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Journal of Wuhan University

A Simple Quantum Inspired Evolutionary Algorithm and Its Application to Numerical Optimization Problems

Qing Yang

Published Jan 1, 2006• 7 citations
OpenAlex

Abstract

The paper develops a Simple Quantum Inspired Evolutionary Algorithm and evaluates it on some classical numerical optimization problems and the Need-in-a-haystack problem.The proposed algorithm represents a qubit with a radian and uses only one quantum chromosome.Special operators of rotation and mutation and the method to evaluate a quantum chromosome are presented too.Compared with some other quantum inspired genetic algorithms and the classical genetic algorithm,the novel algorithm shows the outstanding performance and solves the Need-in-a-haystack problem perfectly.

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The paper develops a Simple Quantum Inspired Evolutionary Algorithm and evaluates it on some classical numerical optimization problems and the Need-in-a-haystack problem.The proposed algorithm represents a qubit with a radian and uses only one quantum chromosome.Special operators of rotation and mutation and the method to evaluate a quantum chromosome are presented too.Compared with some other quantum inspired genetic algorithms and the classical genetic algorithm,the novel algorithm shows the outstanding performance and solves the Need-in-a-haystack problem perfectly.
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.
Coding the individual with amplitude,and applying the crossover operator of classical genetic algorithm to the evolutionary goals of quantum-inspired evolutionary algorithm,a hybrid quantum-inspired evolutionary algorithm is proposed.Combining the self-adaptive rotation,defining a self-adaptive mutation operator with respect to mutation degree,and exchanging the information of the evolutionary goals by crossover operator regularly,the novel algorithm avoids converging prematurely and yields high efficiency.Also the algorithm exceeds QEA and CGA when they solve the numerical optimization problems.The Need-in-a-Haystack problem can be figured out perfectly.Additionally,the algorithm’s computing speed is similar to the classical one.
Due to frequent decoding operations, the efficiency of optimization is severely reduced when the binary quantum genetic algorithm based on qubits measure is applied to the continuous space optimization. To solve this problem, a quantum genetic algorithm based on phase encoding is proposed in this paper. In this method, the chromosomes are encoded by the phase of qubits, evolved by quantum rotation gates, and mutated by quantum Pauli-Z gates. As the optimization process is performed in [0, 2π], which has nothing to do with specific issues, therefore, the proposed method has good adaptability for a variety of optimization problems. With application of function extremum optimization, the simulation results show that the approach is superior to common quantum genetic algorithm and simple genetic algorithm in both search capability and optimization efficiency.
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.
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.