Design of a fractional PI<Superscript>λ</Superscript>D<Superscript>μ</Superscript> controller using the cohort intelligence method

The cohort intelligence (CI) method has recently evolved as an optimization method based on artificial intelligence. We use the CI method for the first time to optimize the parameters of the fractional proportionalintegral- derivative (PID) controller. The performance of the CI method in designing the fractional PID controller was validated and compared with those of some other popular algorithms such as particle swarm optimization, the genetic algorithm, and the improved electromagnetic algorithm. The CI method yielded improved solutions in terms of the cost function, computing time, and function evaluations in comparison with the other three algorithms. In addition, the standard deviations of the CI method demonstrated the robustness of the proposed algorithm in solving control problems.     

A Version of the Mirror descent Method to Solve Variational Inequalities<Superscript>*</Superscript>

Nemirovski and Yudin proposed the mirror descent algorithm at the late 1970s to solve convex optimization problems. This method is suitable to solve huge-scale optimization problems. In the paper, we describe a new version of the mirror descent method to solve variational inequalities with pseudomonotone operators. The method can be interpreted as a modification of Popov’s two-step algorithm with the use of Bregman projections on the feasible set. We prove the convergence of the sequences generated by the proposed method.     

An inverse analysis method for design optimization with both statistical and fuzzy uncertainties

If the statistical data for the input uncertainties are sufficient to construct the distribution function, the input uncertainties can be treated as random variables to use the reliability-based design optimization (RBDO) method; otherwise, the input uncertainties can be treated as fuzzy variables to use the possibility-based design optimization (PBDO) method. However, many structural design problems include both input uncertainties with sufficient and insufficient data. This paper proposes a new mixed-variable design optimization (MVDO) method using the performance measure approach (PMA) for such design problems. For the inverse analysis, this paper proposes a new most probable/possible point (MPPP) search method called maximal failure search (MFS), which is an integration of the enhanced hybrid mean value method (HMV+) and maximal possibility search (MPS) method. This paper also improves the HMV+ method using an angle-based interpolation. Mathematical and physical examples are used to demonstrate the proposed inverse analysis method and MVDO method.     

区间参数高维多目标集合进化优化方法

区间参数高维多目标优化问题是现实生活中常见的一类优化问题,但其有效的求解方法并不是很多.对此,利用集合的概念,提出一种求解此类问题的新方法.首先,利用衡量解集收敛性、分布性、多样性的3种性能指标将原优化问题降为3目标优化问题;其次,采用集合Pareto占优关系和不确定测度来区分转化后优化问题解的优劣;再次,设计自适应变化的交叉、变异概率以提高种群的全局和局部搜索能力;最后,利用4种基准函数优化问题,对所提出方法和对比方法进行测试.测试结果显示,除了收敛性,所提出方法得到的Pareto解集的不确定性、多样性、分布性均优于对比方法.     

Likelihood-based representation of epistemic uncertainty and its application in robustness-based design optimization

In this paper, we propose a new likelihood-based methodology to represent epistemic uncertainty described by sparse point and/or interval data for input variables in uncertainty analysis and design optimization problems. A worst-case maximum likelihood-based approach is developed for the representation of epistemic uncertainty, which is able to estimate the distribution parameters of a random variable described by sparse point and/or interval data. This likelihood-based approach is general and is able to estimate the parameters of any known probability distributions. The likelihood-based representation of epistemic uncertainty is then used in the existing framework for robustness-based design optimization to achieve computational efficiency. The proposed uncertainty representation and design optimization methodologies are illustrated with two numerical examples including a mathematical problem and a real engineering problem.     

An adaptive optimization scheme with satisfactory transient performance

Adaptive optimization (AO) schemes based on stochastic approximation principles such as the Random Directions Kiefer-Wolfowitz (RDKW), the Simultaneous Perturbation Stochastic Approximation (SPSA) and the Adaptive Fine-Tuning (AFT) algorithms possess the serious disadvantage of not guaranteeing satisfactory transient behavior due to their requirement for using random or random-like perturbations of the parameter vector. The use of random or random-like perturbations may lead to particularly large values of the objective function, which may result to severe poor performance or stability problems when these methods are applied to closed-loop controller optimization applications. In this paper, we introduce and analyze a new algorithm for alleviating this problem. Mathematical analysis establishes satisfactory transient performance and convergence of the proposed scheme under a general set of assumptions. Application of the proposed scheme to the adaptive optimization of a large-scale, complex control system demonstrates the efficiency of the proposed scheme.     

