利用演化算法自适应选取正则算子

提出一种新的技术，它自适应地选取正则算子以取得较理想的恢复效果．通过理论分析和实验发现当恢复图像残差的频谱能量分布较均匀时恢复效果较好．这种分布均匀性可以用正则图像残差的各子频段能量偏离平均能量的程度最小来衡量，这个最小化问题以各种各样的正则算子组成的空间为搜索空间．由于一般的优化算法对此优化问题无能为力，演化算法用来求解此问题，从而自适应地选择正则化算子．实验表明新方法选取的正则算子恢复效果较好．     

An operator-theoretic approach to the mixed-sensitivity minimization problem

We consider the mixed-sensitivity minimization problem (scalar case). It gives rise to the so-called two-block problem on the algebra H^∞; we analyze this problem from an operator point of view, using Krein space theory. We obtain a necessary and sufficient condition for the uniqueness of the solution and a parameterization of all solutions in the non-uniqueness case. Moreover, an interpolation interpretation is given for the finite-dimensional case.     

Bicriterial servicing problems for stationary objects in a one-dimensional working zone of a processor

We consider the single-stage servicing model for a group of stationary objects distributed along a one-dimensional working zone of a moving processor. Each object is associated with an individual penalty function with respect to one or two criteria; we consider total penalty minimization and maximal individual penalty minimization criteria. For these bicriterial problems, we study the problems of constructing complete collections of efficient estimates and synthesizing Pareto-optimal solutions; we also consider the computational complexity of the resulting problems.     

Logarithmic aggregation operators and distance measures

The Hamming distance is a well‐known measure that is designed to provide insights into the similarity between two strings of information. In this study, we use the Hamming distance, the optimal deviation model, and the generalized ordered weighted logarithmic averaging (GOWLA) operator to develop the ordered weighted logarithmic averaging distance (OWLAD) operator and the generalized ordered weighted logarithmic averaging distance (GOWLAD) operator. The main advantage of these operators is the possibility of modeling a wider range of complex representations of problems under the assumption of an ideal possibility. We study the main properties, alternative formulations, and families of the proposed operators. We analyze multiple classical measures to characterize the weighting vector and propose alternatives to deal with the logarithmic properties of the operators. Furthermore, we present generalizations of the operators, which are obtained by studying their weighting vectors and the lambda parameter. Finally, an illustrative example regarding innovation project management measurement is proposed, in which a multi‐expert analysis and several of the newly introduced operators are utilized.     

ENDER: a statistical framework for boosting decision rules

Induction of decision rules plays an important role in machine learning. The main advantage of decision rules is their simplicity and human-interpretable form. Moreover, they are capable of modeling complex interactions between attributes. In this paper, we thoroughly analyze a learning algorithm, called ENDER, which constructs an ensemble of decision rules. This algorithm is tailored for regression and binary classification problems. It uses the boosting approach for learning, which can be treated as generalization of sequential covering. Each new rule is fitted by focusing on examples which were the hardest to classify correctly by the rules already present in the ensemble. We consider different loss functions and minimization techniques often encountered in the boosting framework. The minimization techniques are used to derive impurity measures which control construction of single decision rules. Properties of four different impurity measures are analyzed with respect to the trade-off between misclassification (discrimination) and coverage (completeness) of the rule. Moreover, we consider regularization consisting of shrinking and sampling. Finally, we compare the ENDER algorithm with other well-known decision rule learners such as SLIPPER, LRI and RuleFit.     

Extracting image orientation feature by using integration operator

This paper presents an orientation operator to extract image local orientation features. We show that a proper employment of image integration leads to an unbiased orientation estimate, based on which an orientation operator is proposed. The resulting discrete operator has flexibility in the scale selection as the scale change does not violate the bias minimization criteria. An analytical formula is developed to compare orientation biases of various discrete operators. The proposed operator shows lower bias than eight well-known gradient operators. Experiments further demonstrate higher orientation accuracy of the proposed operator than these gradient operators.     

