A self-adaptive genetic algorithm applied to multi-objective optimization of an airfoil

Genetic algorithms (GAs) have been used to tackle non-linear multi-objective optimization (MOO) problems successfully, but their success is governed by key parameters which have been shown to be sensitive to the nature of the particular problem, incorporating concerns such as the numbers of objectives and variables, and the size and topology of the search space, making it hard to determine the best settings in advance. This work describes a real-encoded multi-objective optimizing GA (MOGA) that uses self-adaptive mutation and crossover, and which is applied to optimization of an airfoil, for minimization of drag and maximization of lift coefficients. The MOGA is integrated with a Free-Form Deformation tool to manage the section geometry, and XFoil which evaluates each airfoil in terms of its aerodynamic efficiency. The performance is compared with those of the heuristic MOO algorithms, the Multi-Objective Tabu Search (MOTS) and NSGA-II, showing that this GA achieves better convergence.

Low-rank optimization with trace norm penalty

The paper addresses the problem of low-rank trace norm minimization. We propose an algorithm that alternates between fixed-rank optimization and rank-one updates. The fixed-rank optimization is characterized by an efficient factorization that makes the trace norm differentiable in the search space and the computation of duality gap numerically tractable. The search space is nonlinear but is equipped with a Riemannian structure that leads to efficient computations. We present a second-order trust-region algorithm with a guaranteed quadratic rate of convergence. Overall, the proposed optimization scheme converges superlinearly to the global solution while maintaining complexity that is linear in the number of rows and columns of the matrix. To compute a set of solutions efficiently for a grid of regularization parameters we propose a predictor-corrector approach that outperforms the naive warm-restart approach on the fixed-rank quotient manifold. The performance of the proposed algorithm is illustrated on problems of low-rank matrix completion and multivariate linear regression. © 2013 Society for Industrial and Applied Mathematics.

Optimization of operational conditions in a submerged membrane bioreactor

In this study, optimization of operational conditions of a submerged membrane bioreactor treating municipal waste-water was studied. Mixed liquid suspended solid (MLSS), membrane flux (J(v)), aeration (Q), ratio of pumping, time to break time (t(p)/t(b)), and ratio of up flow area to down flow area (A Ad) were chosen as the easily manipulable parameters to study their effects on removal efficiency and membrane fouling. Totally, 16 different runs were designed to compare and select the best combination of the 5 parameters. The results showed that the optimal operational conditions were MLSS = 7g(.)L(-1), J(v) = 10L(.)m(-2.)h(-1), Q = 6 m(3.)h(-1), t(p)/t(b)= 4 min/1 min, and A(r)/A(d) = 1.7 m(2)/m(2). Under such conditions, the SMBR could achieve a double win of high removal efficiency and low membrane fouling.

Linear dimensionality reduction: Survey, insights, and generalizations

© 2015 John P. Cunningham and Zoubin Ghahramani. Linear dimensionality reduction methods are a cornerstone of analyzing high dimensional data, due to their simple geometric interpretations and typically attractive computational properties. These methods capture many data features of interest, such as covariance, dynamical structure, correlation between data sets, input-output relationships, and margin between data classes. Methods have been developed with a variety of names and motivations in many fields, and perhaps as a result the connections between all these methods have not been highlighted. Here we survey methods from this disparate literature as optimization programs over matrix manifolds. We discuss principal component analysis, factor analysis, linear multidimensional scaling, Fisher's linear discriminant analysis, canonical correlations analysis, maximum autocorrelation factors, slow feature analysis, sufficient dimensionality reduction, undercomplete independent component analysis, linear regression, distance metric learning, and more. This optimization framework gives insight to some rarely discussed shortcomings of well-known methods, such as the suboptimality of certain eigenvector solutions. Modern techniques for optimization over matrix manifolds enable a generic linear dimensionality reduction solver, which accepts as input data and an objective to be optimized, and returns, as output, an optimal low-dimensional projection of the data. This simple optimization framework further allows straightforward generalizations and novel variants of classical methods, which we demonstrate here by creating an orthogonal-projection canonical correlations analysis. More broadly, this survey and generic solver suggest that linear dimensionality reduction can move toward becoming a blackbox, objective-agnostic numerical technology.

Fixed-rank matrix factorizations and Riemannian low-rank optimization

Motivated by the problem of learning a linear regression model whose parameter is a large fixed-rank non-symmetric matrix, we consider the optimization of a smooth cost function defined on the set of fixed-rank matrices. We adopt the geometric framework of optimization on Riemannian quotient manifolds. We study the underlying geometries of several well-known fixed-rank matrix factorizations and then exploit the Riemannian quotient geometry of the search space in the design of a class of gradient descent and trust-region algorithms. The proposed algorithms generalize our previous results on fixed-rank symmetric positive semidefinite matrices, apply to a broad range of applications, scale to high-dimensional problems, and confer a geometric basis to recent contributions on the learning of fixed-rank non-symmetric matrices. We make connections with existing algorithms in the context of low-rank matrix completion and discuss the usefulness of the proposed framework. Numerical experiments suggest that the proposed algorithms compete with state-of-the-art algorithms and that manifold optimization offers an effective and versatile framework for the design of machine learning algorithms that learn a fixed-rank matrix. © 2013 Springer-Verlag Berlin Heidelberg.

