Global optimization for the ℋ∞-norm model reduction problem

A branch and bound algorithm is proposed to solve the [image omitted]-norm model reduction problem for continuous and discrete-time linear systems, with convergence to the global optimum in a finite time. The lower and upper bounds in the optimization procedure are described by linear matrix inequalities (LMI). Also proposed are two methods with which to reduce the convergence time of the branch and bound algorithm: the first one uses the Hankel singular values as a sufficient condition to stop the algorithm, providing to the method a fast convergence to the global optimum. The second one assumes that the reduced model is in the controllable or observable canonical form. The [image omitted]-norm of the error between the original model and the reduced model is considered. Examples illustrate the application of the proposed method.

Uma dedução dos critérios de multicriticalidade e o cálculo de pontos tricríticos via otimização global

Uma dedução dos critérios de multicriticalidade para o cálculo de pontos críticos de qualquer ordem representa a formalização de ideias utilizadas para calcular pontos críticos e tricríticos e ainda amplia tais ideias. De posse desta dedução pode-se compreender os critérios de tricriticalidade e, com isso, através de uma abordagem via problema de otimização global pode-se fazer o cálculo de pontos tricríticos utilizando um método numérico adequado de otimização global. Para evitar um excesso de custo computacional com rotinas numéricas utilizou-se aproximações na forma de diferenças finitas dos termos que compõem a função objetivo. Para simular a relação P v - T optou-se pela equação de estado cúbica de Peng-Robinson e pela regra clássica de fluidos de van der Vaals, para modelagem do problema também se calculou os tensores de ordem 2, 3, 4 e 5 da função do teste de estabilidade. Os resultados obtidos foram comparados com dados experimentais e por resultados obtidos com outros autores que utilizaram métodos numéricos, equação de estado ou abordagem diferente das utilizadas neste trabalho.

Surrogate-based analysis and optimization for the design of heat sinks with jet impingement

Heat sinks are widely used for cooling electronic devices and systems. Their thermal performance is usually determined by the material, shape, and size of the heat sink. With the assistance of computational fluid dynamics (CFD) and surrogate-based optimization, heat sinks can be designed and optimized to achieve a high level of performance. In this paper, the design and optimization of a plate-fin-type heat sink cooled by impingement jet is presented. The flow and thermal fields are simulated using the CFD simulation; the thermal resistance of the heat sink is then estimated. A Kriging surrogate model is developed to approximate the objective function (thermal resistance) as a function of design variables. Surrogate-based optimization is implemented by adaptively adding infill points based on an integrated strategy of the minimum value, the maximum mean square error approach, and the expected improvement approaches. The results show the influence of design variables on the thermal resistance and give the optimal heat sink with lowest thermal resistance for given jet impingement conditions. 

Managing Quality Properties of Web Service Compositions

Web services from different partners can be combined to applications that realize a more complex business goal. Such applications built as Web service compositions define how interactions between Web services take place in order to implement the business logic. Web service compositions not only have to provide the desired functionality but also have to comply with certain Quality of Service (QoS) levels. Maximizing the users' satisfaction, also reflected as Quality of Experience (QoE), is a primary goal to be achieved in a Service-Oriented Architecture (SOA). Unfortunately, in a dynamic environment like SOA unforeseen situations might appear like services not being available or not responding in the desired time frame. In such situations, appropriate actions need to be triggered in order to avoid the violation of QoS and QoE constraints. In this thesis, proper solutions are developed to manage Web services and Web service compositions with regard to QoS and QoE requirements. The Business Process Rules Language (BPRules) was developed to manage Web service compositions when undesired QoS or QoE values are detected. BPRules provides a rich set of management actions that may be triggered for controlling the service composition and for improving its quality behavior. Regarding the quality properties, BPRules allows to distinguish between the QoS values as they are promised by the service providers, QoE values that were assigned by end-users, the monitored QoS as measured by our BPR framework, and the predicted QoS and QoE values. BPRules facilitates the specification of certain user groups characterized by different context properties and allows triggering a personalized, context-aware service selection tailored for the specified user groups. In a service market where a multitude of services with the same functionality and different quality values are available, the right services need to be selected for realizing the service composition. We developed new and efficient heuristic algorithms that are applied to choose high quality services for the composition. BPRules offers the possibility to integrate multiple service selection algorithms. The selection algorithms are applicable also for non-linear objective functions and constraints. The BPR framework includes new approaches for context-aware service selection and quality property predictions. We consider the location information of users and services as context dimension for the prediction of response time and throughput. The BPR framework combines all new features and contributions to a comprehensive management solution. Furthermore, it facilitates flexible monitoring of QoS properties without having to modify the description of the service composition. We show how the different modules of the BPR framework work together in order to execute the management rules. We evaluate how our selection algorithms outperform a genetic algorithm from related research. The evaluation reveals how context data can be used for a personalized prediction of response time and throughput.

