共查询到10条相似文献,搜索用时 156 毫秒
1.
Michela Antonelli Pietro Ducange Beatrice Lazzerini Francesco Marcelloni 《Soft Computing - A Fusion of Foundations, Methodologies and Applications》2011,15(12):2335-2354
In the last few years, several papers have exploited multi-objective evolutionary algorithms (MOEAs) to generate Mamdani fuzzy
rule-based systems (MFRBSs) with different trade-offs between interpretability and accuracy. In this framework, a common approach
is to distinguish between interpretability of the rule base (RB), also known as complexity, and interpretability of fuzzy
partitions, also known as integrity of the database (DB). Typically, complexity has been used as one of the objectives of
the MOEAs, while partition integrity has been ensured by enforcing constraints on the membership function (MF) parameters.
In this paper, we propose to adopt partition integrity as an objective of the evolutionary process. To this aim, we first
discuss how partition integrity can be measured by using a purposely defined index based on the similarity between the partitions
learned during the evolutionary process and the initial interpretable partitions defined by an expert. Then, we introduce
a three-objective evolutionary algorithm which generates a set of MFRBSs with different trade-offs between complexity, accuracy
and partition integrity by concurrently learning the RB and the MF parameters of the linguistic variables. Accuracy is assessed
in terms of mean squared error between the actual and the predicted values, complexity is calculated as the total number of
conditions in the antecedents of the rules and integrity is measured by using the purposely defined index. The proposed approach
has been experimented on six real-world regression problems. The results have been compared with those obtained by applying
the same MOEA, but with only accuracy and complexity as objectives, both to learn only RBs, and to concurrently learn RBs
and MF parameters, with and without constraints on the parameter tuning. We show that our approach achieves the best trade-offs
between interpretability and accuracy. Finally, we compare our approach with a similar MOEA recently proposed in the literature. 相似文献
2.
Marco Cococcioni Pietro Ducange Beatrice Lazzerini Francesco Marcelloni 《Soft Computing - A Fusion of Foundations, Methodologies and Applications》2007,11(11):1013-1031
In the last years, the numerous successful applications of fuzzy rule-based systems (FRBSs) to several different domains have
produced a considerable interest in methods to generate FRBSs from data. Most of the methods proposed in the literature, however,
focus on performance maximization and omit to consider FRBS comprehensibility. Only recently, the problem of finding the right
trade-off between performance and comprehensibility, in spite of the original nature of fuzzy logic, has arisen a growing
interest in methods which take both the aspects into account. In this paper, we propose a Pareto-based multi-objective evolutionary
approach to generate a set of Mamdani fuzzy systems from numerical data. We adopt a variant of the well-known (2+2) Pareto
Archived Evolutionary Strategy ((2+2)PAES), which adopts the one-point crossover and two appropriately defined mutation operators.
(2+2)PAES determines an approximation of the optimal Pareto front by concurrently minimizing the root mean squared error and
the complexity. Complexity is measured as sum of the conditions which compose the antecedents of the rules included in the
FRBS. Thus, low values of complexity correspond to Mamdani fuzzy systems characterized by a low number of rules and a low
number of input variables really used in each rule. This ensures a high comprehensibility of the systems. We tested our version
of (2+2)PAES on three well-known regression benchmarks, namely the Box and Jenkins Gas Furnace, the Mackey-Glass chaotic time
series and Lorenz attractor time series datasets. To show the good characteristics of our approach, we compare the Pareto
fronts produced by the (2+2)PAES with the ones obtained by applying a heuristic approach based on SVD-QR decomposition and
four different multi-objective evolutionary algorithms. 相似文献
3.
This paper presents a bi-objective vendor managed inventory (BOVMI) model for a supply chain problem with a single vendor and multiple retailers, in which the demand is fuzzy and the vendor manages the retailers’ inventory in a central warehouse. The vendor confronts two constraints: number of orders and available budget. In this model, the fuzzy demand is formulated using trapezoidal fuzzy number (TrFN) where the centroid defuzzification method is employed to defuzzify fuzzy output functions. Minimizing both the total inventory cost and the warehouse space are the two objectives of the model. Since the proposed model is formulated into a bi-objective integer nonlinear programming (INLP) problem, the multi-objective evolutionary algorithm (MOEA) of non-dominated sorting genetic algorithm-II (NSGA-II) is developed to find Pareto front solutions. Besides, since there is no benchmark available in the literature to validate the solutions obtained, another MOEA, namely the non-dominated ranking genetic algorithms (NRGA), is developed to solve the problem as well. To improve the performances of both algorithms, their parameters are calibrated using the Taguchi method. Finally, conclusions are made and future research works are recommended. 相似文献
4.
Context adaptation of fuzzy systems through a multi-objective evolutionary approach based on a novel interpretability index 总被引:5,自引:5,他引:0
Alessio Botta Beatrice Lazzerini Francesco Marcelloni Dan C. Stefanescu 《Soft Computing - A Fusion of Foundations, Methodologies and Applications》2009,13(5):437-449
Context adaptation (CA) based on evolutionary algorithms is certainly a promising approach to the development of fuzzy rule-based
systems (FRBSs). In CA, a context-free model is instantiated to a context-adapted FRBS so as to increase accuracy. A typical
requirement in CA is that the context-adapted system maintains the same interpretability as the context-free model, a challenging
constraint given that accuracy and interpretability are often conflicting objectives. Furthermore, interpretability is difficult
to quantify because of its very nature of being a qualitative concept. In this paper, we first introduce a novel index based
on fuzzy ordering relations in order to provide a measure of interpretability. Then, we use the proposed index and the mean
square error as goals of a multi-objective evolutionary algorithm aimed at generating a set of Pareto-optimum context-adapted
Mamdani-type FRBSs with different trade-offs between accuracy and interpretability. CA is obtained through the use of specifically
designed operators that adjust the universe of the input and output variables, and modify the core, the support and the shape
of fuzzy sets characterizing the partitions of these universes. Finally, we show results obtained by using our approach on
synthetic and real data sets. 相似文献
5.
