Himanshu Gupta

Searching for robust pareto-optimal solutions in multi-objective optimization

In optimization studies including multi-objective optimization, the main focus is usually placed in finding the global optimum or global Pareto-optimal frontier, representing the best possible objective values. However, in practice, users may not always be interested in finding the global best solutions, particularly if these solutions are quite sensitive to the variable perturbations which cannot be avoided in practice. In such cases, practitioners are interested in finding the so-called robust solutions which are less sensitive to small changes in variables. Although robust optimization has been dealt in detail in single-objective optimization studies, in this paper, we present two different robust multi-objective optimization procedures, where the emphasis is to find the robust optimal frontier, instead of the global Pareto-optimal front. The first procedure is a straightforward extension of a technique used for single-objective robust optimization and the second procedure is a more practical approach enabling a user to control the extent of robustness desired in a problem. To demonstrate the subtle differences between global and robust multi-objective optimization and the differences between the two robust optimization procedures, we define four test problems and show simulation results using NSGA-II. The results are useful and should encourage further studies considering robustness in multi-objective optimization.

Handling constraints in robust multi-objective optimization

Robust multi-objective optimization has emerged as an active research. A recent study proposed two different definitions of robust solutions in the context of multi-objective optimization. In this paper, we extend the concepts for finding robust solutions in the presence of active constraints. The meaning of robust solutions for constrained problems is demonstrated by suggesting three test problems and simulating an evolutionary multi-objective optimization method using the two definitions of robustness. The inclusion of constraint handling strategies makes the multi-objective robust optimization procedure more pragmatic and the procedure is now ready to be applied to real-world problems

Stochastic scheduling of active support vector learning algorithms

Active learning is a generic approach to accelerate training of classifiers in order to achieve a higher accuracy with a small number of training examples. In the past, simple active learning algorithms like random learning and query learning have been proposed for the design of support vector machine (SVM) classifiers. In random learning, examples are chosen randomly, while in query learning examples closer to the current separating hyperplane are chosen at each learning step. However, it is observed that a better scheme would be to use random learning in the initial stages (more exploration) and query learning in the final stages (more exploitation) of learning. Here we present two novel active SV learning algorithms which use adaptive mixtures of random and query learning. One of the proposed algorithms is inspired by online decision problems, and involves a hard choice among the pure strategies at each step. The other extends this to soft choices using a mixture of instances recommended by the individual pure strategies. Both strategies handle the exploration-exploitation trade-off in an efficient manner. The efficacy of the algorithms is demonstrated by experiments on benchmark datasets.

REVISITING EVIDENCE OF CHAOS IN X-RAY LIGHT CURVES: THE CASE OF GRS 1915+105

Nonlinear time series analysis has been widely used to search for signatures of low-dimensional chaos in light curves emanating from astrophysical bodies. A particularly popular example is the microquasar GRS 1915+105, whose irregular but systematic X-ray variability has been well studied using data acquired by the Rossi X-ray Timing Explorer (RXTE). With a view to building simpler models of X-ray variability, attempts have been made to classify the light curves of GRS 1915+105 as chaotic or stochastic. Contrary to some of the earlier suggestions, after careful analysis, we find no evidence for chaos or determinism in any of the GRS 1915+105 classes. The dearth of long and stationary data sets representing all the different variability classes of GRS 1915+105 make it a poor candidate for analysis using nonlinear time series techniques. We conclude that either very exhaustive data analysis with sufficiently long and stationary light curves should be performed keeping all the pitfalls of nonlinear time series analysis in mind, or alternative schemes of classifying the light curves should be adopted. The generic limitations of the techniques that we point out in the context of GRS 1915+105 affect all similar investigations of light curves from other astrophysical sources.

Stability analysis of convection in the intracluster medium

Abstract We use the machinery usually employed for studying the onset of Rayleigh–Benard convection in hydro- and magnetohydro-dynamic settings to address the onset of convection induced by the magnetothermal instability and the heat-flux-buoyancy-driven-instability in the weakly-collisional magnetized plasma permeating the intracluster medium. Since most of the related numerical simulations consider the plasma being bounded between two ‘plates’ on which boundary conditions are specified, our strategy provides a framework that could enable a more direct connection between analytical and numerical studies. We derive the conditions for the onset of these instabilities considering the effects of induced magnetic tension resulting from a finite plasma beta. We provide expressions for the Rayleigh number in terms of the wave vector associated with a given mode, which allow us to characterize the modes that are first to become unstable. For both the heat-flux-buoyancy-driven-instability and the magnetothermal instability, oscillatory marginal stable states are possible.