E(FG)<Superscript>2</Superscript>: a new fixed-grid shape optimization method based on the element-free galerkin mesh-free analysis

We propose a shape optimization method over a fixed grid. Nodes at the intersection with the fixed grid lines track the domain’s boundary. These “floating” boundary nodes are the only ones that can move/appear/disappear in the optimization process. The element-free Galerkin (EFG) method, used for the analysis problem, provides a simple way to create these nodes. The fixed grid (FG) defines integration cells for EFG method. We project the physical domain onto the FG and numerical integration is performed over partially cut cells. The integration procedure converges quadratically. The performance of the method is shown with examples from shape optimization of thermal systems involving large shape changes between iterations. The method is applicable, without change, to shape optimization problems in elasticity, etc. and appears to eliminate non-differentiability of the objective noticed in finite element method (FEM)-based fictitious domain shape optimization methods. We give arguments to support this statement. A mathematical proof is needed.     

Minmax regret combinatorial optimization problems with investments

A new minmax regret optimization model in a system with uncertain parameters is proposed. In this model it is allowed to make investments before a minmax regret solution is implemented in order to modify the source or the nature of the existing uncertainty. Therefore, it is allowed to spend resources in order to change the basic cost structure of the system and take advantage of the modified system to find a robust solution. Some properties of this model allow us to have proper Mathematical Programming formulations that can be solved by standard optimization packages. As a practical application we consider the shortest path problem in a network in which it is possible to modify the uncertainty intervals for the arc costs by investing in the system. We also give an approximate algorithm and generalize some existing results on constant factor approximations.     

Reducing the Size of a Sample Sufficient for Learning Due to the Symmetrization of Correlation Relationships Between Biometric Data<Superscript>*</Superscript>

This paper shows that correlation coefficients obtained from small test samples for biometric data involve considerable uncertainty. This interferes with using them for machine training (setting) of classical quadratic forms and Bayesian networks. A method for symmetrizing correlation relationships is proposed. The requirement on the volume of biometric data is proved to be reduced considerably in this case. As a consequence, the setting (teaching) of quadratic forms and setting of maximum likelihood Bayesian networks become much more stable problems. This enables many-fold reduction in the requirement on the size of the training sample for an “own” biometric image.     

Inertial Hybrid Splitting Methods for Operator Inclusion Problems<Superscript>*</Superscript>

In this paper, new algorithms are proposed to solve operator inclusion problems with maximal monotone operators acting in a Hilbert space. The algorithms are based on inertial extrapolation and three well-known methods: Tseng forward-backward splitting and two hybrid algorithms for approximation of fixed points of nonexpansive operators. Theorems about strong convergence of the sequences generated by the algorithms are proved.     

An improved firefly algorithm for solving dynamic multidimensional knapsack problems

There is a wide range of publications reported in the literature, considering optimization problems where the entire problem related data remains stationary throughout optimization. However, most of the real-life problems have indeed a dynamic nature arising from the uncertainty of future events. Optimization in dynamic environments is a relatively new and hot research area and has attracted notable attention of the researchers in the past decade. Firefly Algorithm (FA), Genetic Algorithm (GA) and Differential Evolution (DE) have been widely used for static optimization problems, but the applications of those algorithms in dynamic environments are relatively lacking. In the present study, an effective FA introducing diversity with partial random restarts and with an adaptive move procedure is developed and proposed for solving dynamic multidimensional knapsack problems. To the best of our knowledge this paper constitutes the first study on the performance of FA on a dynamic combinatorial problem. In order to evaluate the performance of the proposed algorithm the same problem is also modeled and solved by GA, DE and original FA. Based on the computational results and convergence capabilities we concluded that improved FA is a very powerful algorithm for solving the multidimensional knapsack problems for both static and dynamic environments.     