基于逻辑"或"约束优化的实时系统设计

标准约束优化问题的等式或不等式约束之间是逻辑“与”关系，目前已经有很多高效、收敛的优化算法．但是，在实际应用中有很多更一般的约束优化问题，其等式或不等式约束之间不仅包含逻辑“与”关系，而且还包含逻辑“或”关系，现有的针对标准约束优化问题的各种算法不再适用，给出一种新的数学变换方法，把具有逻辑“或”关系的不等式约束转换为一组具有逻辑“与”关系的不等式，并应用到实时单调速率调度算法的可调度性判定充要条件中，把实时系统设计表示成混合布尔型整数规划问题，利用经典的分支定界法求解．实验部分指出了各种方法的优缺点．

Design optimization of the APF DTL in the SSC-linac

A linear accelerator as a new injector for the SSC (Separated Sector Cyclotron) of the HIRFL (Heavy ton Research Facility Lanzhou) is being designed. The DTL (Drift-Tube-Linac) has been designed to accelerate U-238(34+) from 0.140 MeV/u to 0.97 MeV/u. To the first accelerating tank which accelerates U-238(34+) to 0.54 MeV/u, the approach of Alternating-Phase-Focusing (APF) is applied. The phase array is obtained by coupling optimization software Dakota and beam optics code LINREV. With the hybrid of Multi-objective Genetic Algorithm (MOGA) and a pattern search method, an optimum array of asynchronous phases is determined. The final growth, both transversely and longitudinally, can meet the design requirements. In this paper, the deign optimization of the APF DTL is presented.

ELECTROCATALYSIS AND DETERMINATION OF HYDRAZINE COMPOUNDS IN LIQUID-CHROMATOGRAPHY AT A MIXED-VALENT COBALT OXIDE CYANOCOBALTATE FILM ELECTRODE

A glassy carbon electrode coated with an electrodeposited film of mixed-valent cobalt oxide/cyanocobaltate (Co-O/CN-Co) enabled hydrazine compounds to be catalytically oxidized at the greatly reduced overpotential and in a wide operational pH range (pH 2.0-7.0). Electrocatalytic activity at the Co-O/CN-Co modified electrode was evaluated with respect to solution pH, film thickness, supporting electrolyte ions, potential scan rate, operating potential, concentration dependence and other variables. The Co-O/CN-Co film electrode was completely compatible with a conventional reversed-phase liquid chromatographic (RP-LC) system. Practical RP-LC amperometric detection (RP-LCEC) of hydrazines was performed. A dynamic linear response range over three orders of magnitude and a detection limit at the pmol level were readily obtained. The Co-O/CN-CO film electrode exhibited excellent electrocatalytic stability in the flowing streams.

Resolution prediction and optimization of temperature programme in comprehensive two-dimensional gas chromatography

A model is developed for predicting the resolution of interested component pair and calculating the optimum temperature programming condition in the comprehensive two-dimensional gas chromatography (GC x GC). Based on at least three isothermal runs, retention times and the peak widths at half-height on both dimensions are predicted for any kind of linear temperature-programmed run on the first dimension and isothermal runs on the second dimension. The calculation of the optimum temperature programming condition is based on the prediction of the resolution of "difficult-to-separate components" in a given mixture. The resolution of all the neighboring peaks on the first dimension is obtained by the predicted retention time and peak width on the first dimension, the resolution on the second dimension is calculated only for the adjacent components with un-enough resolution on the first dimension and eluted within a same modulation period on the second dimension. The optimum temperature programming condition is acquired when the resolutions of all components of interest by GC x GC separation meet the analytical requirement and the analysis time is the shortest. The validity of the model has been proven by using it to predict and optimize GC x GC temperature programming condition of an alkylpyridine mixture. (c) 2005 Elsevier B.V. All rights reserved.