Quadratic optimal control of stable systems through spectral factorization

We consider the infinite horizon quadratic cost minimization problem for a linear system with finitely many inputs and outputs. A common approach to treat a problem of this type is to construct a semigroup in an abstract state space, and to use infinite-dimensional control theory. However, this approach is less appealing in the case where there are discrete time delays in the impulse response, because such time delays force both the control operator and the observation operator to be unbounded at the same time. In order to be able to include this case we take an alternative approach. We work in an input-output framework, and reduce the problem to a symmetric Wiener-Hopf problem, that can be solved by means of a canonical factorization of the symbol. In a standard shift semigroup realization this amounts to factorizations of the Riccati operator and the feedback operator into convolution operators and projections. Our approach leads to a new significant discovery: in the case where the impulse response of the system contains discrete time delays, the standard Riccati equation is incorrect; to get the correct Riccati equation the feed-through matrix of the system must be partially replaced by the feed-through matrix of the spectral factor. This means that, before it is even possible to write down the correct Riccati equation, a spectral factorization problem must first be solved to find one of the weighting matrices in this equation.     

Joint Optimization of Hardware and Network Costs for Distributed Computer Systems

Multiple combinations of hardware and network components can be selected to design an information technology (IT) infrastructure that satisfies requirements. The professional criterion to deal with these degrees of freedom is cost minimization. However, a scientific approach has been rarely applied to cost minimization, particularly for the joint optimization of hardware and network systems. This paper provides an overall methodology for combining hardware and network designs in a single cost minimization problem for multisite computer systems. Costs are minimized by applying a heuristic optimization approach to a sound decomposition of the problem. We consider most of the design alternatives that are enabled by current hardware and network technologies, including server sizing, localization of mutitier applications, and reuse of legacy systems. The methodology is empirically verified with a database of costs that has also been built as part of this paper. Verifications consider several test cases with different computing and communication requirements. Cost reductions are evaluated by comparing the cost of methodological results with those of architectural solutions that are obtained by applying professional design guidelines. The quality of heuristic optimization results is evaluated through comparison with lower bounds.     

Energy efficient opportunistic cooperative transmission with different ratio combinings： from a new perspective

In cooperative communication, different ratio combining approaches can be utilized at the receiver based on the channel state information （CSI） available to the destination. In this paper, we focus on optimal energy allocation under amplify-and-forward （AF） cooperative communications when various ratio combining methods are utilized. More specifically, we consider a suite of important and fundamental problems, includ- ing signM-to-noise ratio （SNR） maximization under a weighted total energy constraint, weighted total energy minimization under an SNR constraint, weighted total energy minimization under an outage probability con- straint and outage probability minimization under instantaneous weighted total energy constraint, and analyze the relationship among these problems. We first consider maximal ratio combining （MRC） and derive exact analytical solutions. To reveal the key factors in the resource allocation problem, we further transform the exact results with multiple parameters into more intuitive results with only two quantities. The resulting solutions provide a new perspective to understand optimal energy-efficient opportunistic cooperative transmissions. We then consider fixed ratio combining （FRC） and show that an explicit analytical solution does not exist to the original problem. To this end, based on the convexity proofs for the objective functions, we utilize numerical convex optimizations to obtain the unique solution. Both numerical and simulation studies are conducted to validate our theoretical analysis.     

Composing cardinal direction relations

We study the recent proposal of Goyal and Egenhofer who presented a model for qualitative spatial reasoning about cardinal directions. Our approach is formal and complements the presentation of Goyal and Egenhofer. We focus our efforts on the composition operator for two cardinal direction relations. We consider two interpretations of the composition operator: consistency-based and existential composition. We point out that the only published method to compute the consistency-based composition does not always work correctly. Then, we consider progressively more expressive classes of cardinal direction relations and give consistency-based composition algorithms for these classes. Our theoretical framework allows us to prove formally that our algorithms are correct. When we consider existential composition, we demonstrate that the binary relation resulting from the composition of two cardinal direction relations cannot be expressed using the relations defined by Goyal and Egenhofer. Finally, we discuss some extensions to the basic model and consider the composition problem for these extensions.     

