Quantum-inspired optimization faces limits on complex continuous problems
Landscape Limits of Quantum-Inspired Evolutionary Optimization across 256 continuous functions
Neural and Evolutionary Computing
Summary
Finding the best solution in complex problems often involves trying many options. The paper looks at a special method inspired by quantum computing called quantum-inspired evolutionary optimization (QIEO) that tries to find good solutions efficiently. The authors tested QIEO on 256 different challenging problem types and compared it to other algorithms. They discovered where QIEO works well and where its way of handling each variable separately limits its performance.
What this means in practice
- •For engineering design teams: Choose the best optimization method for multi-variable continuous design problems by understanding QIEO's strengths and weaknesses across problem types.
- •For operations planners: Improve planning algorithms by matching QIEO variants to problem characteristics for potentially better computational efficiency.
Authors
Rishi Govind, Ferdin Sagai Don Bosco, Kasturi Venkata Srikanth, Aman Mittal, Abhishek Singh, Aditya Singh, Abhishek Chopra
Abstract
Quantum-inspired evolutionary optimization (QIEO) represents design variables as a set of qubits and searches a continuous, multi-dimensional landscape through rotation of the qubit's amplitude pair. Every generation rotates those amplitudes toward a single elite, which corresponds to that generation's best. The update is cheap, almost parameter-free, and well-suited for massive parallel implementation, which has encouraged its adoption in engineering, design, and planning applications. However, there are critical issues with this formulation, principally, the treatment of design variables as independent probability components which make it incapable of exploiting local curvature, anisotropy, or variable coupling. Despite this, QIEO is believed to hold promise, and has been used extensively to solve real-world problems, with significant qualitative and computational advantage over its classical counterpart, Genetic Algorithm (GA). A collection of 256 (actually 508; 256 unshifted + 252 shifted, 4 could not be shifted) continuous function are selected from the prior works, in such a way that they represent eleven landscape characteristics, namely continuity, differentiability, separability, scalability, modality, convexity, conditioning, symmetry, maximum dimensionality, dimension dependency, and the coupling pattern of the design variables. These functions are then solved by three QIEO variants, two GA encodings and Hansen's Covariance Matrix Adaptation Evolution Strategy (CMA-ES). The results are evaluated in terms of computational cost, solution precision, and specialization across landscape characteristics. They identify the conditions under which QIEO provides competitive performance, clarify where its independent-variable representation becomes limiting, and establish whether particular QIEO variants offer advantages for specific landscape characteristics.