实数编码量子进化算法及在投资组合中的应用

发布时间：2018-01-03 09:00

本文关键词：实数编码量子进化算法及在投资组合中的应用　出处：《东华大学》2012年博士论文　论文类型：学位论文

【摘要】：量子力学是上个世纪物理学领域最为振奋人心的理论发现之一,它为信息科学的持续创新提供了新的理论基础和发展思路。量子计算成功地融合了量子力学和信息科学,它具有的高度并行性,指数级存储容量和对经典启发式算法的指数加速作用等计算特点,使其迅速成为众多学者的研究热点；与此同时,进化计算作为目前并行算法研究中另一个热点,它把生物界“优胜劣汰”的进化思想模拟成种群个体适者生存的过程,并用于对复杂目标问题的优化求解,取得了很大的成功。上述研究成果的不断积累和突破,使得近些年一些学者开始尝试把量子计算和进化计算相结合,并在此基础上提出了一个新的算法框架一量子进化算法。经典量子进化算法中,定义了一个特殊的量子位表示形式,这使得它能够表示更普遍的种群多样性；量子位通过测量机制能够自由转化为二进制编码的形式；算法进化过程中,通过量子旋转门来取代传统进化计算中的变异算子,交叉算子等操作,然后驱动种群向最优解进化。量子进化算法的这些特性使其具备了良好的算法通用性,更快的收敛速度,以及较强的全局寻优能力,并且易于与其它智能进化算法进行混合演算。现有的研究结果已经表明,量子进化算法在很多优化问题上都能取得比传统进化算法更好的计算性能；与此同时,鉴于量子进化算法若干优越性,其在诸多工程管理领域也得到了广泛应用。这其中,量子进化算法在组合优化领域的使用最为成功。但是在组合优化领域,量子进化算法可以解决的问题类型还很少,已有的文献成果主要都是集中于背包问题,旅行商问题和生产调度问题。因此有必要将量子进化算法的应用推广到其它类型的组合优化问题上这样量子进化算法内涵才能更加丰富和深入；同时也使得量子进化理论及其学习算法的研究不仅仅具有重要的理论意义,也具有实际的现实意义。本文在上述指导思想的基础上,广泛吸收和借鉴国内外相关研究成果,分别以单目标组合优化问题和多目标组合优化问题为研究背景,重新定义了量子进化算法的编解码方式,提出了一个新的实数编码方法。新编码包含了并行的两个基因分支,即实数分支和量子概率幅分支；两个分支分别相互作用,通过实施三角函数变换,能够扩展得到不同的候选解,从而增加种群多样性。在这种新的编码方式下,本文还改进了量子进化算法的寻优策略。并在此基础上,构建了相应的实数编码单目标量子进化算法和实数编码多目标量子进化算法。随后,本文把这两个新算法用于投资组合优化问题中。考虑到投资者在投资决策选择过程会遇到大量模糊性,不确定性因素。这些模糊性,不确定性因素主要表现形式为各种主观不确定性,他们会给投资者的决策带来很大影响,但是,传统数学工具很难对这些非确定因素进行有效表达和求解。因此,本文结合清华大学刘宝碇教授不确定规划的相关理论,分别在模糊环境和不确定环境下,对投资组合问题进行了细致描述,从而构建出更符合实际需要的单目标和多目标投资组合模型；最后,使用相应的量子进化新算法分别对上述投资组合模型进行求解。本文创新之处在于：第一：构筑了一个基于实数编码单目标量子进化算法。新算法定义了一个新的量子染色体编解码方式,在进化过程中,设置了参数加速机制,使用目标函数的梯度信息,并利用一个新的线性交叉重组算子来实施量子位更新,从而自适应调整算法寻优进度,避免算法陷入局部最优,并提高了算法的求解精度；第二：用模糊变量表示投资收益,然后在模糊环境下拓展了“熵”概念,’并结合投资者的风险偏好提出了一个新的风险度量方法,随后以此为基础构筑了一个模糊单目标投资组合优化模型；最后结合模糊模拟技术,提出一个混合实数编码量子进化算法用于对该模型进行求解；第三：以量子位实数编码为基础,结合NSGA-Ⅱ算法思想,引入自适应克隆机制并构建一个动态种群用于加大对优秀个体选择压力,从而构建了一个新的基于实数编码多目标量子进化算法；第四：以不确定测度为基础,用不确定变量表示投资收益,然后以Markowitz的模型为原型,首次在不确定环境下,用不确定期望值来表示投资期望收益,分别用不确定方差,不确定熵和不确定二次熵来表示投资风险,从而在不同的应用背景下,提出了不确定多目标投资组合优化模型,最后把基于实数编码多目标量子进化算法用于对上述模型求解。
[Abstract]:The field of quantum mechanics is the last century physics is one of the most exciting discovery theory, it provides a theoretical basis and new ideas for continuous innovation of information science. Quantum computation successfully combines quantum mechanics and information science, it has high parallelism, refers to the number level storage capacity and the classical heuristic algorithm index the acceleration calculation characteristics, which quickly become the research focus of many scholars; at the same time, the parallel evolutionary computation as another hot algorithm research, the biology of "survival of the fittest" evolutionary thinking simulation into population survival of the fittest, and for the optimization of complex target problem, achieved a great success.
The research results of the continuous accumulation and breakthrough, which in recent years some scholars began to try to put the quantum computation and the combination of evolutionary computation, and put forward a new algorithm framework of a quantum evolutionary algorithm. The classical quantum evolutionary algorithm, defines a special qubit representation, which makes it possible to express more general the diversity of the population; the qubit by measuring mechanism can be transformed into the form of free binary encoding algorithm; the process of evolution, the quantum rotation gate to replace the traditional evolutionary computation of the mutation operator, crossover operator and other operations, and then drive to the optimal solution of population evolution. These characteristics of quantum evolutionary algorithm which has a universal algorithm good, faster convergence speed, and strong ability of global optimization, and is easy to be mixed calculus and other intelligent evolutionary algorithms. The existing research The results have shown that the quantum evolutionary algorithm can achieve better performance than the calculation of traditional evolutionary algorithms in many optimization problems; at the same time, in view of some advantages of quantum evolutionary algorithm, which has been widely used in many engineering management field. The quantum evolutionary algorithm in combinatorial optimization field. But the most successful in the field of combinatorial optimization, quantum evolutionary algorithm can solve the problem of type is few, the existing literature results are mainly concentrated in the knapsack problem, traveling salesman problem and production scheduling problem. So it is necessary to apply the quantum evolutionary algorithm is applied to the combinatorial optimization problem of other types of such quantum evolutionary algorithm can be more rich connotation and deeply; also makes the study of quantum evolutionary theory and learning algorithm not only has important theoretical significance, but also has practical significance.
