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Neural Computing and Applications

Memetic quantum evolution algorithm for global optimization

Deyu Tang, Zhen Liu, Jie Zhao, Shoubin Dong, Yongming Cai

Published Aug 19, 2019• 10 citations
Publisher
DOI
10.1007/s00521-019-04439-8

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The effective resolution of non-deterministic polynomial time hard (NP-hard) combinatorial optimization problems requires a delicate balance between global exploration and local exploitation. While Quantum-Inspired Algorithms (QIAs) leverage principles of superposition to explore vast search spaces, they often lack the fine-grained exploitation capabilities of classical heuristics. To address this limitation, we propose the Quantum-Memetic Hybrid Algorithm (QMHA), a component-based framework that synergistically integrates qubit-based global search with adaptive classical refinement. The QMHA architecture explicitly coordinates five distinct algorithmic components: (1) quantum rotation gates for exploration, (2) a problem-aware memetic operator for immediate solution refinement, (3) an adaptive learning rate schedule, (4) periodic local search, and (5) a stagnation-based population reset for diversity management. We rigorously evaluate the framework against nine established metaheuristics, including Genetic Algorithms (GA), Differential Evolution (DE), Particle Swarm Optimization (PSO), Simulated Annealing (SA), Ant Colony Optimization (ACO), MAX-MIN Ant System (MMAS), Memetic Algorithms (MA), Quantum Evolutionary Algorithm (QEA), and Harmony Search (HS), across a comprehensive benchmark suite comprising six NP-hard problem families: constrained combinatorial (Knapsack), graph-based (Max-Cut), permutation-based (TSP), constraint satisfaction (Graph Coloring), bin optimization (Bin Packing), and scheduling (Flow Shop Scheduling), as well as real-world machine learning (Feature Selection) problems and the continuous Congress on Evolutionary Computation (CEC) 2022 benchmark. Statistical analysis using Friedman tests and Nemenyi post hoc comparisons confirms that QMHA achieves a statistically significant performance advantage (p<0.004) and superior average rank (1.5) compared to component baselines and state-of-the-art competitors. Comprehensive analyses include computational complexity profiling, parameter sensitivity mapping, scalability testing up to D=2000, noise robustness evaluation, variable correlation degradation analysis, a six-component ablation study, exploration–exploitation dynamics tracking, integration mechanism comparison across five architectures, and a multi-objective extension feasibility study. The proposed framework offers a robust, verified approach to hybrid optimization without relying on biological metaphors.
We introduce quantum-enhanced memetic tabu search (QE-MTS), a non-variational hybrid algorithm that achieves state-of-the-art scaling for the low-autocorrelation binary sequence (LABS) problem. By seeding the classical MTS with high-quality initial states from digitized counterdiabatic quantum optimization (DCQO), our method suppresses the empirical time-to-solution scaling to O(1.24N)\mathcal{O}(1.24^N)O(1.24N) for sequence length N∈[27,37]N \in [27,37]N∈[27,37]. This scaling surpasses the best-known classical heuristic O(1.34N)\mathcal{O}(1.34^N)O(1.34N) and improves upon the O(1.46N)\mathcal{O}(1.46^N)O(1.46N) of the quantum approximate optimization algorithm, achieving superior performance with a 6×6\times6× reduction in circuit depth. A two-stage bootstrap analysis confirms the scaling advantage and projects a crossover point at N≳47N \gtrsim 47N≳47, beyond which QE-MTS outperforms its classical counterpart. These results provide evidence that quantum enhancement can directly improve the scaling of classical optimization algorithms for the paradigmatic LABS problem.