一种优化模糊神经网络的多目标微粒群算法

模糊神经网络优化是一个多目标优化问题．通过对模糊神经网络和微粒群算法的深入分析,提出了一种多目标微粒群算法．在算法中将网络的精确性和复杂性分别作为目标进行优化,再用一种启发性分量加权均值法来选取个体极值和全局极值．算法能够引导粒子较快地向非劣最优解区域移动并最终获得多个非劣最优解,为模糊神经网络的精确性和复杂性的折中寻优问题提供了一种解决方法．茶味觉信号识别的仿真实验验证了该算法的有效性．     

Multi-objective evolutionary optimization of polynomial neural networks for modelling and prediction of explosive cutting process

In this paper, evolutionary algorithms (EAs) are deployed for multi-objective Pareto optimal design of group method of data handling (GMDH)-type neural networks which have been used for modelling an explosive cutting process using some input–output experimental data. In this way, multi-objective EAs (non-dominated sorting genetic algorithm, NSGA-II) with a new diversity-preserving mechanism are used for Pareto optimization of such GMDH-type neural networks. The important conflicting objectives of GMDH-type neural networks that are considered in this work are, namely, training error (TE), prediction error (PE), and number of neurons (N) of such neural networks. Different pairs of theses objective functions are selected for 2-objective optimization processes. Therefore, optimal Pareto fronts of such models are obtained in each case which exhibit the trade-off between the corresponding pair of conflicting objectives and, thus, provide different non-dominated optimal choices of GMDH-type neural networks models for explosive cutting process. Moreover, all the three objectives are considered in a 3-objective optimization process, which consequently leads to some more non-dominated choices of GMDH-type models representing the trade-offs among the training error, prediction error, and number of neurons (complexity of network), simultaneously. The overlay graphs of these Pareto fronts also reveal that the 3-objective results include those of the 2-objective results and, thus, provide more optimal choices for the multi-objective design of GMDH-type neural networks in terms of minimum training error, minimum prediction error, and minimum complexity.     

蚁群算法在Web服务组合中的应用

为了在服务组合过程中高效地发现、选择满足用户要求的Web服务,提出基于蚁群算法的多目标优化组合用以实现用户对组合服务质量的需求。该方法根据不同Web服务的QoS属性指标,选择相应的Web服务得到Pareto最优解集合,用户根据实际需要或对目标函数的偏好,从Pareto最优解集中挑选一个或多个解作为组合服务质量问题的最优解,从而形成最后的决策方案。从理论和实验2个方面与相关研究成果进行分析比较。     

Structure optimization of neural network for dynamic system modeling using multi-objective genetic algorithm

The problem of constructing an adequate and parsimonious neural network topology for modeling non-linear dynamic system is studied and investigated. Neural networks have been shown to perform function approximation and represent dynamic systems. The network structures are usually guessed or selected in accordance with the designer’s prior knowledge. However, the multiplicity of the model parameters makes it troublesome to get an optimum structure. In this paper, an alternative algorithm based on a multi-objective optimization algorithm is proposed. The developed neural network model should fulfil two criteria or objectives namely good predictive accuracy and minimum model structure. The result shows that the proposed algorithm is able to identify simulated examples correctly, and identifies the adequate model for real process data based on a set of solutions called the Pareto optimal set, from which the best network can be selected.     

Intelligent modelling and optimization of the gas tungsten arc welding process

This paper describes an application of neural networks and simulated annealing (SA) algorithm to model and optimize the gas tungsten arc welding (GTAW) process. The relationships between welding process parameters and weld pool features are established based on neural networks. In this study, the counter-propagation network (CPN) is selected to model the GTAW process due to the CPN equipped with good learning ability. An SA optimization algorithm is then applied to the CPN for searching for the welding process parameters with optimal weld pool features. Experimental results have shown that GTAW performance can be enhanced by using this approach.     

Multi-objective robust design of helical milling hole quality on AISI H13 hardened steel by normalized normal constraint coupled with robust parameter design