Two novel iterative algorithms for interference alignment with symbol extensions in the MIMO interference channel

Interference alignment(IA)with symbol extensions in the quasi-static flat-fading K-user multipleinput multiple-output(MIMO)interference channel(IC)is considered in this paper.In general,long symbol extensions are required to achieve the optimal fractional degrees of freedom(DOF).However,long symbol extensions over orthogonal dimensions produce structured(diagonal or block diagonal)channel matrices from transmitters to receivers.Most of existing approaches are limited in cases where the channels have some special structures,because they align the interference without preserving the dimensionality of the desired signal explicitly.To overcome this common drawback of most existing IA algorithms,two novel iterative algorithms for IA with symbol extensions are proposed.The first algorithm designs transceivers for IA based on the mean square error(MSE)criterion which minimizes the total MSE of the system while preserving the dimensionality of the desired signal.The novel IA algorithm is a constrained optimization problem which can be solved by Lagrangian method.Its convergence is proven as well.Utilizing the reciprocity of alignment,the second algorithm is proposed based on the maximization of the multidimensional case of the generalized Rayleigh Quotient.It maximizes each receiver’s signal to interference plus noise ratio(SINR)while preserving the dimensionality of the desired signal.In simulation results,we show the superiority of the proposed algorithms in terms of four aspects,i.e.,average sum rate,the fraction of the interfering signal power in the desired signal subspace,bit error rate(BER)and the relative power of the weakest desired data stream.     

遗传算法在风光互补发电系统优化设计中的应用

风光互补发电系统的优化配置是一个多目标优化问题,优化目标为系统安装成本,约束条件为供电可靠性。如何合理的匹配设计是充分发挥风光互补发电优越性的关键。在成本(目标)函数的最小化计算中,采用改进的遗传算法进行优化,随机搜索并采用选择、交叉、变异三种基本算子在全部组合中搜索最优化的配置。结果表明在满足负荷用电的前提下,其经济性能优于单独的光伏系统和单独的风电系统。     

Intuitionistic fuzzy ordered weighted distance operator

The ordered weighted distance [27], [49] is a new decision-making technique, having been proved useful for the treatment of input data in the form of exact numbers. In this paper, we consider the situation with intuitionistic fuzzy information and develop an intuitionistic fuzzy ordered weighted distance (IFOWD) operator. The IFOWD operator is very suitable to deal with the situations where the input data are represented in intuitionistic fuzzy information and includes a wide range of distance measures and aggregation operators. We study some of its main properties and different families of IFOWD operators. Finally, we develop an application of the new approach in a group decision-making under intuitionistic fuzzy environment and illustrate it with a numerical example.     

Decision support for unrelated parallel machine scheduling with discrete controllable processing times

In a manufacturing or service system, the actual processing time of a job can be controlled by the amount of an indivisible resource allocated, such as workers or auxiliary facilities. In this paper, we consider unrelated parallel-machine scheduling problems with discrete controllable processing times. The processing time of a job is discretely controllable by the allocation of indivisible resources. The planner must make decisions on whether or how to allocate resources to jobs during the scheduling horizon to optimize the performance measures. The objective is to minimize the total cost including the cost measured by a standard criterion and the total processing cost. We first consider three scheduling criterions: the total completion time, the total machine load, and the total earliness and tardiness penalties. If the number of machines and the number of possible processing times are fixed, we develop polynomial time algorithms for the considered problems. We then consider the minimization problem of the makespan cost plus the total processing cost and present an integer programming method and a heuristic method to solve the studied problem.     

