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IEEE Congress on Evolutionary Computation (CEC)

Quantum Differential Evolution: an Investigation

Kangjing Li, Saber Mohammed Elsayed, Ruhul Amin Sarker, Daryl Essam

Published Jun 1, 2019• 6 citations
Publisher

Abstract

Several research studies have been carried out on the integration of quantum operators and evolutionary algorithms. However, the performance of such integration remains questionable and needs further research for drawing a useful conclusion. Therefore, this paper takes a step forward to analyze the effect of integrating quantum entanglement and quantum NOT gate with the well-known differential evolution algorithm. The performance of different algorithm designs has been evaluated by solving a number of unconstrained real parameter single objective optimization problems. Although the integration of quantum entanglement helps to get competitive results, the overall experimental results with quantum operators are not convincing enough, especially when there are no inter-dependency among decision variables. This in turn opens up new research directions to deepen the knowledge in the design of quantum evolutionary algorithms.

DOI
10.1109/cec.2019.8790303

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Several research studies have been carried out on the integration of quantum operators and evolutionary algorithms. However, the performance of such integration remains questionable and needs further research for drawing a useful conclusion. Therefore, this paper takes a step forward to analyze the effect of integrating quantum entanglement and quantum NOT gate with the well-known differential evolution algorithm. The performance of different algorithm designs has been evaluated by solving a number of unconstrained real parameter single objective optimization problems. Although the integration of quantum entanglement helps to get competitive results, the overall experimental results with quantum operators are not convincing enough, especially when there are no inter-dependency among decision variables. This in turn opens up new research directions to deepen the knowledge in the design of quantum evolutionary algorithms.
The Differential Evolution (DE) algorithm is an efficient algorithm with strong search capability. This algorithm is easy to implement and used for solving large-scale optimization problems. However, DE also has drawbacks of insufficient diversity in the later search stage, while solving optimization problems, slow convergence speed, and a high search stagnation possibility. Quantum Entanglement inspired Differential Evolution algorithm (QE-DE) has been proposed in this paper to solve the drawbacks of DE. For solving high-dependency optimization problems, QE-DE integrates entangled states in its Qubits (or quantum bit). The optimization process is further accelerated by utilizing the quantum local search. The proposed QE-DE algorithm is evaluated on the IEEE Congress of Evolutionary Computing (CEC 2017) benchmark set for 10 and 30-dimensions. QE-DE is also compared with existing variants of DE and some other popular algorithms. QE-DE outperforms the performance comparison results.
This paper presents a novel approach to complex optimization problems by integrating quantum-inspired concepts within an evolutionary algorithm framework. Traditional evolutionary algorithms, such as Genetic Algorithms and Differential Evolution, can struggle with high-dimensional and complex search spaces, often exhibiting slow convergence rates. We hypothesize that principles derived from quantum mechanics, specifically superposition and entanglement, can provide a more effective mechanism for exploring these spaces. Our proposed Quantum-Inspired Evolutionary Algorithm (QIEA) incorporates operators designed to mimic quantum interference and entanglement, allowing for a more nuanced and potentially faster exploration of the solution landscape. The core claim is that these quantum-inspired mechanisms can significantly enhance the efficiency of evolutionary optimization. The paper details the algorithm's design, including the implementation of interference and entanglement operators, and discusses its potential advantages and challenges. Experimental results (though not presented through dedicated experimental sections) demonstrate the algorithm's ability to outperform standard evolutionary algorithms on a range of benchmark problems.
Quantum evolutionary algorithm is a novel and efficient algorithm which inspired by the ideas of quantum computing,and it has excellent results on the computational efficiency and avoid falling into local extremum problems.Therefore,the combination of quantum mechanics and intelligent optimization algorithms will further expand the application areas of intelligent optimization algorithms to improve the optimization algorithm problem-solving ability.For this,the introduction of quantum computation to the differential evolution algorithm,we proposed a new evolutionary algorithm-quantum differential evolution algorithm.This method is the probability of quantum bits used in the real-coded chromosomes,with the quantum mutation,quantum crossover and quantum choose operation to achieve the update of chromosomal location,and using the quantum NOT gate to swap two probability amplitude of quantum bits,it can prevent the premature algorithm,while the algorithm converges faster.The function extreme value and TSP problems as an example to verify the effectiveness of the proposed algorithm.
Quantum computers are seen as the next generation computing technique with the processing power potential they have. However, currently, quantum computers are limited in terms of hardware and algorithmic capabilities. In this study, quantum-inspired methods which are formed by combining quantum computation techniques with classical algorithms are focused on. It has been emphasized in many studies that quantum-inspired methods provide advantages especially for metaheuristic methods. Different from them, in this study, the performance of population-based quantum-inspired methods are compared. The paper focuses on solving the same optimization problem by using quantum-inspired versions of the population-based optimization algorithms such as evolutionary algorithm, genetic algorithm, and differential evolution algorithm. The experimental results show that, while Quantum-inspired Evolutionary Algorithm is better at global search, Quantum-inspired Differential Evolution Algorithm is better at local search and more accurate results.
A comparative study is presented regarding the evolutionary design of quantum operators in the form of unitary matrices.A comparative study is presented regarding the evolutionary design of quantum operators in the form of unitary matrices. Three existing techniques (representations) which allow generating unitary matrices are used in various evolutionary algorithms in order to optimize their coefficients. The objective is to obtain as precise quantum operators (the resulting unitary matrices) as possible for given quantum transformations. Ordinary evolution strategy, self-adaptive evolution strategy and differential evolution are applied with various settings as the optimization algorithms for the quantum operators. These algorithms are evaluated on the tasks of designing quantum operators for the 3-qubit and 4-qubit maximum amplitude detector and a solver of a logic function of three variables in conjunctive normal form. These tasks require unitary matrices of various sizes. It will be demonstrated that the self-adaptive evolution strategy and differential evolution are able to produce remarkably better results than the ordinary evolution strategy. Moreover, the results can be improved by selecting a proper settings for the evolution as presented by a comparative evaluation.
Differential evolution (DE) is a population based evolutionary algorithm widely used for solving multidimensional global optimization problems over continuous spaces. However, the design of its operators makes it unsuitable for many real-life constrained combinatorial optimization problems which operate on binary space. On the other hand, the quantum inspired evolutionary algorithm (QEA) is very well suitable for handling such problems by applying several quantum computing techniques such as Q-bit representation and rotation gate operator, etc. This paper extends the concept of differential operators with adaptive parameter control to the quantum paradigm and proposes the adaptive quantum-inspired differential evolution algorithm (AQDE). The performance of AQDE is found to be significantly superior as compared to QEA and a discrete version of DE on the standard 0–1 knapsack problem for all the considered test cases.