New Approximation Assisted Multi-objective collaborative Robust Optimization (new AA-McRO) under interval uncertainty

Existing collaborative optimization techniques with multiple coupled subsystems are predominantly focused on single-objective deterministic optimization. However, many engineering optimization problems have system and subsystems that can each be multi-objective, constrained and with uncertainty. The literature reports on a few deterministic Multi-objective Multi-Disciplinary Optimization (MMDO) techniques. However, these techniques in general require a large number of function calls and their computational cost can be exacerbated when uncertainty is present. In this paper, a new Approximation-Assisted Multi-objective collaborative Robust Optimization (New AA-McRO) under interval uncertainty is presented. This new AA-McRO approach uses a single-objective optimization problem to coordinate all system and subsystem multi-objective optimization problems in a Collaborative Optimization (CO) framework. The approach converts the consistency constraints of CO into penalty terms which are integrated into the system and subsystem objective functions. The new AA-McRO is able to explore the design space better and obtain optimum design solutions more efficiently. Also, the new AA-McRO obtains an estimate of Pareto optimum solutions for MMDO problems whose system-level objective and constraint functions are relatively insensitive (or robust) to input uncertainties. Another characteristic of the new AA-McRO is the use of online approximation for objective and constraint functions to perform system robustness evaluation and subsystem-level optimization. Based on the results obtained from a numerical and an engineering example, it is concluded that the new AA-McRO performs better than previously reported MMDO methods.     

Model uncertainty approximation using a copula-based approach for reliability based design optimization

Reliability-based design optimization (RBDO) has been widely used to design engineering products with minimum cost function while meeting reliability constraints. Although uncertainties, such as aleatory uncertainty and epistemic uncertainty, have been well considered in RBDO, they are mainly considered for model input parameters. Model uncertainty, i.e., the uncertainty of model bias indicating the inherent model inadequacy for representing the real physical system, is typically overlooked in RBDO. This paper addresses model uncertainty approximation in a product design space and further integrates the model uncertainty into RBDO. In particular, a copula-based bias modeling approach is proposed and results are demonstrated by two vehicle design problems.     

LMI optimization approach to robust H∞ observer design and static output feedback stabilization for discrete‐time nonlinear uncertain systems

A new approach for the design of robust H_∞ observers for a class of Lipschitz nonlinear systems with time‐varying uncertainties is proposed based on linear matrix inequalities (LMIs). The admissible Lipschitz constant of the system and the disturbance attenuation level are maximized simultaneously through convex multiobjective optimization. The resulting H_∞ observer guarantees asymptotic stability of the estimation error dynamics and is robust against nonlinear additive uncertainty and time‐varying parametric uncertainties. Explicit norm‐wise and element‐wise bounds on the tolerable nonlinear uncertainty are derived. Also, a new method for the robust output feedback stabilization with H_∞ performance for a class of uncertain nonlinear systems is proposed. Our solution is based on a noniterative LMI optimization and is less restrictive than the existing solutions. The bounds on the nonlinear uncertainty and multiobjective optimization obtained for the observer are also applicable to the proposed static output feedback stabilizing controller. Copyright © 2008 John Wiley & Sons, Ltd.     

有色冶金过程不确定优化方法探讨

有色冶金过程受原料来源多样、工况条件波动、生产成分变化等因素的影响,存在大量的不确定性,严重影响了冶炼生产的稳定性与可靠性.鉴于此,综述不同类型不确定性优化问题的描述方法,具体包括概率不确定优化问题、模糊不确定优化问题和区间不确定优化问题.通过分析有色冶金生产过程的特点与需求,以3种典型的有色冶金过程不确定优化问题为例,探讨不同类型的有色冶金过程不确定优化方法.针对氧化铝生料浆配料过程的概率不确定优化问题,采用基于Hammersley sequence sampling(HSS)的方法实现不确定模型的确定性转换;针对湿法炼锌除铜过程的模糊不确定优化问题,采用基于模糊规则的方法进行确定性评估;针对锌电解分时供电过程的区间不确定优化问题,采用基于min-max的方法求解鲁棒解.工业运行数据均验证了上述方法的有效性.     