Based on the guiding ideology, absorbing and drawing on relevant research results at home and abroad, respectively, and the multi-objective combinatorial optimization problems as the research background of single objective combinatorial optimization, redefined the codec quantum evolutionary algorithm, propose a new real number encoding method includes two new encoding. Gene branch parallel, namely real branch and branch of quantum probability amplitude; two branches are interaction, through the implementation of trigonometric function transform, can be extended to get different candidate solutions, so as to increase the diversity of the population. In this new encoding mode, this paper also improves the optimization strategy of quantum evolutionary algorithm based. On the construction of the real number encoding the corresponding single objective quantum evolution algorithm and real encoding multi-objective quantum evolutionary algorithm.
Then, this paper used the two new optimization portfolio. Considering the investors in the investment decision-making process will encounter a lot of fuzzy, uncertain factors. The fuzzy uncertainty factors, mainly in the form of various subjective uncertainty, they will bring great influence to the decision-making of investors, but the traditional mathematics the tool is difficult for these uncertain factors effectively expressed and solved. Therefore, combining with the related theory of Tsinghua University professor Liu Baoding uncertain programming, respectively in the fuzzy and uncertain environment, the portfolio problem are described in detail, in order to build more in line with the actual needs of single objective and multi-objective portfolio model; finally, the use of new quantum evolutionary algorithms corresponding respectively on the portfolio model.
The innovation of this article lies in:
First: to build a real number encoding single target based on quantum evolutionary algorithm. The new algorithm defines a new quantum chromosome encoding, in the evolutionary process, set the parameters of acceleration mechanism, using the gradient information of the objective function, and the use of a new linear crossover to the implementation of quantum update, and adaptive adjust the optimization schedule, to avoid the algorithm into a local optimum, and improves the algorithm accuracy;
Second: by fuzzy variables of investment income, and then in the fuzzy environment to expand the "entropy" concept, "combined with the risk appetite of investors proposed a new risk measure method, then on the basis of constructing a fuzzy single objective portfolio optimization model based on fuzzy simulation; finally, put forward a hybrid encoding quantum evolutionary algorithm for solving the model;
Third: the qubit real encoding as the foundation, combined with the NSGA- II algorithm, adaptive cloning mechanism and construct a dynamic population for increase of the outstanding individual selection pressure, in order to build a new encoding based on real multi-objective quantum evolutionary algorithm;
Fourth: the uncertainty measure based, with uncertain variables that investment income, then taking the Markowitz model as the prototype, for the first time in an uncertain environment, with the uncertainty of expected value of investment expected revenue, respectively with uncertain variance, uncertain entropy and uncertainty two entropy to represent the investment risk, and in different application background, put forward the uncertain multi-objective optimization model of investment portfolio, the real number encoding multi-objective quantum evolutionary algorithm is used to solve the model based on.

【学位授予单位】：东华大学
【学位级别】：博士
【学位授予年份】：2012
【分类号】：F224;F830.59

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