Stochastic Hill-climbing Algorithm Research Articles

Optimal control of coupled quantum systems based on the first-order Magnus expansion: Application to multiple dipole-dipole-coupled molecular rotors

We develop a methodology for performing approximate optimal control simulations for quantum systems with multiple interacting degrees of freedom. The quantum dynamics are modeled using the first-order Magnus approximation in the interaction picture, where the interactions between different degrees of freedom are treated as the perturbation. We present a numerical procedure for implementing this approximation, which leverages the separability of the zeroth-order time evolution operator and the pairwise nature of common interactions for a reduced computational cost. This formulation of the first-order Magnus approximation is suitable to be combined with gradient-free methods for control field optimization; to this end, we adopt a Stochastic Hill Climbing algorithm. The associated computational costs are analyzed and compared with those of the exact simulation in the large N limit. For numerical illustrations, we perform approximate optimal control simulations for systems of two and three dipole-dipole coupled molecular rotors under the influence of a global control field. For the two rotor system, we optimize fields for both orientation and entanglement control objectives. For the three rotor system, we optimize fields for orienting rotors in the same direction as well as in opposite directions.

Empirical Evaluation of Hill Climbing Algorithm

The software is growing in size and complexity every day due to which strong need is felt by the research community to search for the techniques which can optimize test cases effectively. The current study is inspired by the collective behavior of finding paths from the colony of food and uses different versions of Hill Climbing Algorithm (HCA) such as Stochastic, and Steepest Ascent HCA for the purpose of finding a good optimal solution. The performance of the proposed algorithm is verified on the basis of three parameters comprising of optimized test cases, time is taken during the optimization process, and the percentage of optimization achieved. The results suggest that proposed Stochastic HCA is significantly average percentage better than Steepest Ascent HCA in reducing the number of test cases in order to accomplish the optimization target.

Variability-Aware, Discrete Optimization for Analog Circuits

This paper explores the use of discrete optimization techniques for variability-aware analog circuit synthesis, with an observation that the continuous design space can be effectively covered by a finite number of discrete points when parameter variation is present. Three algorithms are described that can leverage a discretized design space yet mitigate its dimensionality scaling problem: an isotropic discretization scheme, which can fill the neighborhood of any given point with only quadratically-increasing number of nearest neighbors placed at equal distances as the space dimension increases, a stochastic hill-climbing algorithm, which evaluates only a partial set of nearest neighbors yet finds the local optimum at the reduced cost, and an incremental Monte Carlo sampling algorithm, which draws the minimal number of Monte Carlo samples just enough to determine the superior design point during the local search process. These algorithms help in finding the optimal design of analog circuits efficiently. For instance, for a digitally-controlled oscillator example, its discretized design space consists of 5 565 907 points but the optimal point was found by evaluating only 40 design points and running only 21 Monte Carlo simulations per point in average (824 in total).

Automatic Isotherm Derivation From Field Data for Oilfield Scale-Inhibitor Squeeze Treatments

SummaryOilfield scale formation represents a significant flow-assurance challenge to the oil and gas industry, because of increasing water production worldwide and higher oil prices. Scale-inhibitor (SI) squeeze treatment is the most widespread method to combat downhole scaling. To predict SI squeeze treatments accurately for further optimization, it is necessary to simulate the SI retention in the formation, which may be described by a pseudoadsorption isotherm. Although these are often derived from coreflood experiments, sometimes they are not appropriate for modeling well treatments because the core tests on which they are based cannot fully represent field-scale processes. In practice, the parameters of an analytic form of the isotherm equation are modified by trial and error by an experienced practitioner until a match is obtained between the prediction and the return profile of the first treatment in the field.The main purpose of this paper is to present a stochastic hill-climbing algorithm for automatic isotherm derivation. The performance of the algorithm was evaluated by use of data from three field cases. Two success criteria were defined: the ability to match a single historical treatment and the ability to predict subsequent successive treatments. To test for the second criterion, a candidate isotherm was derived from the first treatment in a well that was treated with the same chemical package on consecutive occasions, and then the predictions by use of the suggested solution were compared with the observed SI concentration-return profiles from the subsequent treatments. In all the calculations, the performances of both the isotherms suggested by the hill-climbing algorithm and the isotherms derived by trial and error were compared. The results demonstrate that the hill-climbing algorithm is an effective technique for deriving an isotherm for a single treatment, although predictions for successive treatments worsened slightly with each treatment.

Open-loop simulations of the primate saccadic system using burst cell discharge from the superior colliculus.

Saccade-related burst neurons (SRBNs) in the monkey superior colliculus (SC) have been hypothesized to provide the brainstem saccadic burst generator with the dynamic error signal and the movement initiating trigger signal. To test this claim, we performed two sets of open-loop simulations on a burst generator model with the local feedback disconnected using experimentally obtained SRBN activity as both the driving and trigger signal inputs to the model. First, using neural data obtained from cells located near the middle of the rostral to caudal extent of the SC, the internal parameters of the model were optimized by means of a stochastic hill-climbing algorithm to produce an intermediate-sized saccade. The parameter values obtained from the optimization were then fixed and additional simulations were done using the experimental data from rostral collicular neurons (small saccades) and from more caudal neurons (large saccades); the model generated realistic saccades, matching both position and velocity profiles of real saccades to the centers of the movement fields of all these cells. Second, the model was driven by SRBN activity affiliated with interrupted saccades, the resumed eye movements observed following electrical stimulation of the omnipause region. Once again, the model produced eye movements that closely resembled the interrupted saccades produced by such simulations, but minor readjustment of parameters reflecting the weight of the projection of the trigger signal was required. Our study demonstrates that a model of the burst generator produces reasonably realistic saccades when driven with actual samples of SRBN discharges.