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Kongzhi yu juece

A new phase angle encoded quantum evolutionary algorithm

Le Zhang

Published Jan 1, 2015• 2 citations
OpenAlex

Abstract

In order to optimize the numerical functions with the continuous solution space, a new phase angle encoded quantum evolutionary algorithm(PAQEA) is proposed based on the quantum computing and real encoded evolutionary algorithm. In PAQEA, a quantum chromosome with probabilistic representation can represent all the feasible solution probabilistically, and the dynamic quantum rotation gate is used to update chromosomes. Thus, the population diversity and directional evolution realize a good balance between exploration and exploitation. Theoretical analysis shows that the PAQEA is a global convergence algorithm. Simulation results show that the algorithm is suitable for the optimization of complex numerical functions, and has the characteristics of rapider convergence, powerful global search capability and better stability.

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In order to optimize the numerical functions with the continuous solution space, a new phase angle encoded quantum evolutionary algorithm(PAQEA) is proposed based on the quantum computing and real encoded evolutionary algorithm. In PAQEA, a quantum chromosome with probabilistic representation can represent all the feasible solution probabilistically, and the dynamic quantum rotation gate is used to update chromosomes. Thus, the population diversity and directional evolution realize a good balance between exploration and exploitation. Theoretical analysis shows that the PAQEA is a global convergence algorithm. Simulation results show that the algorithm is suitable for the optimization of complex numerical functions, and has the characteristics of rapider convergence, powerful global search capability and better stability.
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.
For optimzing complex functions with high-dimension, a real-coded quantum evolutionary algorithm (RCQEA) is proposed on the basis of the concept and principles of quantum computing such as qubits and superposition of states. Firstly, in this algorithm, real-coded triploid chromosomes, whose alleles are composed of real variable and a pair of probability amplitudes of the correspinding states of one qubit, are constructed to keep the diversity of solution. Secondly, complementary double mutation operator (CDMO), which is designed according to a pair of probability amplitudes of the correspinding states of one qubit satisfying the normalization condition, as well as quantum rotation gate (QRG) are used to update chromosomes, which can treat the balance between exploration and exploitation. Thirdly, discrete crossover (DC) is employed to expand search space. Finally, "Hill-climbing" selection (HCS) is adopted to accelerate the convergence speed. Simulation results on 4 benchmark complex functions with high-dimension show that RCQEA is not only effective, efficient, but also very adaptive to the dimensions, and has the characteristics of rapider convergence, more powerful global search capability and better stability.
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.
Based on the probability amplitude ratio of the corresponding states of quantum bits, the rotation angle of quantum rotation gate is calculated adaptively and a new quantum rotation gate is constructed. A novel quantum evolutionary algorithms (NQEA), whose core is that the designed quantum rotation gate is used as evolutionary strategy is introduced, rapid convergence and good global search capability characterize the performance of NQEA, and NQEA is able to possess the two characteristics of exploration and exploitation, simultaneously. NQEA is applied on the physical distribution vehicle routing problem - a typical combinatorial optimization problem, the results show that NQEA is superior to the previous quantum evolutionary algorithm as well as other conventional genetic algorithms
By combining quantum evolutionary algorithms and simulated annealing algorithm, this paper presented a quantum simulated annealing algorithm. In this algorithm, chromosome is encoded according to the phase; This study defined the phase neighborhood space and narrowed the scope of the algorithm search. The concept of information entropy was introduced to avoid searching blindness and the expression of the angle of rotation increments based on quantum revolving door was derived to simplify the calculation process. This study adopted the Boltzmann probability distribution principle to accept the new solution and improve the search performance of the algorithm; at the same time, the mutation operation and quantum random behavior were added to prevent the phenomenon of prematurity. It has proved the global convergence of the algorithm. Function optimization problem and PID controller parameter optimization problems were simulated. The results show that the algorithm has stronger global convergence and searching ability.
Optimization method is important in engineering design and application. Quantum genetic algorithm has the characteristics of good population diversity, rapid convergence and good global search capability and so on. It combines quantum algorithm with genetic algorithm. A novel quantum genetic algorithm is proposed, which is called Variable-boundary-coded Quantum Genetic Algorithm (vbQGA) in which qubit chromosomes are collapsed into variable-boundary-coded chromosomes instead of binary-coded chromosomes. Therefore much shorter chromosome strings can be gained. The method of encoding and decoding of chromosome is first described before a new adaptive selection scheme for angle parameters used for rotation gate is put forward based on the core ideas and principles of quantum computation. Eight typical functions are selected to optimize to evaluate the effectiveness and performance of vbQGA against standard Genetic Algorithm (sGA) and Genetic Quantum Algorithm (GQA). The simulation results show that vbQGA is significantly superior to sGA in all aspects and outperforms GQA in robustness and solving velocity, especially for multidimensional and complicated functions.