2,954 research outputs found
Multiple Objective Step Function Maximization with Genetic Algorithms and Simulated Annealing
We develop a hybrid algorithm using Genetic Algorithms (GA) and Simulated Annealing (SA) to solve multi-objective step function maximization problems. We then apply the algorithm to a specific economic problem which is taken out of the corporate governance literature.Numerical computation, Genetic algorithms, Simulated annealing
Quantum Algorithms for Solving Ordinary Differential Equations via Classical Integration Methods
Identifying computational tasks suitable for (future) quantum computers is an
active field of research. Here we explore utilizing quantum computers for the
purpose of solving differential equations. We consider two approaches: (i)
basis encoding and fixed-point arithmetic on a digital quantum computer, and
(ii) representing and solving high-order Runge-Kutta methods as optimization
problems on quantum annealers. As realizations applied to two-dimensional
linear ordinary differential equations, we devise and simulate corresponding
digital quantum circuits, and implement and run a 6 order
Gauss-Legendre collocation method on a D-Wave 2000Q system, showing good
agreement with the reference solution. We find that the quantum annealing
approach exhibits the largest potential for high-order implicit integration
methods. As promising future scenario, the digital arithmetic method could be
employed as an "oracle" within quantum search algorithms for inverse problems
Optimization of Discrete-parameter Multiprocessor Systems using a Novel Ergodic Interpolation Technique
Modern multi-core systems have a large number of design parameters, most of
which are discrete-valued, and this number is likely to keep increasing as chip
complexity rises. Further, the accurate evaluation of a potential design choice
is computationally expensive because it requires detailed cycle-accurate system
simulation. If the discrete parameter space can be embedded into a larger
continuous parameter space, then continuous space techniques can, in principle,
be applied to the system optimization problem. Such continuous space techniques
often scale well with the number of parameters.
We propose a novel technique for embedding the discrete parameter space into
an extended continuous space so that continuous space techniques can be applied
to the embedded problem using cycle accurate simulation for evaluating the
objective function. This embedding is implemented using simulation-based
ergodic interpolation, which, unlike spatial interpolation, produces the
interpolated value within a single simulation run irrespective of the number of
parameters. We have implemented this interpolation scheme in a cycle-based
system simulator. In a characterization study, we observe that the interpolated
performance curves are continuous, piece-wise smooth, and have low statistical
error. We use the ergodic interpolation-based approach to solve a large
multi-core design optimization problem with 31 design parameters. Our results
indicate that continuous space optimization using ergodic interpolation-based
embedding can be a viable approach for large multi-core design optimization
problems.Comment: A short version of this paper will be published in the proceedings of
IEEE MASCOTS 2015 conferenc
Quantum algorithm for estimating volumes of convex bodies
Estimating the volume of a convex body is a central problem in convex
geometry and can be viewed as a continuous version of counting. We present a
quantum algorithm that estimates the volume of an -dimensional convex body
within multiplicative error using
queries to a membership oracle and
additional arithmetic operations. For
comparison, the best known classical algorithm uses
queries and
additional arithmetic operations. To the
best of our knowledge, this is the first quantum speedup for volume estimation.
Our algorithm is based on a refined framework for speeding up simulated
annealing algorithms that might be of independent interest. This framework
applies in the setting of "Chebyshev cooling", where the solution is expressed
as a telescoping product of ratios, each having bounded variance. We develop
several novel techniques when implementing our framework, including a theory of
continuous-space quantum walks with rigorous bounds on discretization error. To
complement our quantum algorithms, we also prove that volume estimation
requires quantum membership queries, which rules
out the possibility of exponential quantum speedup in and shows optimality
of our algorithm in up to poly-logarithmic factors.Comment: 61 pages, 8 figures. v2: Quantum query complexity improved to
and number of additional arithmetic
operations improved to . v3: Improved
Section 4.3.3 on nondestructive mean estimation and Section 6 on quantum
lower bounds; various minor change
A New Hybrid Descent Method with Application to the Optimal Design of Finite Precision FIR Filters
In this paper, the problem of the optimal design of discrete coefficient FIR filters is considered. A novelhybrid descent method, consisting of a simulated annealing algorithm and a gradient-based method, isproposed. The simulated annealing algorithm operates on the space of orthogonal matrices and is used tolocate descent points for previously converged local minima. The gradient-based method is derived fromconverting the discrete problem to a continuous problem via the Stiefel manifold, where convergence canbe guaranteed. To demonstrate the effectiveness of the proposed hybrid descent method, several numericalexamples show that better discrete filter designs can be sought via this hybrid descent method
Matter wave coupling of spatially separated and unequally pumped polariton condensates
Spatial quantum coherence between two separated driven-dissipative polariton
condensates created non-resonantly and with a different occupation is studied.
We identify the regions where the condensates remain coherent with the phase
difference continuously changing with the pumping imbalance and the regions
where each condensate acquires its own chemical potential with phase
differences exhibiting time-dependent oscillations. We show that in the mutual
coherence limit the coupling consists of two competing contributions: a
symmetric Heisenberg exchange and the Dzyloshinskii-Moriya asymmetric
interactions that enable a continuous tuning of the phase relation across the
dyad and derive analytic expressions for these types of interactions. The
introduction of non-equal pumping increases the complexity of the type of the
problems that can be solved by polariton condensates arranged in a graph
configuration. If equally pumped polaritons condensates arrange their phases to
solve the constrained quadratic minimisation problem with a real symmetric
matrix, the non-equally pumped condensates solve that problem for a general
Hermitian matrix.Comment: 3 figures, 16 page
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