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Dianzi xuebao

The Quantum Evolutionary Strategies

Yang Shu

Published Jan 1, 2001• 17 citations
OpenAlex

Abstract

In this paper,a novel kind of algorithm,the quantum evolutionary strategies QES,is proposed based on the combination of quantum theory and evolutionary theory.It is a kind of evolutionary strategies with the form of quantum chromosome,whose core lies on the concept and principles of quantum computing,such as qubits and superposition of states.By using qubit mutation,we can make full use of the information of the currently best individual to perform the next search,and use whole interference to avoid prematurity,so it has rapid convergence and good global search capacity.The paper not only proves the global convergence of the QES,but some simulated experimentats are given to prove its superiority to other algorithms.

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In this paper,a novel kind of algorithm,the quantum evolutionary strategies QES,is proposed based on the combination of quantum theory and evolutionary theory.It is a kind of evolutionary strategies with the form of quantum chromosome,whose core lies on the concept and principles of quantum computing,such as qubits and superposition of states.By using qubit mutation,we can make full use of the information of the currently best individual to perform the next search,and use whole interference to avoid prematurity,so it has rapid convergence and good global search capacity.The paper not only proves the global convergence of the QES,but some simulated experimentats are given to prove its superiority to other algorithms.
Evolutionary programming (EP) is an efficient algorithm in solving optimization problems, but the criterion EP is of torpid convergence. In this paper, a novel kind of algorithm, the quantum evolutionary programming (QEP), is proposed based on the combination of quantum theory with evolutionary theory. It is a kind of evolutionary programming with the form of quantum chromosome, whose core lies on the concept and principles of quantum computing, such as quantum bit and superposition of states. Using quantum mutation, we can make full use of the information of the current best individual to perform the next search, so QEP has rapid convergence and global searching capacity. Some simulation experiments are also given to prove its superiority over its counterpart.
The genetic algorithm is an efficient optimization tool for its independence of problems, intrinsic parallelism and inherent learning capacity; however, it has some disadvantages such as slow convergence and prematurity. In this paper, a novel algorithm, called the quantum genetic algorithm—QGA, is proposed based on the combination of the quantum theory with the evolutionary theory. By adopting the qubit chromosome as a representation, QGA can represent a linear superposition of solutions due to its probabilistic representation. The random observation simulating the quantum collapse can bring diverse individuals, and the evolution of quantum chromosome can also pilot the evolution. So it has better diversity than the classical genetic algorithm. Rapid convergence and good global search capacity characterize the performance of QGA. The paper not only proves the global convergence of the QGA, but also some simulation experiments are shown to prove its superiority over other algorithms.
In this paper, we propose a novel genetic algorithm based on the quantum chromosome - QGA. We adopt quantum chromosome to represent a linear superposition of solutions, after the observation that simulates the quantum collapse. The algorithm has better diversity than its counterpart. In addition, the quantum evolutionary operator - quantum mutation is constructed, which is used to speed up the convergence. Rapid convergence and global search capacity characterize the performance of QGA. The paper also gives some simulation experiments to prove its superiority over the classical genetic algorithm.
This paper proposes a novel evolutionary computing method called a genetic quantum algorithm (GQA). GQA is based on the concept and principles of quantum computing such as qubits and superposition of states. Instead of binary, numeric, or symbolic representation, by adopting qubit chromosome as a representation GQA can represent a linear superposition of solutions due to its probabilistic representation. As genetic operators, quantum gates are employed for the search of the best solution. Rapid convergence and good global search capability characterize the performance of GQA. The effectiveness and the applicability of GQA are demonstrated by experimental results on the knapsack problem, which is a well-known combinatorial optimization problem. The results show that GQA is superior to other genetic algorithms using penalty functions, repair methods and decoders.
In this paper,two aspects of the quantum-inspired evolutionary algorithm are improved:(1)Quantum chromosomes qubits in superposition and entangled states can not use the traditional cross-qubit operation,the full interference cross is designed for measured clas-sic chromosome,which could not undermine the inherent parallelism of quantum chromosome,and could increase the diversity of the chro-mosomes after the measurement,affect the direction of chromosome evolution,and effectively prevent premature;(2)The probability trigger is designed to start the quantum NOT gate for quantum variation.The experiments show that the improved quantum evolution opera-tor has better search ability than the previous algorithm over into a more stable convergence degree.
In order to optimize the complex functions,a real-coded quantum evolutionary algorithm is proposed based on the relational concepts and principles of quantum computing.Real-coded triploid chromosomes,whose alleles are composed of a component of the independent variable vector and a pair of probability amplitudes of the corresponding states of a qubit,are constructed to keep the population diversity.The complementary double mutation operator,which is designed according to the probability amplitudes of a qubit fulfilling the normalization conditions,and the quantum rotation gate are used to update chromosomes and realize a good balance between exploration and exploitation.Simulation results on benchmark functions show that the algorithm is well suitable for the complex function optimization,and has the characteristics of rapider convergence,more powerful global search capability and better stability.