进化个体不确定适应值交互式遗传算法理论与关键技术
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摘要
在工业生产、工程技术、经济和社会等许多领域,都存在大量的隐式性能指标优化问题,即其性能指标难以甚至无法用明确定义的函数描述,对于这样的问题,传统的智能优化方法将难以奏效。交互式遗传算法将传统的进化机制与用户的智能评价相结合,可以有效地解决隐式性能指标优化问题。但是,用户的疲劳和评价的不确定性问题极大地影响了交互式遗传算法的性能,严重制约了其在复杂优化问题中的应用。为解决这些问题,本论文主要研究进化个体不确定适应值交互式遗传算法的理论与关键技术。
首先,在不考虑用户评价不确定性的情况下,研究交互式遗传算法的适应值估计理论,以减轻用户疲劳,并为后续研究奠定基础。提出了搜索空间自适应分割的多代理模型算法,自适应地分割搜索空间,在各子空间上构造不同的代理模型,代替用户估计进化个体适应值,有效减轻了用户疲劳;提出了基于有向图的进化知识提取和应用策略,给出了基于子种群有向图的进化个体适应值估计方法、优势个体识别和应用方法,加快了算法的收敛速度,减轻了用户疲劳。
然后,研究用户评价的不确定性,给出了进化个体适应值采用2类不确定数表示的方法。针对用户认知的模糊性,采用高斯型隶属函数刻画的模糊数表示进化个体适应值,给出了基于模糊截集的进化个体优劣比较策略,有效反映了用户评价的不确定性;在此基础上,进一步考虑评价过程中的随机不确定性,采用服从正态分布的随机变量表示该类不确定性,提出了模糊随机适应值交互式遗传算法,给出了基于模糊截集和随机变量置信水平的进化个体优劣比较策略,以及基于模糊熵的随机变量分布参数和新的截集水平的确定方法,该方法同时有效地反映了用户的认知不确定性和评价过程中的随机不确定性,较好地保持了种群多样性。
最后,研究了3类进化个体不确定适应值表示情况下,用户认知代理模型的构造方法。基于区间适应值交互式遗传算法的研究成果,提出了区间适应值神经网络代理模型构造方法,采用两个RBF网络分别逼近区间适应值的上限和下限;针对模糊适应值交互式遗传算法,提出了基于支持向量分类机和回归机的代理模型构造方法,给出了基于最优个体模糊熵的训练数据选择方法,以及代理模型的应用策略;针对模糊随机适应值交互式遗传算法,提出了基于有向模糊图和支持向量回归机的代理模型构造方法,采用有向模糊图存储进化知识,将模糊随机适应值转化为精确适应值,再利用该精确适应值构造支持向量机代理模型。从理论上分析了上述3类算法的性能,基于代理模型的适应值估计有效减轻了用户疲劳,增强了进化个体不确定适应值交互式遗传算法的搜索性能。
研究成果在服装进化设计系统中得到了成功应用,结果表明,本文的研究成果有效地表示了用户评价的不确定性,减轻了用户疲劳,提高了交互式遗传算法的性能,为其在复杂领域的应用提供了技术保障。
There exist a lot of optimization problems with implicit indices in many fields, such as industrial production, engineering, economy and society. These problems are difficult or even impossible to be expressed with explicitly defined objective functions, hence traditional intelligent optimization methods are not applicable. Interactive genetic algorithms can effectively solve these kinds of problems by embedding user’s intelligent evaluation into traditional evolution mechanism. However, user fatigue and evaluation uncertainties greatly influence the performance of interactive genetic algorithms, and restrict their applications to more complicated optimization problems. In order to overcome the above disadvantages, theories and key technologies of interactive genetic algorithms with an individual’s uncertain fitness are mainly researched in this dissertation.
Firstly, the theory of fitness estimation in interactive genetic algorithms without considering evaluation uncertainties is studied, so as to alleviate user fatigue and establish foundations for the subsequent work. An interactive genetic algorithm with multiple surrogate models based on adaptive space division is proposed. The search space is adaptively separated, and multiple surrogate models are constructed in every subspace and applied to estimate an individual’s fitness instead of the user, which effectively alleviate user fatigue. Then a method of evolutionary knowledge extraction and applications based on directed graphs is presented. The fitness estimation of an individual is obtained based on the directed graph. With the estimated fitness, methods of identifying and applying superior individuals are given. The proposed algorithm effectively accelerates convergence and alleviates user fatigue.