Helical milling is a hole-making process which has been applied in hardened materials. Due to the difficulties on achieving high-quality boreholes in these materials, the influence of noise factors, and multi-quality performance outcomes, this work aims the multi-objective robust design of hole quality on AISI H13 hardened steel. Experiments were carried out through a central composite design considering process and noise factors. The process factors were the axial and tangential feed per tooth of the helix, and the cutting velocity. The noise factors considered were the tool overhang length, the material hardness and the borehole height of measurement. Response models were obtained through response surface methodology for roughness and roundness outcomes. The models presented good explanation of data variability and good prediction capability. Mean and variance models were derived through robust parameter design for all responses. Similarity analysis through cluster analysis was performed, and average surface roughness and total roundness were selected to multi-objective optimization. Mean square error optimization was performed to achieve bias and variance minimization. Multi-objective optimization through normalized normal constraint was performed to achieve a robust Pareto set for the hole quality outcomes. The normalized normal constraint optimization results outperformed the results of other methods in terms of evenness of the Pareto solutions and number of Pareto optimal solutions. The most compromise solution was selected considering the lowest Euclidian distance to the utopia point in the normalized space. Individual and moving range control charts were used to confirm the robustness achievement with regard to noise factors in the most compromise Pareto optimal solution. The methodology applied for robust modelling and optimization of helical milling of AISI H13 hardened steel was confirmed and may be applied to other manufacturing processes.     

Speeding up backpropagation using multiobjective evolutionary algorithms

The use of backpropagation for training artificial neural networks (ANNs) is usually associated with a long training process. The user needs to experiment with a number of network architectures; with larger networks, more computational cost in terms of training time is required. The objective of this letter is to present an optimization algorithm, comprising a multiobjective evolutionary algorithm and a gradient-based local search. In the rest of the letter, this is referred to as the memetic Pareto artificial neural network algorithm for training ANNs. The evolutionary approach is used to train the network and simultaneously optimize its architecture. The result is a set of networks, with each network in the set attempting to optimize both the training error and the architecture. We also present a self-adaptive version with lower computational cost. We show empirically that the proposed method is capable of reducing the training time compared to gradient-based techniques.     

基于蚁群优化的多目标社区检测算法

蚁群优化算法作为单目标优化问题,由于只有一个目标函数,通常会将解限制到特定的范围内。当优化的目标不恰当时,算法可能失效,比如分辨率限制问题。我们将多目标优化的思想与传统的用于社区检测的蚁群优化算法相结合,增加了目标函数个数,即增加了解的评价指标数目。该算法引入多目标策略,提出多目标ACO算法,该算法在一次运行过程中会产生一组Pareto最优解。并在三个真实世界网络证明该算法的有效性和准确性。     

Modeling and Pareto optimization of multi-objective order scheduling problems in production planning

This paper addresses a multi-objective order scheduling problem in production planning under a complicated production environment with the consideration of multiple plants, multiple production departments and multiple production processes. A Pareto optimization model, combining a NSGA-II-based optimization process with an effective production process simulator, is developed to handle this problem. In the NSGA-II-based optimization process, a novel chromosome representation and modified genetic operators are presented while a heuristic pruning and final selection decision-making process is developed to select the final order scheduling solution from a set of Pareto optimal solutions. The production process simulator is developed to simulate the production process in the complicated production environment. Experiments based on industrial data are conducted to validate the proposed optimization model. Results show that the proposed model can effectively solve the order scheduling problem by generating Pareto optimal solutions which are superior to industrial solutions.     

An interactive fuzzy multi-objective optimization method for engineering design

The coupling of performance functions due to common design variables and uncertainties in an engineering design process will result in difficulties in optimization design problems, such as poor collaboration among design objectives and poor resolution of design conflicts. To handle these problems, a fuzzy interactive multi-objective optimization model is developed based on Pareto solutions, where the metric function and some additional constraints are added to ensure the collaboration among design objectives. The trade-off matrix at the Pareto solutions was developed, and the method for selecting weighting coefficients of optimization objectives is also provided. The proposed method can generate a Pareto optimal set with the maximum satisfaction degree and the minimum distance from ideal solution. The favorable optimal solution can be then selected from the Pareto optimal set by analyzing the trade-off matrix and collaborative sensitivity. Two examples are presented to illustrate the proposed method.     

Multi-objective optimization of a stacked neural network using an evolutionary hyper-heuristic

The present paper deals with the development and optimization of a stacked neural network (SNN) through an evolutionary hyper-heuristic, called NSGA-II-QNSNN. The proposed hyper-heuristic is based on the NSGA-II (Non-dominated Sorting Genetic Algorithm - II) multi-objective optimization evolutionary algorithm which incorporates the Quasi-Newton (QN) optimization algorithm. QN is used for training each neural network from the stack. The final global optimal solution provided by NSGA-II-QNSNN algorithm is a Pareto optimal front. It represents all the equally good compromises that can be made between the structural complexity of the stacked neural network and its modelling performance. The set of decision variables, which led to obtaining the set of points in the Pareto optimal front, represents the optimum values for the parameters of the stacked neural network: the number of networks in the stack, the weights for every output of the composing networks, and the number of hidden neurons in each individual neural network. Each stacked neural network determined through the optimization process was trained and tested by applying it to a real world problem: the modelling of the polyacrylamide-based multicomponent hydrogels synthesis. The neural modelling established the influence of the reaction conditions on the reaction yield and the swelling degree. The results provided by NSGA-II-QNSNN were superior, not only in terms of performance, but also in terms of structural complexity, to those obtained in our previous works, where individual or aggregated neural networks were used, but the stacks were developed manually, based on successive trials.     