Transistor size optimization in digital circuits using ant colony optimization for continuous domain

In this paper, ant colony optimization ACO algorithm is presented, as a tool to find transistor sizes in digital circuits. Performance of ACO has been tested on four digital circuits, of different complexity, to find optimum balance between power and delay of circuits. Optimization problem has been set up by first, formulating an objective function, to be minimized, for each circuit and then finding the values of variables of circuits, using optimization algorithm. For the purpose of examining the results, circuits are optimized using genetic algorithm GA also. Results show that, ACO performs better than GA, for all the four circuits, in finding optimized transistor sizes. Copyright

On the helium fingers in the intracluster medium

In this paper we investigate the convection phenomenon in the intracluster medium (the weakly-collisional magnetized inhomogeneous plasma permeating galaxy clusters) where the concentration gradient of the Helium ions is not ignorable. To this end, we build upon the general machinery employed to study the salt finger instability found in the oceans. The salt finger instability is a form of double diffusive convection where the diffusions of two physical quantities---heat and salt concentrations---occur with different diffusion rates. The analogous instability in the intracluster medium may result owing to the magnetic field mediated anisotropic diffusions of the heat and the Helium ions (in the sea of the Hydrogen ions and the free electrons). These two diffusions have inherently different diffusion rates. Hence the convection caused by the onset of this instability is an example of double diffusive convection in the astrophysical settings. A consequence of this instability is the formation of the vertical filamentary structures having more concentration of the Helium ions with respect to the immediate neighbourhoods of the filaments. We term these structures as Helium fingers in analogy with the salt fingers found in the case of the salt finger instability. Here we show that the width of a Helium finger scales as one-fourth power of the radius of the inner region of the intracluster medium in the supercritical regime. We also determine the explicit mathematical expression of the criterion for the onset of the heat-flux-driven buoyancy instability modified by the presence of inhomogeneously distributed Helium ions.

Robust estimation of aerospace propulsion parameters using optimization techniques based on evolutionary algorithms

Robust estimation generally refers to the process of identifying the most probable set of parameters in the presence of wild points or outliers in the measurement. But besides removing the influence of outliers a robust estimator should also return the most probable set of parameters even when multiple minima in the cost function are there. When minima are almost of the same order this requirement amounts to finding out the minimum value with the largest basin of attraction. Traditional optimization algorithms are not very suitable for robust estimators because cost function obtained with various robust estimation norms may not have continuous first and second derivatives with respect to parameters. This precludes the possibility of using many of the traditional optimization algorithms. Also when multiple minima exist the convergence of traditional algorithm to a particular solution depends largely on the initial guess. In this scenario optimization tools based on evolutionary algorithms can be a very attractive option. Evolutionary algorithms require only function value evaluations and through population based approach the dependence on an initial guess to converge to a particular solution is overcome. Here a new method for the robust estimation of propulsion parameters using evolutionary optimization techniques is proposed. There are both, equality and inequality constraints, to take into account the expected range of deviations in parameters. The method incorporates GA in C, which is an optimization code based on evolutionary algorithms and is developed at KANGAL, Indian Institute of Technology, Kanpur. The method has been tested with various robust estimation norms using simulated data for a typical solid motor in the presence of multiple minima in the cost function. The proposed method has been able to estimate propulsions parameters in all the cases successfully.

Effect of composition gradient on magnetothermal instability modified by shear and rotation

We model the intracluster medium as a weakly collisional plasma that is a binary mixture of the hydrogen and the helium ions, along with free electrons. When, owing to the helium sedimentation, the gradient of the mean molecular weight (or equivalently, composition or helium ions concentration) of the plasma is not negligible, it can have appreciable influence on the stability criteria of the thermal convective instabilities, e.g., the heat-flux-buoyancy instability and the magnetothermal instability (MTI). These instabilities are consequences of the anisotropic heat conduction occurring preferentially along the magnetic field lines. In this paper, without ignoring the magnetic tension, we first present the mathematical criterion for the onset of composition gradient modified MTI. Subsequently, we relax the commonly adopted equilibrium state in which the plasma is at rest, and assume that the plasma is in a sheared state which may be due to differential rotation. We discuss how the concentration gradient affects the coupling between the Kelvin--Helmholtz instability and the MTI in rendering the plasma unstable or stable. We derive exact stability criterion by working with the sharp boundary case in which the physical variables---temperature, mean molecular weight, density, and magnetic field---change discontinuously from one constant value to another on crossing the boundary. Finally, we perform the linear stability analysis for the case of the differentially rotating plasma that is thermally and compositionally stratified as well. By assuming axisymmetric perturbations, we find the corresponding dispersion relation and the explicit mathematical expression determining the onset of the modified MTI.

Neural network modeling of degradation of solar cells

Recently, there has been substantial interest in solar cells as possible replacements of conventional energy sources, [1, 2]. However, significant light induced degradation of solar cell characteristics such as the conversion efficiency has been observed in the literature, [3,4]. Therefore, there is a need of a model to predict the degradation behavior of solar cells. In this paper, neural network has been used to model the degradation of solar cells. Back propagation algorithm has been used to train the neural network model with different parameters of a solar cell as input and conversion efficiency as output. This model has been developed for experimental data taken from [3] and [4].Some of the data were used for training the network and then the trained network was tested for the rest of the data and computed results were compared with experimental data.