834 research outputs found
Algorithms for the continuous nonlinear resource allocation problem---new implementations and numerical studies
Patriksson (2008) provided a then up-to-date survey on the
continuous,separable, differentiable and convex resource allocation problem
with a single resource constraint. Since the publication of that paper the
interest in the problem has grown: several new applications have arisen where
the problem at hand constitutes a subproblem, and several new algorithms have
been developed for its efficient solution. This paper therefore serves three
purposes. First, it provides an up-to-date extension of the survey of the
literature of the field, complementing the survey in Patriksson (2008) with
more then 20 books and articles. Second, it contributes improvements of some of
these algorithms, in particular with an improvement of the pegging (that is,
variable fixing) process in the relaxation algorithm, and an improved means to
evaluate subsolutions. Third, it numerically evaluates several relaxation
(primal) and breakpoint (dual) algorithms, incorporating a variety of pegging
strategies, as well as a quasi-Newton method. Our conclusion is that our
modification of the relaxation algorithm performs the best. At least for
problem sizes up to 30 million variables the practical time complexity for the
breakpoint and relaxation algorithms is linear
Time out of mind: Subben's checklist revisited: A partial description of the development of quantitative OR papers over a period of 25 years
This short paper aims to investigate some of the historical developments of
one classic, well-cited and highly esteemed scientific journal in the domain of
quantitative operations research - namely the INFORMS journal Operations
Research - over a period of 25 years between 1981 and 2006. As such this paper,
and the journal in question, represents one representative attempt to analyze -
for the purpose of possible future generalization - how research production has
evolved, and evolves, over time. Among the general developments that we think
we can trace are that (a) the historical overviews (i.e., literature surveys)
in the articles, as well as the list of references, somewhat
counter-intuitively shrink over time, while (b) the motivating and modelling
parts grow. We also attempt to characterize - in some detail - the appearance
and character, over time, of the most cited, as well as the least cited, papers
over the years studied. In particular, we find that many of the least cited
papers are quite imbalanced. For example, some of them include one main section
only, and the least cited papers also have shorter reference lists.
We also analyse the articles' utilization of important buzz words
representing the constitutive parts of an OR journal paper, based on Subben's
checklist (Larsson and Patriksson, 2014, 2016). Based on a word count of these
buzz words we conclude through a citation study, utilizing a collection of
particularly highly or little cited papers, that there is a quite strong
positive correlation between a journal paper being highly cited and its degree
of utilization of this checklist
Optimal scheduling of the next preventive maintenance activity for a wind farm
Global warming has been attributed to increased greenhouse gas emission
concentrations in the atmosphere through the burning of fossil fuels. Renewable
energy, as an alternative, is capable of displacing energy from fossil fuels.
Wind power is abundant, renewable, and produces almost no greenhouse gas during
operation. A large part of the cost of operations is due to the cost of
maintaining the wind power equipment, especially for offshore wind farms. How
to reduce the maintenance cost is what this article focus on.
This article presents a binary linear optimisation model whose solution may
suggest wind turbine owners which components, and when, should undergo the next
preventive maintenance (PM). The scheduling strategy takes into account
eventual failure events of the multi-component system, in that after the failed
system is repaired, the previously scheduled PM plan should be updated treating
the restored components to be as good as new.
The optimisation model NextPM is tested through three numerical case studies.
The first study addresses the illuminating case of a single component system.
The second study analyses the case of seasonal variations of set-up costs, as
compared to the constant set-up cost setting. Among other things, this analysis
reveals a dramatic cost reduction achieved by the NextPM model as compared to
the the pure CM strategy. In these two case studies, the cost are reduced by
around 35%. The third case study compares the NextPM model with another
optimisation model preventive maintenance scheduling problem with interval
costs(PMSPIC) which was the major source of inspiration for this article. This
comparison demonstrates that the NextPM model is accurate and much more
effective.
In conclusion, the NextPM model is both accurate and fast to solve. The
algorithm stemming from the proposed model can be used as a key module in a
maintenance scheduling app.Comment: 16 pages, 2 figures. Submitted to Wind Energy Scienc
An Optimal Number-Dependent Preventive Maintenance Strategy for Offshore Wind Turbine Blades Considering Logistics
In offshore wind turbines, the blades are among the most critical and expensive components that suffer from different types of damage due to the harsh maritime environment and high load. The blade damages can be categorized into two types: the minor damage, which only causes a loss in wind capture without resulting in any turbine stoppage, and the major (catastrophic) damage, which stops the wind turbine and can only be corrected by replacement. In this paper, we propose an optimal number-dependent preventive maintenance (NDPM) strategy, in which a maintenance team is transported with an ordinary or expedited lead time to the offshore platform at the occurrence of the Nth minor damage or the first major damage, whichever comes first. The long-run expected cost of the maintenance strategy is derived, and the necessary conditions for an optimal solution are obtained. Finally, the proposed model is tested on real data collected from an offshore wind farm database. Also, a sensitivity analysis is conducted in order to evaluate the effect of changes in the model parameters on the optimal solution
Column Generation Algorithms for Nonlinear Optimization II: Numerical Investigations
García et al. present a class of column generation (CG) algorithms for nonlinear programs. Its main
motivation from a theoretical viewpoint is that under some circumstances, finite convergence can be
achieved, in much the same way as for the classic simplicial decomposition method; the main practical
motivation is that within the class there are certain nonlinear column generation problems that can
accelerate the convergence of a solution approach which generates a sequence of feasible points. This
algorithm can, for example, accelerate simplicial decomposition schemes by making the subproblems
nonlinear. This paper complements the theoretical study on the asymptotic and finite convergence of
these methods given in
[1]
with an experimental study focused on their computational efficiency.
Three types of numerical experiments are conducted. The first group of test problems has been
designed to study the parameters involved in these methods. The second group has been designed to
investigate the role and the computation of the prolongation of the generated columns to the relative
boundary. The last one has been designed to carry out a more complete investigation of the difference
in computational efficiency between linear and nonlinear column generation approaches.
In order to carry out this investigation, we consider two types of test problems: the first one is the
nonlinear, capacitated single-commodity network flow problem of which several large-scale instances
with varied degrees of nonlinearity and total capacity are constructed and investigated, and the second
one is a combined traffic assignment mode
Sensitivity analysis of the variable demand probit stochastic user equilibrium with multiple user classes
This paper presents a formulation of the multiple user class, variable demand, probit stochastic user equilibrium model. Sufficient conditions are stated for differentiability of the equilibrium flows of this model. This justifies the derivation of sensitivity expressions for the equilibrium flows, which are presented in a format that can be implemented in commercially available software. A numerical example verifies the sensitivity expressions, and that this formulation is applicable to large networks
Integration of expert knowledge into radial basis function surrogate models
A current application in a collaboration between Chalmers University of Technology and Volvo Group Trucks Technology concerns the global optimization of a complex simulation-based function describing the rolling resistance coefficient of a truck tyre. This function is crucial for the optimization of truck tyres selection considered. The need to explicitly describe and optimize this function provided the main motivation for the research presented in this article. Many optimization algorithms for simulation-based optimization problems use sample points to create a computationally simple surrogate model of the objective function. Typically, not all important characteristics of the complex function (as, e.g., non-negativity)—here referred to as expert knowledge—are automatically inherited by the surrogate model. We demonstrate the integration of several types of expert knowledge into a radial basis function interpolation. The methodology is first illustrated on a simple example function and then applied to a function describing the rolling resistance coefficient of truck tyres. Our numerical results indicate that expert knowledge can be advantageously incorporated and utilized when creating global approximations of unknown functions from sample points
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