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Research on Optimization Problems Based on Evolutionary Algorithms and Quantum Computing

Author: LiangXiao
Tutor: XiongYan; YueLiHua
School: University of Science and Technology of China
Course: Applied Computer Technology
Keywords: Optimization Problem Evolutionary algorithms Quantum Computing Evolutionary Programming Self-adaptive Cauchy Evolutionary Programming Markov Chain Pauli Evolutionary Quantum Algorithm Loans CombinatorialOptimization
CLC: TP18
Type: PhD thesis
Year: 2012
Downloads: 331
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Abstract


The optimization problem is that chooses the best solution from the alternate options, and then achieves the optimization of the time, engineering quantities and the economy. Based on the method of numerical calculation, the classic optimization problem is used to solve the complex engineering optimization. However, the conditions of mathematical modeling which based on numerical methods are required complex, such as the objective function is differentiable and the region of the solution is connected. So, complex engineering optimization problems are difficult to be solved.The theories of the optimization problems and the practical applications are developing rapidly by the rapid development of computer technology and the progress of the optimization algorithm.Now, a lot of large-scale optimization problem can be solved by the development of computer technology, the theories and methods of optimization problems are used to solve engineering design, production management, operations scheduling. In this paper, we do the research on the evolutionary algorithms and quantum computing deeply. Through the knapsack problem, function optimization problems and the actual application, we improved new algorithms and analysis the capability of the algorithms. The details are as follow:(1) Self-adaptive Cauchy evolutionary programming and its applications on optimization problemThe standard evolutionary programming (CEP) adopts Gaussian mutation for operator, the step of mutation is smaller; hence the results in some optimization problems tend to converge prematurely. Fast evolutionary programming (FEP) with the mutation operator based on the Cauchy probability distribution, Cauchy probability distribution has much longer tails in the distribution, but the convergence rate of FEP in later period declined obviously. We proposed an evolutionary programming:self-adaptive Cauchy evolutionary programming (ACEP). Based on the current point and the optimization point, we adjust the parameters r of ACEP gradually in optimizing the functions at a period, and find the optimal solution quickly. In this paper, the difference between the Gauss step and the Cauchy step, the time complexity of the select operation were analyzed detail, through the markov chain analysis and the capacity of the spatial search, we confirmed its rapid convergence property.Finally the experiments of test functions show the superiority of the algorithm ACEP.(2) Pauli Evolutionary Quantum Algorithm and its applications on optimization problemQuantum computing is an emerging discipline based on the quantum mechanics and the information science; it used to solve a difficult problem which adopts the particle’s law of motion such as quantum superposition state, entangled and coherent state. The Quantum Evolutionary algorithm QEA is a probabilistic algorithm, without the operations of crossover and mutation as in classical evolutionary algorithms, so it is limited by the local optimum problem in many applications. We proposed an evolutionary quantum algorithm with Pauli mutation PEQA, it employs quantum bit coding, the quantum rotating gate and the Pauli mutation, and only requires a single individual’s evolution to find the optimal solution in a short time. The analysis of Markov chain and Shannon entropy are carried out. The experiment results on0/1knapsack problem show that PEQA can outperform traditional genetic and quantum evolutionary algorithms.(3) Research on the Loans Combinatorial OptimizationThe computer technology based on information science was widely used in the banking sector. Traditional banking operations were changed and the artificial intelligence was used in the bank decision making gradually. In order to solve the problem of loans Combinatorial Optimization, based on the Pauli Evolutionary Quantum Algorithm, the concept of risk factors was proposed. Then we do the risk assessment in the borrowers, set up the computing model with the risk factors, and maximize the expert income at a certain risk. Finally, the reasonable of the algorithm was proved by the experiment results.

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