Secondly, the uncertainties in interactive genetic algorithms are researched, and two kinds of uncertain numbers are adopted to express an individual’s fitness. A fuzzy number with Gaussian membership function is adopted to express an individual’s fitness in order to characterize the user’s fuzzy cognition. Comparison of individuals is performed by using cut sets of fuzzy numbers. This method well reflects the user’s evaluation uncertainty. Based on the above study, the stochastic uncertainty in the evaluation process is further considered by using a stochastic variable with normal distribution to express the stochastic uncertainty, and an interactive genetic algorithm with an individual’s fuzzy and stochastic fitness is presented. By using cut sets of fuzzy numbers and confidence levels of stochastic variables, a method of individuals’ comparison is obtained. The approaches to calculate the stochastic parameters and cut set levels are proposed based on the fuzzy entropy. The above expression method of an individual’s fitness simultaneously reflects the user’s cognitive uncertainty and stochastic uncertainty, and maintains the diversity of an evolutionary population.
Finally, the investigation on building surrogate models to approximate a user’s cognition is performed for interactive genetic algorithms whose individual’s fitness is expressed with three kinds of uncertain numbers. Neural networks based surrogate models of interactive genetic algorithms with an individual’s interval fitness is proposed based on our previous studies. Two RBF neural networks are adopted to approximate an interval’s upper limit and lower limit, respectively. When an individual’s fitness is a fuzzy number, a support vector classification (SVC) and a support vector regressor (SVR) are both adopted to construct surrogate models. A selection strategy of training data is presented based on the fuzzy entropy of the best individual’s fuzzy fitness, and applications of these models are also demonstrated. As for the interactive genetic algorithms with an individual’s fuzzy and stochastic fitness, the surrogate models are obtained based on directed fuzzy graphs and support vector machines (SVMs). Directed fuzzy graphs are used to extract evolutionary knowledge, and based on the graphs, an individual’s fuzzy and stochastic fitness is converted into a precise one. The SVMs are then trained as surrogate models based on these precise fitness. The above three algorithms are quantitatively analyzed. By applying surrogate models to estimate an individual’s fitness instead of the user, user fatigue is effectively alleviated and the performance of interactive genetic algorithms with an individual’s uncertain fitness in searching is improved.
The above researches are successfully applied in fashion evolutionary design systems, and the applied results show that our work effectively expresses the user’s evaluation uncertainties, alleviates user fatigue, and improves the performance of interactive genetic algorithms, which provide guarantees for applying these algorithms in more complicated fields.
首先,在不考虑用户评价不确定性的情况下,研究交互式遗传算法的适应值估计理论,以减轻用户疲劳,并为后续研究奠定基础。提出了搜索空间自适应分割的多代理模型算法,自适应地分割搜索空间,在各子空间上构造不同的代理模型,代替用户估计进化个体适应值,有效减轻了用户疲劳;提出了基于有向图的进化知识提取和应用策略,给出了基于子种群有向图的进化个体适应值估计方法、优势个体识别和应用方法,加快了算法的收敛速度,减轻了用户疲劳。
然后,研究用户评价的不确定性,给出了进化个体适应值采用2类不确定数表示的方法。针对用户认知的模糊性,采用高斯型隶属函数刻画的模糊数表示进化个体适应值,给出了基于模糊截集的进化个体优劣比较策略,有效反映了用户评价的不确定性;在此基础上,进一步考虑评价过程中的随机不确定性,采用服从正态分布的随机变量表示该类不确定性,提出了模糊随机适应值交互式遗传算法,给出了基于模糊截集和随机变量置信水平的进化个体优劣比较策略,以及基于模糊熵的随机变量分布参数和新的截集水平的确定方法,该方法同时有效地反映了用户的认知不确定性和评价过程中的随机不确定性,较好地保持了种群多样性。
最后,研究了3类进化个体不确定适应值表示情况下,用户认知代理模型的构造方法。基于区间适应值交互式遗传算法的研究成果,提出了区间适应值神经网络代理模型构造方法,采用两个RBF网络分别逼近区间适应值的上限和下限;针对模糊适应值交互式遗传算法,提出了基于支持向量分类机和回归机的代理模型构造方法,给出了基于最优个体模糊熵的训练数据选择方法,以及代理模型的应用策略;针对模糊随机适应值交互式遗传算法,提出了基于有向模糊图和支持向量回归机的代理模型构造方法,采用有向模糊图存储进化知识,将模糊随机适应值转化为精确适应值,再利用该精确适应值构造支持向量机代理模型。从理论上分析了上述3类算法的性能,基于代理模型的适应值估计有效减轻了用户疲劳,增强了进化个体不确定适应值交互式遗传算法的搜索性能。
研究成果在服装进化设计系统中得到了成功应用,结果表明,本文的研究成果有效地表示了用户评价的不确定性,减轻了用户疲劳,提高了交互式遗传算法的性能,为其在复杂领域的应用提供了技术保障。
There exist a lot of optimization problems with implicit indices in many fields, such as industrial production, engineering, economy and society. These problems are difficult or even impossible to be expressed with explicitly defined objective functions, hence traditional intelligent optimization methods are not applicable. Interactive genetic algorithms can effectively solve these kinds of problems by embedding user’s intelligent evaluation into traditional evolution mechanism. However, user fatigue and evaluation uncertainties greatly influence the performance of interactive genetic algorithms, and restrict their applications to more complicated optimization problems. In order to overcome the above disadvantages, theories and key technologies of interactive genetic algorithms with an individual’s uncertain fitness are mainly researched in this dissertation.