Optimization of physical and optical properties of biodegradable edible films based on pea starch and guar gum

The influence of process variables (pea starch, guar gum and glycerol) on the viscosity (V), solubility (SOL), moisture content (MC), transparency (TR), Hunter parameters (L, a, and b), total color difference (ΔE), yellowness index (YI), and whiteness index (WI) of the pea starch based edible films was studied using three factors with three level Box–Behnken response surface design. The individual linear effect of pea starch, guar and glycerol was significant (p < 0.05) on all the responses. However, a value was only significantly (p < 0.05) affected by pea starch and guar gum in a positive and negative linear term, respectively. The effect of interaction of starch × glycerol was also significant (p < 0.05) on TR of edible films. Interaction between independent variables starch × guar gum had a significant impact on the b and YI values. The quadratic regression coefficient of pea starch showed a significant effect (p < 0.05) on V, MC, L, b, ΔE, YI, and WI; glycerol level on ΔE and WI; and guar gum on ΔE and SOL value. The results were analyzed by Pareto analysis of variance (ANOVA) and the second order polynomial models were developed from the experimental design with reliable and satisfactory fit with the corresponding experimental data and high coefficient of determination (R2) values (>0.93). Three-dimensional response surface plots were established to investigate the relationship between process variables and the responses. The optimized conditions with the goal of maximizing TR and minimizing SOL, YI and MC were 2.5 g pea starch, 25% glycerol and 0.3 g guar gum. Results revealed that pea starch/guar gum edible films with appropriate physical and optical characteristics can be effectively produced and successfully applied in the food packaging industry.

The Synthesis of Arbitrary Stable Dynamics in Non-linear Neural Networks II: Feedback and Universality

We wish to construct a realization theory of stable neural networks and use this theory to model the variety of stable dynamics apparent in natural data. Such a theory should have numerous applications to constructing specific artificial neural networks with desired dynamical behavior. The networks used in this theory should have well understood dynamics yet be as diverse as possible to capture natural diversity. In this article, I describe a parameterized family of higher order, gradient-like neural networks which have known arbitrary equilibria with unstable manifolds of known specified dimension. Moreover, any system with hyperbolic dynamics is conjugate to one of these systems in a neighborhood of the equilibrium points. Prior work on how to synthesize attractors using dynamical systems theory, optimization, or direct parametric. fits to known stable systems, is either non-constructive, lacks generality, or has unspecified attracting equilibria. More specifically, We construct a parameterized family of gradient-like neural networks with a simple feedback rule which will generate equilibrium points with a set of unstable manifolds of specified dimension. Strict Lyapunov functions and nested periodic orbits are obtained for these systems and used as a method of synthesis to generate a large family of systems with the same local dynamics. This work is applied to show how one can interpolate finite sets of data, on nested periodic orbits.

Communications inspired linear discriminant analysis

We study the problem of supervised linear dimensionality reduction, taking an information-theoretic viewpoint. The linear projection matrix is designed by maximizing the mutual information between the projected signal and the class label. By harnessing a recent theoretical result on the gradient of mutual information, the above optimization problem can be solved directly using gradient descent, without requiring simplification of the objective function. Theoretical analysis and empirical comparison are made between the proposed method and two closely related methods, and comparisons are also made with a method in which Rényi entropy is used to define the mutual information (in this case the gradient may be computed simply, under a special parameter setting). Relative to these alternative approaches, the proposed method achieves promising results on real datasets. Copyright 2012 by the author(s)/owner(s).

Dissipative scheme to approach the boundary of two-qubit entangled mixed states

We discuss the generation of states close to the boundary family of maximally entangled mixed states as defined by the use of concurrence and linear entropy. The coupling of two qubits to a dissipation-affected bosonic mode is able to produce a bipartite state having, for all practical purposes, the entanglement and mixedness properties of one of such boundary states. We thoroughly study the effects that thermal and squeezed characters of the bosonic mode have in such a process and we discuss tolerance to qubit phase-damping mechanisms. The nondemanding nature of the scheme makes it realizable in a matter-light-based physical setup, which we address in some details.

Catalytic Hydrogenolysis of Aromatic Ketones in Mixed Choline-Betainium Ionic Liquids

The palladium-catalyzed hydrogenolysis of aromatic ketones to alkylbenzenes was studied in mixtures of ionic liquids to explore the promotional effect of these reaction media. Choline-based ionic liquids displayed complete miscibility with the aromatic ketone substrate at reaction temperature and a clear phase separation of the derived alkylbenzene product at room temperature. Selected ionic liquids were then assessed as reaction media in the hydrogenolysis of aromatic ketones over palladium catalysts. A binary mixture of choline and betainium bis(trifluoromethylsulfonyl)imide ionic liquids resulted in the highest conversion and selectivity values in the hydrogenolysis of acetophenone. At the end of the reaction, the immiscible alkylbenzene separates from the ionic liquid mixture and the pure product phase can be isolated by simple decantation. After optimization of the reaction conditions, high yields (>90%) of alkylbenzene were obtained in all cases. The catalyst and the ionic liquid could be used at least three times without any loss of activity or selectivity.

Teleporting bipartite entanglement using maximally entangled mixed channels

The ability to teleport entanglement through maximally entangled mixed states as defined by concurrence and linear entropy is studied. We show how the teleported entanglement depends on the quality of the quantum channel used, as defined through its entanglement and mixedness, as well as the form of the target state to be teleported. We present new results based on the fidelity of the teleported state as well as an experimental setup that is immediately implementable with currently available technology.