A Quantum-Memetic Hybrid Framework for Combinatorial Optimization: Synergistic Integration of Superposition-Based Exploration with Adaptive Exploitation

Abstract

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.