Traveling salesman problems with profits and stochastic customers

In this paper, we introduce a class of new selection and routing problems, and name it as the traveling salesman problem with profits and stochastic customers (TSPPSC), which is an extension of the traveling salesman problem with profits (TSPP). The class of new problems is put forward to address how to deal with stochastic customer presence under the environment in which an associated profit is obtained once a customer is visited. It is defined on a complete graph in which profits are associated with the vertices and travel costs are associated with the edges. Each vertex (customer) has a probability of requiring a visit. The objective is the simultaneous optimization of the expected collected profits and expected travel costs. According to the way the two objectives (profits and travel costs) are addressed, TSPPSC is categorized into three subproblems. Mathematical formulations are provided for these problems and a genetic algorithm is proposed to solve one of these subproblems. Computational experiments conducted on several sets of instances show a good performance of the proposed algorithm.     

Topology optimization of structures using modified binary differential evolution

Differential evolution (DE) is an efficient population based algorithm used to solve real-valued optimization problems. It has the advantage of incorporating relatively simple and efficient mutation and crossover operators. However, the DE operator is based on floating-point representation only, and is difficult to use when solving combinatorial optimization problems. In this paper, a modified binary differential evolution (MBDE) based on a binary bit-string framework with a simple and new binary mutation mechanism is proposed. Two test functions are applied to verify the MBDE framework with the new binary mutation mechanism, and four structural topology optimization problems are used to study the performance of the proposed MBDE algorithm. The experimental studies show that the proposed MBDE algorithm is not only suitable for structural topology optimization, but also has high viability in terms of solving numerical optimization problems.     

A new nearest neighbor classification method based on fuzzy set theory and aggregation operators

The Fuzzy Nearest Neighbor Classification (FuzzyNNC) has been successfully used, as a tool to deal with supervised classification problems. It has significantly increased the classification accuracy by considering the uncertainty associated with the class labels of the training patterns. Nevertheless, FuzzyNNC's limited methods fail to efficiently handle the imprecision in features measurement and the uncertainty induced by the choice of the distance measure and the number of neighbors in the decision rule. In this paper, we propose a new method called Fuzzy Analogy-based Classification (FABC) to tackle the FuzzyNNC limitations. In this work, we exploit the fuzzy linguistic modeling and approximate reasoning materials in order to endow FABC with intelligent capabilities, like imprecision tolerance, optimization, adaptability and trade-off. Hence, our approach is composed of two main steps. Firstly, we describe the domain features using fuzzy linguistic variables. Secondly, we define the classification process using two intelligent aggregation operators. The first one allows the optimization of the similarity evaluation, by defining the adequate features to be considered. The second one integrates a trade-off strategy within the decision rule, by using a global voting approach with compensation property. The integration of such mechanisms will increase the classification accuracy and make the FuzzyNNC approach more useful for classification problems where imprecision and uncertainty are unavoidable. The proposed FABC is validated on the most known datasets, representing various classification difficulties and compared to the many extensions of the FuzzyNNC approach. The results obtained show that our proposed FABC method can be adapted to different classification problems and improve the classification accuracy. Thus, the FABC has the best rank value against the comparison methods with high significant level. Moreover, we conclude that our optimized similarity and global voting rule are more robust to handle the uncertainty in the classification process than those used by the comparison methods.     

A comparison index for interval ordering based on generalized Hukuhara difference

Interval methods is one option for managing uncertainty in optimization problems and in decision management. The precise numerical estimation of coefficients may be meaningless in real-world applications, because data sources are often uncertain, vague and incomplete. In this paper we introduce a comparison index for interval ordering based on the generalized Hukuhara difference; we show that the new index includes the commonly used order relations proposed in literature. The definition of a risk measure guarantees the possibility to quantify a worst-case loss when solving maximization or minimization problems with intervals.     

Approaches to uncertainties in facility layout problems: Perspectives at the beginning of the 21<Superscript>st</Superscript> Century

Production uncertainty is one of the most challenging aspects in manufacturing environments in the 21st century. The next generation of intelligent manufacturing is dynamically depending on the production requirements, and success in designing agile facilities is closely related to what extent these requirements are satisfied. This paper presents the most recent advancements in designing robust and flexible facilities under uncertainty. The focus is on exploring the way uncertainty is incorporated in facility design, namely dynamic and stochastic facility layout problems. Recent approaches are explored and categorized in detail, and previous approaches are briefly reviewed in the related categories. Furthermore, research avenues warranting exploration in the emerging field of facility design are also discussed.