69,637 research outputs found
Multiple bottlenecks sorting criterion at initial sequence in solving permutation flow shop scheduling problem
This paper proposes a heuristic that introduces the
application of bottleneck-based concept at the beginning of an initial sequence
determination with the objective of makespan minimization. Earlier studies
found that the scheduling activity become complicated when dealing with
machine, m greater than 2, known as non-deterministic polynomial-time
hardness (NP-hard). To date, the Nawaz-Enscore-Ham (NEH) algorithm is
still recognized as the best heuristic in solving makespan problem in
scheduling environment. Thus, this study treated the NEH heuristic as the
highest ranking and most suitable heuristic for evaluation purpose since it is
the best performing heuristic in makespan minimization. This study used the
bottleneck-based approach to identify the critical processing machine which
led to high completion time. In this study, an experiment involving machines
(m =4) and n-job (n = 6, 10, 15, 20) was simulated in Microsoft Excel Simple
Programming to solve the permutation flowshop scheduling problem. The
overall computational results demonstrated that the bottleneck machine M4
performed the best in minimizing the makespan for all data set of problems
Heuristics for The Whitehead Minimization Problem
In this paper we discuss several heuristic strategies which allow one to
solve the Whitehead's minimization problem much faster (on most inputs) than
the classical Whitehead algorithm. The mere fact that these strategies work in
practice leads to several interesting mathematical conjectures. In particular,
we conjecture that the length of most non-minimal elements in a free group can
be reduced by a Nielsen automorphism which can be identified by inspecting the
structure of the corresponding Whitehead Graph
Guaranteed Minimum-Rank Solutions of Linear Matrix Equations via Nuclear Norm Minimization
The affine rank minimization problem consists of finding a matrix of minimum
rank that satisfies a given system of linear equality constraints. Such
problems have appeared in the literature of a diverse set of fields including
system identification and control, Euclidean embedding, and collaborative
filtering. Although specific instances can often be solved with specialized
algorithms, the general affine rank minimization problem is NP-hard. In this
paper, we show that if a certain restricted isometry property holds for the
linear transformation defining the constraints, the minimum rank solution can
be recovered by solving a convex optimization problem, namely the minimization
of the nuclear norm over the given affine space. We present several random
ensembles of equations where the restricted isometry property holds with
overwhelming probability. The techniques used in our analysis have strong
parallels in the compressed sensing framework. We discuss how affine rank
minimization generalizes this pre-existing concept and outline a dictionary
relating concepts from cardinality minimization to those of rank minimization
CVaR minimization by the SRA algorithm
Using the risk measure CV aR in �nancial analysis has become
more and more popular recently. In this paper we apply CV aR for portfolio optimization. The problem is formulated as a two-stage stochastic programming model, and the SRA algorithm, a recently developed heuristic algorithm, is applied for minimizing CV aR
A Hybrid Search Algorithm for the Whitehead Minimization Problem
The Whitehead Minimization problem is a problem of finding elements of the
minimal length in the automorphic orbit of a given element of a free group. The
classical algorithm of Whitehead that solves the problem depends exponentially
on the group rank. Moreover, it can be easily shown that exponential blowout
occurs when a word of minimal length has been reached and, therefore, is
inevitable except for some trivial cases.
In this paper we introduce a deterministic Hybrid search algorithm and its
stochastic variation for solving the Whitehead minimization problem. Both
algorithms use search heuristics that allow one to find a length-reducing
automorphism in polynomial time on most inputs and significantly improve the
reduction procedure. The stochastic version of the algorithm employs a
probabilistic system that decides in polynomial time whether or not a word is
minimal. The stochastic algorithm is very robust. It has never happened that a
non-minimal element has been claimed to be minimal
Four payment models for the multi-mode resource constrained project scheduling problem with discounted cash flows
In this paper, the multi-mode resource constrained project scheduling problem with discounted cash flows is considered. The objective is the maximization of the net present value of all cash flows. Time value of money is taken into consideration, and cash in- and outflows are associated with activities and/or events. The resources can be of renewable, nonrenewable, and doubly constrained resource types. Four payment models are considered: Lump sum payment at the terminal event, payments at prespecified event nodes, payments at prespecified time points and progress payments. For finding solutions to problems proposed, a
genetic algorithm (GA) approach is employed, which uses a special crossover operator that can exploit the multi-component nature of the problem. The models are investigated at the hand of an example problem. Sensitivity analyses are performed over the mark up and the discount rate. A set of 93 problems from literature are solved under the four different payment models and resource type combinations with the GA approach employed resulting in satisfactory computation times. The GA approach is compared with a domain specific heuristic for the lump sum payment case with renewable resources and is shown to outperform it
A Simplified Approach to Recovery Conditions for Low Rank Matrices
Recovering sparse vectors and low-rank matrices from noisy linear
measurements has been the focus of much recent research. Various reconstruction
algorithms have been studied, including and nuclear norm minimization
as well as minimization with . These algorithms are known to
succeed if certain conditions on the measurement map are satisfied. Proofs of
robust recovery for matrices have so far been much more involved than in the
vector case.
In this paper, we show how several robust classes of recovery conditions can
be extended from vectors to matrices in a simple and transparent way, leading
to the best known restricted isometry and nullspace conditions for matrix
recovery. Our results rely on the ability to "vectorize" matrices through the
use of a key singular value inequality.Comment: 6 pages, This is a modified version of a paper submitted to ISIT
2011; Proc. Intl. Symp. Info. Theory (ISIT), Aug 201
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