QWMO: A Quantum Wave-function Inspired Metaheuristic for Multimodal Optimization

Abstract
This paper introduces QWMO (Quantum Wave-function Metaheuristic Optimizer), a quantum-inspired population-based optimization framework designed to investigate the role of probabilistic operators in balancing exploration and exploitation in multimodal optimization landscapes.

The proposed framework combines three operators: (i) Adaptive Orbital Sampling, which controls Gaussian search dispersion
according to relative solution quality; (ii) Pauli-Inspired Exclusion, which preserves population diversity through orthogonal displacement dynamics; and (iii) Adaptive Quantum Escape, which enables stagnating agents to probabilistically leave local optima through stochastic relocation.

Unlike classical physics-inspired optimizers relying on deterministic force interactions, QWMOmodels search dynamics through wave-function-guided stochastic transitions. Experiments on five representative CEC-style benchmark functions in 30 dimensions with 30 independent runs indicate that QWMO consistently outperforms its direct physics-inspired counterparts ASO and AOS underWilcoxon signed-rank analysis (p < 0.05), while maintaining competitive behavior against classical swarm-based optimizers on multimodal and hybrid landscapes.

An ablation study further shows that QWMO’s behavior emerges from the interaction between adaptive orbital sampling,
diversity-preserving exclusion, and stochastic escape dynamics, rather than from any single operator alone.

Source code and reproducibility materials are available at:
https://github.com/OmerSamuk/QWMO