

Abstract

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.