本文關(guān)鍵詞：實數(shù)編碼量子進(jìn)化算法及在投資組合中的應(yīng)用　出處：《東華大學(xué)》2012年博士論文　論文類型：學(xué)位論文

  更多相關(guān)文章： 量子進(jìn)化 實數(shù)編碼 投資組合 模糊 不確定

【摘要】：量子力學(xué)是上個世紀(jì)物理學(xué)領(lǐng)域最為振奮人心的理論發(fā)現(xiàn)之一,它為信息科學(xué)的持續(xù)創(chuàng)新提供了新的理論基礎(chǔ)和發(fā)展思路。量子計算成功地融合了量子力學(xué)和信息科學(xué),它具有的高度并行性,指數(shù)級存儲容量和對經(jīng)典啟發(fā)式算法的指數(shù)加速作用等計算特點,使其迅速成為眾多學(xué)者的研究熱點；與此同時,進(jìn)化計算作為目前并行算法研究中另一個熱點,它把生物界“優(yōu)勝劣汰”的進(jìn)化思想模擬成種群個體適者生存的過程,并用于對復(fù)雜目標(biāo)問題的優(yōu)化求解,取得了很大的成功。 上述研究成果的不斷積累和突破,使得近些年一些學(xué)者開始嘗試把量子計算和進(jìn)化計算相結(jié)合,并在此基礎(chǔ)上提出了一個新的算法框架一量子進(jìn)化算法。經(jīng)典量子進(jìn)化算法中,定義了一個特殊的量子位表示形式,這使得它能夠表示更普遍的種群多樣性；量子位通過測量機制能夠自由轉(zhuǎn)化為二進(jìn)制編碼的形式；算法進(jìn)化過程中,通過量子旋轉(zhuǎn)門來取代傳統(tǒng)進(jìn)化計算中的變異算子,交叉算子等操作,然后驅(qū)動種群向最優(yōu)解進(jìn)化。量子進(jìn)化算法的這些特性使其具備了良好的算法通用性,更快的收斂速度,以及較強的全局尋優(yōu)能力,并且易于與其它智能進(jìn)化算法進(jìn)行混合演算�，F(xiàn)有的研究結(jié)果已經(jīng)表明,量子進(jìn)化算法在很多優(yōu)化問題上都能取得比傳統(tǒng)進(jìn)化算法更好的計算性能；與此同時,鑒于量子進(jìn)化算法若干優(yōu)越性,其在諸多工程管理領(lǐng)域也得到了廣泛應(yīng)用。這其中,量子進(jìn)化算法在組合優(yōu)化領(lǐng)域的使用最為成功。但是在組合優(yōu)化領(lǐng)域,量子進(jìn)化算法可以解決的問題類型還很少,已有的文獻(xiàn)成果主要都是集中于背包問題,旅行商問題和生產(chǎn)調(diào)度問題。因此有必要將量子進(jìn)化算法的應(yīng)用推廣到其它類型的組合優(yōu)化問題上這樣量子進(jìn)化算法內(nèi)涵才能更加豐富和深入；同時也使得量子進(jìn)化理論及其學(xué)習(xí)算法的研究不僅僅具有重要的理論意義,也具有實際的現(xiàn)實意義。 本文在上述指導(dǎo)思想的基礎(chǔ)上,廣泛吸收和借鑒國內(nèi)外相關(guān)研究成果,分別以單目標(biāo)組合優(yōu)化問題和多目標(biāo)組合優(yōu)化問題為研究背景,重新定義了量子進(jìn)化算法的編解碼方式,提出了一個新的實數(shù)編碼方法。新編碼包含了并行的兩個基因分支,即實數(shù)分支和量子概率幅分支；兩個分支分別相互作用,通過實施三角函數(shù)變換,能夠擴展得到不同的候選解,從而增加種群多樣性。在這種新的編碼方式下,本文還改進(jìn)了量子進(jìn)化算法的尋優(yōu)策略。并在此基礎(chǔ)上,構(gòu)建了相應(yīng)的實數(shù)編碼單目標(biāo)量子進(jìn)化算法和實數(shù)編碼多目標(biāo)量子進(jìn)化算法。 隨后,本文把這兩個新算法用于投資組合優(yōu)化問題中�？紤]到投資者在投資決策選擇過程會遇到大量模糊性,不確定性因素。這些模糊性,不確定性因素主要表現(xiàn)形式為各種主觀不確定性,他們會給投資者的決策帶來很大影響,但是,傳統(tǒng)數(shù)學(xué)工具很難對這些非確定因素進(jìn)行有效表達(dá)和求解。因此,本文結(jié)合清華大學(xué)劉寶碇教授不確定規(guī)劃的相關(guān)理論,分別在模糊環(huán)境和不確定環(huán)境下,對投資組合問題進(jìn)行了細(xì)致描述,從而構(gòu)建出更符合實際需要的單目標(biāo)和多目標(biāo)投資組合模型；最后,使用相應(yīng)的量子進(jìn)化新算法分別對上述投資組合模型進(jìn)行求解。 本文創(chuàng)新之處在于： 第一：構(gòu)筑了一個基于實數(shù)編碼單目標(biāo)量子進(jìn)化算法。新算法定義了一個新的量子染色體編解碼方式,在進(jìn)化過程中,設(shè)置了參數(shù)加速機制,使用目標(biāo)函數(shù)的梯度信息,并利用一個新的線性交叉重組算子來實施量子位更新,從而自適應(yīng)調(diào)整算法尋優(yōu)進(jìn)度,避免算法陷入局部最優(yōu),并提高了算法的求解精度； 第二：用模糊變量表示投資收益,然后在模糊環(huán)境下拓展了“熵”概念,’并結(jié)合投資者的風(fēng)險偏好提出了一個新的風(fēng)險度量方法,隨后以此為基礎(chǔ)構(gòu)筑了一個模糊單目標(biāo)投資組合優(yōu)化模型；最后結(jié)合模糊模擬技術(shù),提出一個混合實數(shù)編碼量子進(jìn)化算法用于對該模型進(jìn)行求解； 第三：以量子位實數(shù)編碼為基礎(chǔ),結(jié)合NSGA-Ⅱ算法思想,引入自適應(yīng)克隆機制并構(gòu)建一個動態(tài)種群用于加大對優(yōu)秀個體選擇壓力,從而構(gòu)建了一個新的基于實數(shù)編碼多目標(biāo)量子進(jìn)化算法； 第四：以不確定測度為基礎(chǔ),用不確定變量表示投資收益,然后以Markowitz的模型為原型,首次在不確定環(huán)境下,用不確定期望值來表示投資期望收益,分別用不確定方差,不確定熵和不確定二次熵來表示投資風(fēng)險,從而在不同的應(yīng)用背景下,提出了不確定多目標(biāo)投資組合優(yōu)化模型,最后把基于實數(shù)編碼多目標(biāo)量子進(jìn)化算法用于對上述模型求解。
[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.

【學(xué)位授予單位】：東華大學(xué)
【學(xué)位級別】：博士
【學(xué)位授予年份】：2012
【分類號】：F224;F830.59

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