Kyle Willick

Multiobjective evolutionary algorithm with risk minimization applied to a fleet mix problem

We apply the non-dominated sorting genetic algorithm-II (NSGA-II) to a multi-objective fleet-mix problem for risk mitigation. The Stochastic Fleet Estimation (SaFE) model, a Monte Carlo-based model, is used to determine average annual requirements which a fleet must meet. We search for Pareto-optimal combinations of platform-to-task assignments that can be used to complete SaFE generated scenarios. Solutions are evaluated using three objectives, with a goal of minimizing fleet cost, total task duration, and the risk that a solution will not be able to accomplish future scenarios. Optimization over all three objectives allowed for exploration of configurations which were low cost and low risk, a region not explored by prior experiments without the risk objective.

Sensitive magnetic force detection with a carbon nanotube resonator

We propose a technique for sensitive magnetic point force detection using a suspended carbon nanotube (CNT) mechanical resonator combined with a magnetic field gradient generated by a ferromagnetic gate electrode. Numerical calculations of the mechanical resonance frequency show that single Bohr magneton changes in the magnetic state of an individual magnetic molecule grafted to the CNT can translate to detectable frequency shifts, on the order of a few kHz. The dependences of the resonator response to device parameters such as length, tension, CNT diameter, and gate voltage are explored and optimal operating conditions are identified. A signal-to-noise analysis shows that, in principle, magnetic switching at the level of a single Bohr magneton can be read out in a single shot on timescales as short as 10 μs. This force sensor should enable new studies of spin dynamics in isolated single molecule magnets, free from the crystalline or ensemble settings typically studied.

Probing the non-linear transient response of a carbon nanotube mechanical oscillator

X iv :1 70 7. 03 02 5v 1 [ co nd -m at .m es -h al l] 1 0 Ju l 2 01 7 Fast measurement of carbon nanotube resonator amplitude with a heterojunction bipolar transistor Kyle Willick, 2, 3 Xiaowu (Shirley) Tang, 4 and Jonathan Baugh 2, 4, a) Institute for Quantum Computing, University of Waterloo, Waterloo, Ontario, Canada Waterloo Institute for Nanotechnology, University of Waterloo, Waterloo, Ontario, Canada Department of Physics and Astronomy, University of Waterloo, Waterloo, Ontario, Canada Department of Chemistry, University of Waterloo, Waterloo, Ontario, CanadaCarbon nanotube (CNT) electromechanical resonators have demonstrated unprecedented sensitivities for detecting small masses and forces. The detection speed in a cryogenic setup is usually limited by the CNT contact resistance and parasitic capacitance of cabling. We report the use of a cold heterojunction bipolar transistor amplifying circuit near the device to measure the mechanical amplitude at microsecond timescales. A Coulomb rectification scheme, in which the probe signal is at much lower frequency than the mechanical drive signal, allows investigation of the strongly non-linear regime. The behaviour of transients in both the linear and non-linear regimes is observed and modeled by including Duffing and non-linear damping terms in a harmonic oscillator equation. We show that the non-linear regime can result in faster mechanical response times, on the order of 10 μs for the device and circuit presented, potentially enabling the magnetic moments of single molecules to be measured within their spin rela...

Multi-objective optimization of the fleet mix problem using the SaFER model

One of the most important tasks for an organization which transports cargo and people is the determination of number and type of platforms which will be needed. Due to the presence of multiple conflicting objectives, such as cost and performance, this problem may be considered multi-objective. In order to estimate the fleet that can fulfill the scenario requirements, the Stochastic Fleet Estimation - Robust (SaFER) model was previously developed. It uses scheduling heuristics and optimization. However, using the SaFER model within a multi-objective optimization framework is not computationally feasible; therefore, a surrogate model is proposed in this paper to approximate SaFER for use in the fitness evaluations of schedule cost objectives. An artificial military air mobility dataset is used to demonstrate the increase in speed of the surrogate model over SaFER, and the accuracy of the surrogate model in estimating schedule costs versus SaFER.

A new principal curve algorithm and standard deviation clouds for non-parametric ordered data analysis

Principal curves are a study of the underlying structure of a data cloud. We modify Kegls [2] polygonal line algorithm by assuming that data points are vertices on different continuous curves which implies data ordering. We also develop a representation of curve deviation from the polygonal path by creating a deviation cloud based on computing a measure of the variance of the curves from the polygonal path. For the purposes of this paper, we consider the input curves to be vertex representations of independent polygonal paths. Comparisons of the presented algorithm on various data sets with that of Verbeek et al. [3] are given to illustrate differences when using ordered data represented as multiple continuous curves. We further consider applications of this algorithm to the evaluation of multiobjective optimization algorithm convergence for biobjective optimization. We present preliminary results for NSGA-II on ZDT1, ZDT2, and ZDT3 in order to show how this methodology could be used.