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Kongzhi yu juece

Real-coded Chaotic Quantum-inspired Genetic Algorithm

Chao Zhang

Published Jan 1, 2005• 9 citations
OpenAlex

Abstract

This paper proposed a real-coded chaotic quantum-inspired genetic algorithm(RCQGA) based on the chaotic and coherent characters of Q-bits.In this algorithm,real chromosomes are inversely mapped to Qbits in the solution space.Q-bits probability guided real cross and chaos mutation are used to real chromosomes evolution and searching;Simulation shows that the proposed RCQGA not only avoids the shortcoming of binary system coding based QGA prematurity but it also reduces the optimizing complexity with faster convergence speed,more stability,more powerful optimizing ability.

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This paper proposed a real-coded chaotic quantum-inspired genetic algorithm(RCQGA) based on the chaotic and coherent characters of Q-bits.In this algorithm,real chromosomes are inversely mapped to Qbits in the solution space.Q-bits probability guided real cross and chaos mutation are used to real chromosomes evolution and searching;Simulation shows that the proposed RCQGA not only avoids the shortcoming of binary system coding based QGA prematurity but it also reduces the optimizing complexity with faster convergence speed,more stability,more powerful optimizing ability.
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.
Qubit-inspired Genetic Algorithm (QGA) is an extension of genetic algorithm in which quantum mechanics and its representations are introduced. A chromosome in our QGA is concretized as a series of quantum-bit (qubit) described by its complex-valued representation, and phase-rotation gates are embedded into the selection process over generations. In our previous work, it has been shown that this scheme has better performances than the classical ones in several problems such as N-K landscape problem, Knapsack Problem, Maximum Search, and Construction of image filters. In this paper, we make clear the effectiveness of the QGA by comparing QGA with GA through minimum solution problem on De Jong's functions.
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.
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.
The quantum-inspired genetic algorithm (QGA), which combines quantum mechanics concepts and GA to enhance search capability, has been popular and provides an efficient search mechanism. This paper proposes a modified QGA, called dynamic QGA (DQGA). The proposed algorithm utilizes a lengthening chromosome strategy for a balanced and smooth transition between exploration and exploitation phases to avoid local optima and premature convergence. Apart from that, a novel adaptive look-up table for rotation gates is presented to boost the algorithm’s optimization abilities. To evaluate the effectiveness of these ideas, DQGA is tested by various mathematical benchmark functions as well as real-world constrained engineering problems against several well-known and state-of-the-art algorithms. The obtained results indicate the merits of the proposed algorithm and its superiority for solving multimodal benchmark functions and real-world constrained engineering problems.
From the recent research on combinational optimization of the knapsack problem, the quantum-inspired genetic algorithm (QGA) was proved to be better than conventional genetic algorithms. To accelerate the convergence speed of the QGA, the paper proposes research issues on QGA such as Q-gate. A novel Q-gate updating algorithm called chaos updating rotated gates quantum-inspired genetic algorithm (CQGA) is proposed. An analysis of the two main characters of quantum computing and chaos is also presented. This algorithm demonstrates the convergence of the quantum genetic algorithm (QGA). Several experiments are carried out on a class of numerical and combinatorial optimization problems. The results show the updated QGA makes QGA more powerful than the previous QGA in convergence speed.