Firstly, the theory of fitness estimation in interactive genetic algorithms without considering evaluation uncertainties is studied, so as to alleviate user fatigue and establish foundations for the subsequent work. An interactive genetic algorithm with multiple surrogate models based on adaptive space division is proposed. The search space is adaptively separated, and multiple surrogate models are constructed in every subspace and applied to estimate an individual’s fitness instead of the user, which effectively alleviate user fatigue. Then a method of evolutionary knowledge extraction and applications based on directed graphs is presented. The fitness estimation of an individual is obtained based on the directed graph. With the estimated fitness, methods of identifying and applying superior individuals are given. The proposed algorithm effectively accelerates convergence and alleviates user fatigue.
Secondly, the uncertainties in interactive genetic algorithms are researched, and two kinds of uncertain numbers are adopted to express an individual’s fitness. A fuzzy number with Gaussian membership function is adopted to express an individual’s fitness in order to characterize the user’s fuzzy cognition. Comparison of individuals is performed by using cut sets of fuzzy numbers. This method well reflects the user’s evaluation uncertainty. Based on the above study, the stochastic uncertainty in the evaluation process is further considered by using a stochastic variable with normal distribution to express the stochastic uncertainty, and an interactive genetic algorithm with an individual’s fuzzy and stochastic fitness is presented. By using cut sets of fuzzy numbers and confidence levels of stochastic variables, a method of individuals’ comparison is obtained. The approaches to calculate the stochastic parameters and cut set levels are proposed based on the fuzzy entropy. The above expression method of an individual’s fitness simultaneously reflects the user’s cognitive uncertainty and stochastic uncertainty, and maintains the diversity of an evolutionary population.
Finally, the investigation on building surrogate models to approximate a user’s cognition is performed for interactive genetic algorithms whose individual’s fitness is expressed with three kinds of uncertain numbers. Neural networks based surrogate models of interactive genetic algorithms with an individual’s interval fitness is proposed based on our previous studies. Two RBF neural networks are adopted to approximate an interval’s upper limit and lower limit, respectively. When an individual’s fitness is a fuzzy number, a support vector classification (SVC) and a support vector regressor (SVR) are both adopted to construct surrogate models. A selection strategy of training data is presented based on the fuzzy entropy of the best individual’s fuzzy fitness, and applications of these models are also demonstrated. As for the interactive genetic algorithms with an individual’s fuzzy and stochastic fitness, the surrogate models are obtained based on directed fuzzy graphs and support vector machines (SVMs). Directed fuzzy graphs are used to extract evolutionary knowledge, and based on the graphs, an individual’s fuzzy and stochastic fitness is converted into a precise one. The SVMs are then trained as surrogate models based on these precise fitness. The above three algorithms are quantitatively analyzed. By applying surrogate models to estimate an individual’s fitness instead of the user, user fatigue is effectively alleviated and the performance of interactive genetic algorithms with an individual’s uncertain fitness in searching is improved.
The above researches are successfully applied in fashion evolutionary design systems, and the applied results show that our work effectively expresses the user’s evaluation uncertainties, alleviates user fatigue, and improves the performance of interactive genetic algorithms, which provide guarantees for applying these algorithms in more complicated fields.
引文
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