On the Convergence of Sample Approximations for Stochastic Programming Problems with Probabilistic Criteria

We consider stochastic programming problems with probabilistic and quantile criteria. We describe a method for approximating these problems with a sample of realizations for random parameters. When we use this method, criterial functions of the problems are replaced with their sample estimates. We show the hypoconvergence of sample probability functions to its exact value that guarantees the convergence of approximations for the probability function maximization problem on a compact set with respect to both the value of the criterial function and the optimization strategy. We prove a theorem on the convergence of approximation for the quantile function minimization problem with respect to the value of the criterial function and the optimization strategy.     

Bisimulation Minimization and Symbolic Model Checking

State space minimization techniques are crucial for combating state explosion. A variety of explicit-state verification tools use bisimulation minimization to check equivalence between systems, to minimize components before composition, or to reduce a state space prior to model checking. Experimental results on bisimulation minimization in symbolic model checking contexts, however, are mixed. This paper explores bisimulation minimization as an optimization in symbolic model checking of invariance properties. We consider three bisimulation minimization algorithms. From each, we produce a BDD-based model checker for invariant properties and compare this model checker to a conventional one based on backwards reachability. Our comparisons, both theoretical and experimental, suggest that bisimulation minimization is not viable in the context of invariance verification, because performing the minimization requires as many, if not more, computational resources as model checking the unminimized system through backwards reachability.     

On the Optimal Linear Convergence Rate of a Generalized Proximal Point Algorithm

The proximal point algorithm (PPA) has been well studied in the literature. In particular, its linear convergence rate has been studied by Rockafellar in 1976 under certain condition. We consider a generalized PPA in the generic setting of finding a zero point of a maximal monotone operator, and show that the condition proposed by Rockafellar can also sufficiently ensure the linear convergence rate for this generalized PPA. Indeed we show that these linear convergence rates are optimal. Both the exact and inexact versions of this generalized PPA are discussed. The motivation of considering this generalized PPA is that it includes as special cases the relaxed versions of some splitting methods that are originated from PPA. Thus, linear convergence results of this generalized PPA can be used to better understand the convergence of some widely used algorithms in the literature. We focus on the particular convex minimization context and specify Rockafellar’s condition to see how to ensure the linear convergence rate for some efficient numerical schemes, including the classical augmented Lagrangian method proposed by Hensen and Powell in 1969 and its relaxed version, the original alternating direction method of multipliers (ADMM) by Glowinski and Marrocco in 1975 and its relaxed version (i.e., the generalized ADMM by Eckstein and Bertsekas in 1992). Some refined conditions weaker than existing ones are proposed in these particular contexts.     

Optimization problems in contracted tensor networks

We discuss the calculus of variations in tensor representations with a special focus on tensor networks and apply it to functionals of practical interest. The survey provides all necessary ingredients for applying minimization methods in a general setting. The important cases of target functionals which are linear and quadratic with respect to the tensor product are discussed, and combinations of these functionals are presented in detail. As an example, we consider the representation rank compression in tensor networks. For the numerical treatment, we use the nonlinear block Gauss?CSeidel method. We demonstrate the rate of convergence in numerical tests.     

A Class of Generalized Laplacians on Vector Bundles Devoted to Multi-Channel Image Processing

In the context of fibre bundles theory, there exist some differential operators of order 2, called generalized Laplacians, acting on sections of vector bundles over Riemannian manifolds, and generalizing the Laplace-Beltrami operator. Such operators are determined by covariant derivatives on vector bundles. In this paper, we construct a class of generalized Laplacians, devoted to multi-channel image processing, from the construction of optimal covariant derivatives. The key idea is to consider an image as a section of an associate bundle, that is a vector bundle related to a principal bundle through a group representation. In this context, covariant derivatives are determined by connection 1-forms on principal bundles. We construct optimal connection 1-forms by the minimization of a variational problem on principal bundles. From the heat equations of the generalized Laplacians induced by the corresponding optimal covariant derivatives, we obtain diffusions whose behaviors depend of the choice of the group representation. We provide experiments on color images.