Investigation of Bare-bones Algorithms from Quantum Perspective: A Quantum Dynamical Global Optimizer

TL;DR

This paper models simple optimization algorithms as quantum physical systems using the Schrödinger equation, revealing their fundamental search behaviors and comparing them with classical bare-bones algorithms.

Contribution

It introduces a quantum perspective to analyze bare-bones algorithms, deriving their basic search behavior through quantum dynamics and validating similarities with classical schemes.

Findings

Quantum-based analysis of search behavior

Derivation of basic iterative process

Comparison with classical bare-bones algorithms

Abstract

Recent decades, the emergence of numerous novel algorithms makes it a gimmick to propose an intelligent optimization system based on metaphor, and hinders researchers from exploring the essence of search behavior in algorithms. However, it is difficult to directly discuss the search behavior of an intelligent optimization algorithm, since there are so many kinds of intelligent schemes. To address this problem, an intelligent optimization system is regarded as a simulated physical optimization system in this paper. The dynamic search behavior of such a simplified physical optimization system are investigated with quantum theory. To achieve this goal, the Schroedinger equation is employed as the dynamics equation of the optimization algorithm, which is used to describe dynamic search behaviours in the evolution process with quantum theory. Moreover, to explore the basic behaviour of the optimization system, the optimization problem is assumed to be decomposed and approximated. Correspondingly, the basic search behaviour is derived, which constitutes the basic iterative process of a simple optimization system. The basic iterative process is compared with some classical bare-bones schemes to verify the similarity of search behavior under different metaphors. The search strategies of these bare bones algorithms are analyzed through experiments.