Michela Antonelli Pietro Ducange Beatrice Lazzerini Francesco Marcelloni 《Soft Computing - A Fusion of Foundations, Methodologies and Applications》2011,15(10):1981-1998
Interpretability of Mamdani fuzzy rule-based systems (MFRBSs) has been widely discussed in the last years, especially in the
framework of multi-objective evolutionary fuzzy systems (MOEFSs). Here, multi-objective evolutionary algorithms (MOEAs) are
applied to generate a set of MFRBSs with different trade-offs between interpretability and accuracy. In MOEFSs interpretability
has often been measured in terms of complexity of the rule base and only recently partition integrity has also been considered.
In this paper, we introduce a novel index for evaluating the interpretability of MFRBSs, which takes both the rule base complexity
and the data base integrity into account. We discuss the use of this index in MOEFSs, which generate MFRBSs by concurrently
learning the rule base, the linguistic partition granularities and the membership function parameters during the evolutionary
process. The proposed approach has been experimented on six real world regression problems and the results have been compared
with those obtained by applying the same MOEA, with only accuracy and complexity of the rule base as objectives. We show that
our approach achieves the best trade-offs between interpretability and accuracy. 相似文献
6.
高维多目标优化问题普遍存在且难以解决, 到目前为止, 尚缺乏有效解决该问题的进化优化方法. 本文提出一种基于目标分解的高维多目标并行进化优化方法, 首先, 将高维多目标优化问题分解为若干子优化问题, 每一子优化问题除了包含原优化问题的少数目标函数之外, 还具有由其他目标函数聚合成的一个目标函数, 以降低问题求解的难度; 其次, 采用多种群并行进化算法, 求解分解后的每一子优化问题, 并在求解过程中, 充分利用其他子种群的信息, 以提高Pareto非被占优解的选择压力; 最后, 基于各子种群的非被占优解形成外部保存集, 从而得到高维多目标优化问题的Pareto 最优解集. 性能分析表明, 本文提出的方法具有较小的计算复杂度. 将所提方法应用于多个基准优化问题, 并与NSGA-II、PPD-MOEA、ε-MOEA、HypE和MSOPS等方法比较, 实验结果表明, 所提方法能够产生收敛性、分布性, 以及延展性优越的Pareto最优解集. 相似文献
7.
Taher Niknam Mokhtar Sha Sadeghi 《International Journal of Control, Automation and Systems》2011,9(1):112-117
In this paper, a Multi-objective Modified Honey Bee Mating Optimization (MMHBMO) evolutionary algorithm is proposed to solve
the multi-objective Distribution Feeder Reconfiguration (DFR). The real power loss, the number of the switching operations
and the deviation of the voltage at each node are considered as the objective functions. Conventional algorithms for solving
the multiobjective optimization problems convert the multiple objectives into a single objective using a vector of the user-predefined
weights. This paper presents a new MHBMO algorithm for the DFR problem. In the proposed algorithm an external repository is
utilized to save non-dominated solutions found during the search process. A fuzzy clustering technique is used to control
the size of the repository within the limits because of the objective functions are not the same. The proposed algorithm is
tested on a distribution test feeder. 相似文献
8.
约束优化是多数实际工程应用优化问题的呈现方式.进化算法由于其高效的表现,近年来被广泛应用于约束优化问题求解.但约束条件使得问题解空间离散、缩小、改变,给进化算法求解约束优化问题带来极大挑战.在此背景下,融合约束处理技术的进化算法成为研究热点.此外,随着研究的深入,近年来约束处理技术在复杂工程应用问题优化中得到了广泛发展,例如多目标、高维、等式优化等.根据复杂性的缘由,将面向复杂约束优化问题的进化优化分为面向复杂目标的进化约束优化算法和面向复杂约束场景的进化算法两种类别进行综述,其中,重点探讨了实际工程应用的复杂性对约束处理技术的挑战和目前研究的最新进展,并最后总结了未来的研究趋势与挑战. 相似文献
9.
It has been shown that the multi-objective evolutionary algorithms (MOEAs) act poorly in solving many-objective optimization problems which include more than three objectives. The research emphasis, in recent years, has been put into improving the MOEAs to enable them to solve many-objective optimization problems efficiently. In this paper, we propose a new composite fitness evaluation function, in a novel way, to select quality solutions from the objective space of a many-objective optimization problem. Using this composite function, we develop a new algorithm on a well-known NSGA-II and call it FR-NSGA-II, a fast reference point based NSGA-II. The algorithm is evaluated for producing quality solutions measured in terms of proximity, diversity and computational time. The working logic of the algorithm is explained using a bi-objective linear programming problem. Then we test the algorithm using experiments with benchmark problems from DTLZ family. We also compare FR-NSGA-II with four competitive algorithms from the extant literature to show that FR-NSGA-II will produce quality solutions even if the number of objectives is as high as 20. 相似文献