Investigating Smart Sampling as a population initialization method for Differential Evolution in continuous problems

Recently, researches have shown that the performance of metaheuristics can be affected by population initialization. Opposition-based Differential Evolution (ODE), Quasi-Oppositional Differential Evolution (QODE), and Uniform-Quasi-Opposition Differential Evolution (UQODE) are three state-of-the-art methods that improve the performance of the Differential Evolution algorithm based on population initialization and different search strategies. In a different approach to achieve similar results, this paper presents a technique to discover promising regions in a continuous search-space of an optimization problem. Using machine-learning techniques, the algorithm named Smart Sampling (SS) finds regions with high possibility of containing a global optimum. Next, a metaheuristic can be initialized inside each region to find that optimum. SS and DE were combined (originating the SSDE algorithm) to evaluate our approach, and experiments were conducted in the same set of benchmark functions used by ODE, QODE and UQODE authors. Results have shown that the total number of function evaluations required by DE to reach the global optimum can be significantly reduced and that the success rate improves if SS is employed first. Such results are also in consonance with results from the literature, stating the importance of an adequate starting population. Moreover, SS presents better efficacy to find initial populations of superior quality when compared to the other three algorithms that employ oppositional learning. Finally and most important, the SS performance in finding promising regions is independent of the employed metaheuristic with which SS is combined, making SS suitable to improve the performance of a large variety of optimization techniques. (C) 2012 Elsevier Inc. All rights reserved.

Finding the Relationship between a Search Algorithm and a Class of Functions on Discrete Space by Exhaustive Search

* The work is supported by RFBR, grant 04-01-00858-a.

A Global Constraint On Relative Rotation To Avoid Lumped Compliant Mechanisms In Topology Optimization

Some of the well known formulations for topology optimization of compliant mechanisms could lead to lumped compliant mechanisms. In lumped compliance, most of the elastic deformation in a mechanism occurs at few points, while rest of the mechanism remains more or less rigid. Such points are referred to as point-flexures. It has been noted in literature that high relative rotation is associated with point-flexures. In literature we also find a formulation of local constraint on relative rotations to avoid lumped compliance. However it is well known that a global constraint is easier to handle than a local constraint, by a numerical optimization algorithm. The current work presents a way of putting global constraint on relative rotations. This constraint is also simpler to implement since it uses linearized rotation at the center of finite-elements, to compute relative rotations. I show the results obtained by using this constraint oil the following benchmark problems - displacement inverter and gripper.

Connectionist approach for global optimization

A connectionist approach for global optimization is proposed. The standard function set is tested. Results obtained, in the case of large scale problems, indicate excellent scalability of the proposed approach

A perturbed martingale approach to global optimization

A new global stochastic search, guided mainly through derivative-free directional information computable from the sample statistical moments of the design variables within a Monte Carlo setup, is proposed. The search is aided by imparting to the directional update term additional layers of random perturbations referred to as `coalescence' and `scrambling'. A selection step, constituting yet another avenue for random perturbation, completes the global search. The direction-driven nature of the search is manifest in the local extremization and coalescence components, which are posed as martingale problems that yield gain-like update terms upon discretization. As anticipated and numerically demonstrated, to a limited extent, against the problem of parameter recovery given the chaotic response histories of a couple of nonlinear oscillators, the proposed method appears to offer a more rational, more accurate and faster alternative to most available evolutionary schemes, prominently the particle swarm optimization. (C) 2014 Elsevier B.V. All rights reserved.