Robust Design using Pareto type optimization: A genetic algorithm with arithmetic crossover

In dual response systems (DRSs) optimization restrictions on the secondary response may rule out better conditions, since an acceptable value for the secondary response is usually unknown. In fact, process conditions that result in a smaller standard deviation are often preferable. Recently, several authors stated that the standard deviation of any performance property could be treated as a new property in its own right as far as Pareto optimizer was concerned. By doing this, there will be many alternative solutions (i.e., the trade-offs between the mean and standard deviation responses) of the DRS problem and Pareto optimization can explore them all. Such analysis is useful, and that is required in order to achieve an improved understanding of the problem before searching for a final optimal solution. In this paper, we again follow this new philosophy and solve the DRS problem by using a genetic algorithm with arithmetic crossover. The genetic algorithm is applied to the printing process problem for improving the quality of a printing process. Genetic algorithms, in contrast to the one-solution-at-a-time approach of most optimization algorithms, maintain a population of hundreds, or thousands, of solutions in speedy manner.     

A new neural network technique for the design of multilayered microwave shielded bandpass filters

In this work, we propose a novel technique based on neural networks, for the design of microwave filters in shielded printed technology. The technique uses radial basis function neural networks to represent the non linear relations between the quality factors and coupling coefficients, with the geometrical dimensions of the resonators. The radial basis function neural networks are employed for the first time in the design task of shielded printed filters, and permit a fast and precise operation with only a limited set of training data. Thanks to a new cascade configuration, a set of two neural networks provide the dimensions of the complete filter in a fast and accurate way. To improve the calculation of the geometrical dimensions, the neural networks can take as inputs both electrical parameters and physical dimensions computed by other neural networks. The neural network technique is combined with gradient based optimization methods to further improve the response of the filters. Results are presented to demonstrate the usefulness of the proposed technique for the design of practical microwave printed coupled line and hairpin filters. © 2008 Wiley Periodicals, Inc. Int J RF and Microwave CAE, 2009.     

Multicriteria optimization of cylindrical sandwich shells under combined loads

The paper is about multicriteria optimization of thin-walled cylindrical shells subjected to simple loads, such as axial compression and external pressure, and combined loads (axial compression and pressure). The optimization problem is given as a bicriterial one, with the weight of the shell as the first objective, and the flexibility of the shell as the second. The set of constraints includes the stability condition, strength conditions for each layer, technological and constructional requirements, and so on. Numerical calculations were obtained with the help of the program MOST. MOST is designed to solve multicriteria optimization problems for nonlinear engineering models with discrete and continuous decision variables. In MOST a concept of Pareto optimum is introduced for generating a set of optimal compromise solutions. The best optimal solution must be chosen from the Pareto optimal set with the help of the preference functions. Results of numerical calculations are presented in the form of tables and diagrams.     

冷轧机组批量作业计划模型与算法

针对编制冷轧机组作业计划受到钢卷宽度跳跃、入口厚度跳跃和出口厚度跳跃等多个工艺约束的问题, 把排产过程归纳为非对称双旅行商问题, 建立了冷轧机组生产作业计划的Pareto多目标模型. 提出了基于Pareto非支配集的自适应多目标蚁群算法, 利用自适应蚁群算法和Pareto非支配集思想, 综合考虑多个目标, 自适应地提供蚂蚁路径搜索参数, 并对得到的非支配解集对应路径更新信息素, 引导蚂蚁向最优解集方向搜索, 最终提供多个可行的批量作业计划, 根据生产要求从中选择合适的最优排产结果. 利用某冷轧薄板厂实际的生产数据进行仿真实验, 表明模型与算法在冷轧机组批量作业计划编制过程中具有可行性.     

