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International Conference on Algorithms, Computing and Systems (ICACS)

Investigating the Dynamical Behavior of Quantum Dynamics Framework Algorithm with the Rastrigin-like Test Benchmark

Limeng Luo, Peng Wang, Minghui Zhao

Published Oct 11, 2024• 0 citations
Publisher

Abstract

With the emergence of various optimization algorithms, studying the specific dynamic evolution process of algorithms is of significant importance for proposing new algorithms and optimizing classical ones. The Quantum Dynamics Framework(QDF) Optimization Algorithm is derived from the Taylor expansion of the Schrödinger equation, providing a rigorous mathematical and physical foundation. Its iterative behavior can reflect the generality of evolution in most optimization algorithms. However, the iteration process of QDF on the multi-modal Rastrigin function faces challenges in convergence, necessitating meticulous evaluation and research of test functions. Therefore, this paper constructs an adjustable, scalable, and diverse Rastrigin-like Test Benchmark (RTB) collection, extending, shifting, and rotating the Rastrigin function in multi-modal scenarios. By viewing the algorithm's iteration process from the perspective of quantum dynamics as the evolution of sampling particles over time, and utilizing RTB to delve into the dynamical behavior of QDF algorithm, this research approach effectively supports the observation and improvement of algorithmic iteration processes, providing fundamental guidance for algorithmic optimization decisions.

DOI
10.1145/3708597.3708618

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With the emergence of various optimization algorithms, studying the specific dynamic evolution process of algorithms is of significant importance for proposing new algorithms and optimizing classical ones. The Quantum Dynamics Framework(QDF) Optimization Algorithm is derived from the Taylor expansion of the Schrödinger equation, providing a rigorous mathematical and physical foundation. Its iterative behavior can reflect the generality of evolution in most optimization algorithms. However, the iteration process of QDF on the multi-modal Rastrigin function faces challenges in convergence, necessitating meticulous evaluation and research of test functions. Therefore, this paper constructs an adjustable, scalable, and diverse Rastrigin-like Test Benchmark (RTB) collection, extending, shifting, and rotating the Rastrigin function in multi-modal scenarios. By viewing the algorithm's iteration process from the perspective of quantum dynamics as the evolution of sampling particles over time, and utilizing RTB to delve into the dynamical behavior of QDF algorithm, this research approach effectively supports the observation and improvement of algorithmic iteration processes, providing fundamental guidance for algorithmic optimization decisions.
In recent years, optimization algorithms have developed rapidly, especially those which introduce quantum ideas, which perform excellently. Inspired by quantum thought, this paper proposes a quantum dynamics framework (QDF) which converts optimization problems into the problem of the constrained ground state of the quantum system and analyzes optimization algorithms by simulating the dynamic evolution process of physical optimization systems in the ground state. Potential energy equivalence and Taylor expansion are performed on the objective function to obtain the basic iterative operations of optimization algorithms. Furthermore, a quantum dynamics framework based on the quantum tunneling effect (QDF-TE) is proposed which adopts dynamic multiple group collaborative sampling to improve the quantum tunneling effect of the QDF, thereby increasing the population diversity and improving algorithm performance. The probability distribution of solutions can be visually observed through the evolution of the wave function, which also indicates that the QDF-TE can strengthen the tunneling effect. The QDF-TE was evaluated on the CEC 2017 test suite and shown to be competitive with other heuristic optimization algorithms. The experimental results reveal the effectiveness of introducing a quantum mechanism to analyze and improve optimization algorithms.
The use of Evolutionary Algorithms (EA) for solving Mathematical/Computational Optimization Problems is inspired by the biological processes of Evolution. Few of the primitives involved in the Evolutionary process/paradigm are selection of ’Fit’ individuals (from a population sample) for retention, cloning, mutation, discarding, breeding, crossover etc. In the Evolutionary Algorithm abstraction, the individuals are deemed to be solution candidates to an Optimization problem and additional solution(/sets) are built by applying analogies to the above primitives (cloning, mutation etc.) by means of evaluating a ’Fitness’ function/criterion. One such algorithm is Differential Evolution(DE) which can be used to compute the minima of functions such as the rastrigin function and rosenbrock function. This work is an attempt to study the result of applying the DE method on these functions with candidate individuals generated on classical Turing modeled computation and comparing the same with those on state of the art Quantum computation.The study benchmarks the convergence of these functions by varying the parameters initialized and reports timing, convergence, and resource utilization results.
Quantum algorithms hold immense potential for revolutionizing various fields, and a key challenge in their development lies in optimizing their performance across diverse input datasets. This paper proposes a novel approach to quantum algorithm optimization centered around a dynamically adaptive optimization framework. We introduce a quantum algorithm that adapts its parameter adjustments based on the characteristics of the input data, achieving improved efficiency and performance through real-time parameter tuning. This system, termed "Quantum Adaptive Tuning," leverages a combination of quantum optimization techniques with a dynamic parameter adjustment mechanism. The core mechanism is to iteratively refine the quantum algorithm's parameters to maximize the likelihood of finding optimal solutions. We present a theoretical analysis and initial experimental validation demonstrating the effectiveness of this approach. The paper concludes with a discussion of the implications of this work and future research directions.
This paper presents a novel framework for iterative optimization that draws inspiration from quantum-inspired algorithms. Traditional optimization methods often struggle with convergence issues, particularly in complex, high-dimensional spaces. This work introduces a quantum-inspired iterative approach, utilizing a novel process of candidate generation and evaluation to accelerate convergence and improve solution quality. We demonstrate the effectiveness of this framework through a series of simulations and analysis, highlighting its potential to overcome limitations of conventional optimization techniques. The core mechanism centers around employing quantum-mechanical concepts to guide the exploration of potential solutions, thereby fostering a more efficient and robust optimization process. This research explores the potential for leveraging quantum-inspired algorithms to achieve superior performance compared to existing methods, specifically targeting scenarios with complex landscapes and high-dimensional parameter spaces.
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.
In recent years, a study focused on the quantum dynamics framework (QDF) process has revealed significant, random structural bias in QDF’s optimization of symmetric and asymmetric forms of double-well functions (DWF). Such bias means that the algorithm tends to favor specific solutions in the search space while ignoring other possible solutions. This tendency may cause the algorithm to become trapped in local optima, preventing it from finding global optima and ultimately compromising its performance. To address this performance gap, this paper proposes a dimension-decoupling sampling mechanism and random-neighborhood sampling mechanism. The proposed mechanism effectively reduces the coupling between dimensions during the optimization of the objective function and increases the search space diversity, thereby mitigating the structural bias of the algorithm. It successfully solves the issue of performance degradation observed in the optimization of symmetric double-well functions. We refer to the modified algorithm as the dimension-decoupling and random-neighborhood quantum dynamics framework (DR-QDF).