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Journal of Computer Applications

Quantum harmonic oscillator optimization algorithm

Youming Guo

Published Jan 1, 2012• 0 citations
OpenAlex

Abstract

An optimization algorithm named quantum harmonic oscillator optimization algorithm based on quantum harmonic oscillator ground state of optimality was proposed,combined with the stable convergence of the vibration space and the ground state Gaussian curve distribution characteristics of quantum harmonic oscillator.The vibration of the physical processes of the quantum harmonic oscillator has an inherent similarity with the working mechanism of the intelligent algorithm.This paper mainly analyzed the characteristics of quantum harmonic oscillator and its relation to optimization algorithm,and the relationship between them is one of the reasons to construct the algorithm model.It is theoretically proved that the algorithm based on quantum harmonic oscillator will make the solution space form the Gaussian distribution,and will provide a better searching capability.In order to test the performance,the algorithm was used to solve the corresponding scale of Traveling Saleman Problem(TSP),and compared with the simulated anneal algorithm under equal scale,the results of experiment show that the algorithm has better convergence and enhanced optimization capability.

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An optimization algorithm named quantum harmonic oscillator optimization algorithm based on quantum harmonic oscillator ground state of optimality was proposed,combined with the stable convergence of the vibration space and the ground state Gaussian curve distribution characteristics of quantum harmonic oscillator.The vibration of the physical processes of the quantum harmonic oscillator has an inherent similarity with the working mechanism of the intelligent algorithm.This paper mainly analyzed the characteristics of quantum harmonic oscillator and its relation to optimization algorithm,and the relationship between them is one of the reasons to construct the algorithm model.It is theoretically proved that the algorithm based on quantum harmonic oscillator will make the solution space form the Gaussian distribution,and will provide a better searching capability.In order to test the performance,the algorithm was used to solve the corresponding scale of Traveling Saleman Problem(TSP),and compared with the simulated anneal algorithm under equal scale,the results of experiment show that the algorithm has better convergence and enhanced optimization capability.
The authors analyzed the current problems of ant colony algorithm and the advantages of improved algorithm,and then found that the physical properties of quantum harmonic oscillators would guarantee the convergence of final algorithm.Changing process of the quantum harmonic oscillators from high energy state to low energy state and increment of pheromone had a corresponding relationship,and thereby updated pheromone,and physically it provided the algorithmic theoretical basis.Quantum rotation door changed the transfer rules of city.Mutations by Pauli matrix allowed ants have a wider space.Integrating the above advantages of quantum harmonic oscillator,the authors proposed a quantum harmonic oscillator ant colony algorithm,and achieved better optimization path in the Traveling Saleman Problem(TSP) problems.
With the multi-scale binary sampling methods on the basis of Gaussian scaling function,the model of multi-scale quantum harmonic oscillator algorithm for high-dimensional function global optimization problems is proposed.High-dimensional function optimization process is divided into two steps,scale convergence and quantum harmonic oscillator convergence.This algorithm model is based on the same convergence process probability interpretations between function optimization problem and quantum harmonic oscillator from high-energy state to ground state.This algorithm,which has explicit physical model,can realize highdimensional function optimization without coding or complex initial conditions.Experiments and analysis are done for 15 typical two-dimensional optimized test functions and 6 typical high-dimensional optimized test functions.The results show that multi-scale quantum harmonic oscillator algorithm gets precise global optimum for high-dimensional function quickly,and withreduced frequencyapproach,the search speed of function withhigh frequency component improves significantly.
Multi-scale Quantum Oscillator Harmonic Algorithm( MQHOA) has good characteristics of global convergence and adaptability. For analyzing the specific performance of MQHOA on solution precision and speed, the comparisons of theoretical models and experiments were completed among the MQHOA, the classic Quantum Particle Swarm Optimization( QPSO) algorithm adopting the quantum-behaved model and having been widely used, and the QPSO with Random Mean best position( QPSO-RM) through solving the integer nonlinear programming problems. In simulation experiments, MQHOA achieved 100% success rate in solving seven unconstrained integer nonlinear programming problems, and was faster than QPSO and QPSO-RM in most cases. MQHOA was a little slower than QPSO and QPSO-RM in solving the two constrained integer nonlinear programming problems, but could obtain 100% success rate which was higher than the latter. Through the comparison of the convergence process of QPSO, QPSO-RM, MQHOA was faster and earlier on converging to the global optimal solution. The experimental results show that MQHOA can effectively adapt to solving the integer programming problems, and can avoid falling into the local optimal solution so as to obtain the global optimal solution. MQHOA is better than the contrast algorithms of QPSO and QPSO-RM in accuracy and convergence rate.
This paper presents a variant of multiscale quantum harmonic oscillator algorithm for multimodal optimization named MQHOA-MMO. MQHOA-MMO has only two main iterative processes: quantum harmonic oscillator process and multiscale process. In the two iterations, MQHOA-MMO only does one thing: sampling according to the wave function at different scales. A set of benchmark test functions including some challenging functions are used to test the performance of MQHOA-MMO. Experimental results demonstrate good performance of MQHOA-MMO in solving multimodal function optimization problems. For the 12 test functions, all of the global peaks can be found without being trapped in a local optimum, and MQHOA-MMO converges within 10 iterations.
The wavefunction is an important element of the multiscale quantum harmonic oscillator algorithm (MQHOA). To verify the physical model and the multimode optimization performance of the MQHOA for multimode optimization in this paper, we define a multidimensional harmonic-Gaussian potential function. When the wavefunction of the MQHOA for multimode optimization and the probability amplitude of an ammonia molecule are compared, the ground-state wavefunction can reflect the probability distribution of the two-state ammonia molecule. We obtain the extrema of the proposed function using the Hessian matrix and optimize the proposed function with the multimode algorithm. The experiments show that the multimode algorithm can determine the extrema of the proposed function with appropriate parameters. Changes in the proposed function barriers have little effect on the optimization ability of the multimode algorithm. The optimization ability of the multimode algorithm is determined by its own wavefunction.
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.