基于神经网络和SQP算法的焊接飞溅优化控制

提出了神经网络和逐次二次规划法的在线优化控制方法,在神经网络建模的基础上, 把SQP算法和直接搜索两种寻优方法作了比较;用NN-SQP方法对焊接过程飞溅进行了控制, 取得较好的效果．并提出了用电弧声表征焊接飞溅量的软测量方法．     

Towards faster convergence of evolutionary multi-criterion optimization algorithms using Karush Kuhn Tucker optimality based local search

Evolutionary multi-criterion optimization (EMO) algorithms emphasize non-dominated and less crowded solutions in a population iteratively until the population converges close to the Pareto optimal set. During the search process, non-dominated solutions are differentiated only by their local crowding or contribution to hypervolume or using a similar other metric. Thus, during evolution and even at the final iteration, the true convergence behavior of each non-dominated solutions from the Pareto optimal set is unknown. Recent studies have used Karush Kuhn Tucker (KKT) optimality conditions to develop a KKT Proximity Measure (KKTPM) for estimating proximity of a solution from Pareto optimal set for a multi-objective optimization problem. In this paper, we integrate KKTPM with a recently proposed EMO algorithm to enhance its convergence properties towards the true Pareto optimal front. Specifically, we use KKTPM to identify poorly converged non-dominated solutions in every generation and apply an achievement scalarizing function based local search procedure to improve their convergence. Assisted by the KKTPM, the modified algorithm is designed in a way that maintains the total number of function evaluations as low as possible while making use of local search where it is most needed. Simulations on both constrained and unconstrained multi- and many objectives optimization problems demonstrate that the hybrid algorithm significantly improves the overall convergence properties. This study brings evolutionary optimization closer to mainstream optimization field and should motivate researchers to utilize KKTPM measure further within EMO and other numerical optimization algorithms.     

Estimation of the Pareto front in stochastic simulation through stochastic Kriging

Multi-objective optimization of simulated stochastic systems aims at estimating a representative set of Pareto optimal solutions and a common approach is to rely on metamodels to alleviate computational costs of the optimization process. In this article, both the objective and constraint functions are assumed to be smooth, highly non-linear and computationally expensive and are emulated by stochastic Kriging models. Then a novel global optimization algorithm, combing the expected hypervolume improvement of approximated Pareto front and the probability of feasibility of new points, is proposed to identify the Pareto front (set) with a minimal number of expensive simulations. The algorithm is suitable for the situations of having disconnected feasible regions and of having no feasible solution in initial design. Then, we also quantify the variability of estimated Pareto front caused by the intrinsic uncertainty of stochastic simulation using nonparametric bootstrapping method to better support decision making. One test function and an (s, S) inventory system experiment illustrate the potential and efficiency of the proposed sequential optimization algorithm for constrained multi-objective optimization problems in stochastic simulation, which is especially useful in Operations Research and Management Science.     

Hybrid-Game Strategies for multi-objective design optimization in engineering

A number of Game Strategies (GS) have been developed in past decades. They have been used in the fields of economics, engineering, computer science and biology due to their efficiency in solving design optimization problems. In addition, research in multi-objective (MO) and multidisciplinary design optimization (MDO) has focused on developing robust and efficient optimization methods to produce a set of high quality solutions with low computational cost. In this paper, two optimization techniques are considered; the first optimization method uses multi-fidelity hierarchical Pareto optimality. The second optimization method uses the combination of two Game Strategies; Nash-equilibrium and Pareto optimality. The paper shows how Game Strategies can be hybridised and coupled to Multi-Objective Evolutionary Algorithms (MOEA) to accelerate convergence speed and to produce a set of high quality solutions. Numerical results obtained from both optimization methods are compared in terms of computational expense and model quality. The benefits of using Hybrid-Game Strategies are clearly demonstrated.     

A new method to solve generalized multicriteria optimization problems using the simple genetic algorithm

Genetic algorithms (GAs), which are directed stochastic hill climbing algorithms, are a commonly used optimization technique and are generally applied to single criterion optimization problems with fairly complex solution landscapes. There has been some attempts to apply GA to multicriteria optimization problems. The GA selection mechanism is typically dependent on a single-valued objective function and so no general methods to solve multicriteria optimization problems have been developed so far. In this paper, a new method of transformation of the multiple criteria problem into a single-criterion problem is presented. The problem of transformation brings about the need for the introduction of thePareto set estimation method to perform the multicriteria optimization using GAs. From a given solution set, which is the population of a certain generation of the GA, the Pareto set is found. The fitness of population members in the next GA generation is calculated by a distance metric with a reference to the Pareto set of the previous generation. As we are unable to combine the objectives in some way, we resort to this distance metric in the positive Pareto space of the previous solutions, as the fitness of the current solutions. This new GA-based multicriteria optimization method is proposed here, and it is capable of handling any generally formulated multicriteria optimization problem. The main idea of the method is described in detail in this paper along with a detailed numerical example. Preliminary computer generated results show that our approach produces better, and far more Pareto solutions, than plain stochastic optimization methods.