332 research outputs found
The rate of convergence to optimality of the LPT rule
The LPT rule is a heuristic method to distribute jobs among identical machines so as to minimize the makespan of the resulting schedule. If the processing times of the jobs are assumed to be independent identically distributed random variables, then (under a mild condition on the distribution) the absolute error of this heuristic is known to converge to 0 almost surely. In this note we analyse the asymptotic behaviour of the absolute error and its first and higher moments to show that under quite general assumptions the speed of convergence is proportional to appropriate powers of (log log n)/n and 1/n. Thus, we simplify, strengthen and extend earlier results obtained for the uniform and exponential distribution.
The rate of convergence to optimality of the LPT rule
The LPT rule is a heuristic method to distribute jobs among identical machines so as to minimize the makespan of the resulting schedule. If the processing times of the jobs are assumed to be independent identically distributed random variables, then (under a mild condition on the distribution) the absolute error of this heuristic is known to converge to 0 almost surely. In this note we analyse the asymptotic behaviour of the absolute error and its first and higher moments to show that under quite general assumptions the speed of convergence is proportional to appropriate powers of (log log n)/n and 1/n. Thus, we simplify, strengthen and extend earlier results obtained for the uniform and exponential distribution
On the rate of convergence to optimality of the LPT rule - postscript
This postscript contains the proofs of two results listed in the paper 'On the rate of convergence to optimality of the LPT rule'
Towards Dual-functional Radar-Communication Systems: Optimal Waveform Design
We focus on a dual-functional multi-input-multi-output (MIMO)
radar-communication (RadCom) system, where a single transmitter communicates
with downlink cellular users and detects radar targets simultaneously. Several
design criteria are considered for minimizing the downlink multi-user
interference. First, we consider both the omnidirectional and directional
beampattern design problems, where the closed-form globally optimal solutions
are obtained. Based on these waveforms, we further consider a weighted
optimization to enable a flexible trade-off between radar and communications
performance and introduce a low-complexity algorithm. The computational costs
of the above three designs are shown to be similar to the conventional
zero-forcing (ZF) precoding. Moreover, to address the more practical constant
modulus waveform design problem, we propose a branch-and-bound algorithm that
obtains a globally optimal solution and derive its worst-case complexity as a
function of the maximum iteration number. Finally, we assess the effectiveness
of the proposed waveform design approaches by numerical results.Comment: 13 pages, 10 figures. This work has been submitted to the IEEE for
possible publication. Copyright may be transferred without notice, after
which this version may no longer be accessibl
Functional quantization rate and mean regularity of processes with an application to L\'evy processes
We investigate the connections between the mean pathwise regularity of
stochastic processes and their L^r(P)-functional quantization rates as random
variables taking values in some L^p([0,T],dt)-spaces (0 < p <= r). Our main
tool is the Haar basis. We then emphasize that the derived functional
quantization rate may be optimal (e.g., for Brownian motion or symmetric stable
processes) so that the rate is optimal as a universal upper bound. As a first
application, we establish the O((log N)^{-1/2}) upper bound for general It\^o
processes which include multidimensional diffusions. Then, we focus on the
specific family of L\'evy processes for which we derive a general quantization
rate based on the regular variation properties of its L\'evy measure at 0. The
case of compound Poisson processes, which appear as degenerate in the former
approach, is studied specifically: we observe some rates which are between the
finite-dimensional and infinite-dimensional ``usual'' ratesComment: 43p., issued in Annals of Applied Probability, 18(2):427-46
A stochastic programming approach for chemotherapy appointment scheduling
Chemotherapy appointment scheduling is a challenging problem due to the
uncertainty in pre-medication and infusion durations. In this paper, we
formulate a two-stage stochastic mixed integer programming model for the
chemotherapy appointment scheduling problem under limited availability and
number of nurses and infusion chairs. The objective is to minimize the expected
weighted sum of nurse overtime, chair idle time, and patient waiting time. The
computational burden to solve real-life instances of this problem to optimality
is significantly high, even in the deterministic case. To overcome this burden,
we incorporate valid bounds and symmetry breaking constraints. Progressive
hedging algorithm is implemented in order to solve the improved formulation
heuristically. We enhance the algorithm through a penalty update method, cycle
detection and variable fixing mechanisms, and a linear approximation of the
objective function. Using numerical experiments based on real data from a major
oncology hospital, we compare our solution approach with several scheduling
heuristics from the relevant literature, generate managerial insights related
to the impact of the number of nurses and chairs on appointment schedules, and
estimate the value of stochastic solution to assess the significance of
considering uncertainty
Non-Reversible Parallel Tempering: a Scalable Highly Parallel MCMC Scheme
Parallel tempering (PT) methods are a popular class of Markov chain Monte
Carlo schemes used to sample complex high-dimensional probability
distributions. They rely on a collection of interacting auxiliary chains
targeting tempered versions of the target distribution to improve the
exploration of the state-space. We provide here a new perspective on these
highly parallel algorithms and their tuning by identifying and formalizing a
sharp divide in the behaviour and performance of reversible versus
non-reversible PT schemes. We show theoretically and empirically that a class
of non-reversible PT methods dominates its reversible counterparts and identify
distinct scaling limits for the non-reversible and reversible schemes, the
former being a piecewise-deterministic Markov process and the latter a
diffusion. These results are exploited to identify the optimal annealing
schedule for non-reversible PT and to develop an iterative scheme approximating
this schedule. We provide a wide range of numerical examples supporting our
theoretical and methodological contributions. The proposed methodology is
applicable to sample from a distribution with a density with respect
to a reference distribution and compute the normalizing constant. A
typical use case is when is a prior distribution, a likelihood
function and the corresponding posterior.Comment: 74 pages, 30 figures. The method is implemented in an open source
probabilistic programming available at
https://github.com/UBC-Stat-ML/blangSD
Fault diagnostics for advanced cycle marine gas turbine using genetic algorithm
The
major challenges faced by the gas turbine industry, for both the users and the
manufacturers, is the reduction in life cycle costs , as well as the safe and efficient
running of
gas turbines. In view of the above, it would be advantageous to have a
diagnostics system capable of reliably detecting component faults (even though limited
to
gas path components) in a quantitative marmer. V
This thesis
presents the development an integrated fault diagnostics model for
identifying shifts in component performance and sensor faults using advanced concepts
in
genetic algorithm. The diagnostics model operates in three distinct stages. The rst
stage uses response surfaces for computing objective functions to increase the
exploration potential of the search space while easing the computational burden. The
second
stage uses the heuristics modification of genetics algorithm parameters through a
master-slave
type configuration. The third stage uses the elitist model concept in genetic
algorithm to preserve the accuracy of the solution in the face of randomness.
The above fault
diagnostics model has been integrated with a nested neural network to
form a
hybrid diagnostics model. The nested neural network is employed as a pre-
processor or lter to reduce the number of fault classes to be explored by the genetic
algorithm based diagnostics model. The hybrid model improves the accuracy, reliability
and
consistency of the results obtained. In addition signicant improvements in the total
run time have also been observed. The advanced
cycle Intercooled Recuperated WR2l
engine has been used as the test engine for implementing the diagnostics model.SOE Prize winne
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