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.
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.
Aiming at the issue that quantum genetic algorithm is not suitable for continuons function optimization,an improved quantum genetic algorithm is proposed.This algorithm directly compares the quantum chromosomes with the current best solution to determine the rotating angle of the rotating gate.Every individual in population evolves with different rates to complete local search and global search simultaneously.Mutation operation is used to prevent the premature convergence.After analyzing the algorithm and its global convergence,this algorithm is applied to solve the function extremum and to optimize the PID controller parameters,and it is compared with the standard genetic algorithm and the quantum genetic algorithm.Experimental results illustrate that the proposed algorithm has better performance.
In order to save computation time and avoid falling into local optima in quantum genetic algorithm (QGA), this paper proposes a quantum genetic algorithm based on Boltzmann selection mechanism (B_QGA). The proposed algorithm has several novel characteristics. Firstly, Quantum bits are encoded by angle and introduce the constant factor, aiming at enhancing calculated amount. Secondly, a new dynamic rotation angle adjustment strategy is presented to achieve updated chromosome, and individuals directly evolve to the current optimal solution with linear increasing rate, which greatly improve the rate of convergence and the ability of global search. Thirdly, instead of roulette selection mode, Boltzmann selection mechanism is employed for avoiding the local optimal problem. Finally, for the selected offspring's individuals, Hadamard door is proposed to perform mutation operation to sustain stability and diversity of population. The experiment results on three complicated continuous functions show the proposed algorithm is able to find the best solution in very short time and has excellent global search ability comparing to quantum genetic algorithm (QGA) and genetic algorithm (GA).
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 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.
In this paper, a novel quantum genetic algorithm is proposed. This algorithm compares the probability expectation of the quantum chromosome with the best binary solution to determine rotation angle of rotation gate. Different individual in population evolve with different rate to complete local search and global search simultaneously. Hε gate is used to prevent the algorithm from premature convergence. After analyzing the algorithm and its global convergence, applying this approach to the optimization of function extremum, and comparing with the simple genetic algorithm and the quantum genetic algorithm, the simulation result illustrates that the algorithm has the characteristic of quick convergence speed and high solution precision.
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.