Triangle Evolution-A Hybrid Heuristic for Global Optimization

Abstract This paper presents a hybrid heuristic{triangle evolution (TE) for global optimization. It is a real coded evolutionary algorithm. As in di®erential evolution (DE), TE targets each individual in current population and attempts to replace it by a new better individual. However, the way of generating new individuals is di®erent. TE generates new individuals in a Nelder- Mead way, while the simplices used in TE is 1 or 2 dimensional. The proposed algorithm is very easy to use and e±cient for global optimization problems with continuous variables. Moreover, it requires only one (explicit) control parameter. Numerical results show that the new algorithm is comparable with DE for low dimensional problems but it outperforms DE for high dimensional problems.

An Integrated Evolutionary Algorithm for Expensive Global Optimization

We propose an integrated algorithm named low dimensional simplex evolution extension (LDSEE) for expensive global optimization in which only a very limited number of function evaluations is allowed. The new algorithm accelerates an existing global optimization, low dimensional simplex evolution (LDSE), by using radial basis function (RBF) interpolation and tabu search. Different from other expensive global optimization methods, LDSEE integrates the RBF interpolation and tabu search with the LDSE algorithm rather than just calling existing global optimization algorithms as subroutines. As a result, it can keep a good balance between the model approximation and the global search. Meanwhile it is self-contained. It does not rely on other GO algorithms and is very easy to use. Numerical results show that it is a competitive alternative for expensive global optimization.

Designing superresolution optical pupil filter with constrained global optimization algorithm

In this paper, a new method for designing three-zone optical pupil filter is presented. The phase-only optical pupil filter and the amplitude-only optical pupil filters were designed. The first kind of pupil for optical data storage can increase the transverse resolution. The second kind of pupil filter can increase the axial and transverse resolution at the same time, which is applicable in three-dimension imaging in confocal microscopy. (C) 2007 Elsevier GmbH. All rights reserved.

The global optimization of phase-incoherent signals

The problem of global optimization of M phase-incoherent signals in N complex dimensions is formulated. Then, by using the geometric approach of Landau and Slepian, conditions for optimality are established for N = 2 and the optimal signal sets are determined for M = 2, 3, 4, 6, and 12.

The method is the following: The signals are assumed to be equally probable and to have equal energy, and thus are represented by points ṡ_i, i = 1, 2, …, M, on the unit sphere S₁ in C^N. If W_ik is the halfspace determined by ṡ_i and ṡ_k and containing ṡ_i, i.e. W_ik = {ṙϵC^N:| ≥ | ˂ṙ, ṡ_k˃|}, then the Ʀ_i = ∩/k≠i W_ik, i = 1, 2, …, M, the maximum likelihood decision regions, partition S₁. For additive complex Gaussian noise ṅ and a received signal ṙ = ṡ_ie^jϴ + ṅ, where ϴ is uniformly distributed over [0, 2π], the probability of correct decoding is P_C = 1/π^N ∞/ʃ/0 r^2N-1e^-(r2+1)U(r)dr, where U(r) = 1/M M/Ʃ/i=1 Ʀ_i ʃ/∩ S₁ I₀(2r | ˂ṡ, ṡ_i˃|)dσ(ṡ), and r = ǁṙǁ.

For N = 2, it is proved that U(r) ≤ ʃ/C_α I₀(2r|˂ṡ, ṡ_i˃|)dσ(ṡ) – 2K/M. h(1/2K [Mσ(C_α)-σ(S₁)]), where C_α = {ṡϵS₁:|˂ṡ, ṡ_i˃| ≥ α}, K is the total number of boundaries of the net on S₁ determined by the decision regions, and h is the strictly increasing strictly convex function of σ(C_α∩W), (where W is a halfspace not containing ṡ_i), given by h = ʃ/C_α∩W I₀ (2r|˂ṡ, ṡ_i˃|)dσ(ṡ). Conditions for equality are established and these give rise to the globally optimal signal sets for M = 2, 3, 4, 6, and 12.