30 research outputs found
An analysis of minimax facility location problems with area demands /
The unconstrained model, and its solution technique can be easily modified to solve the limiting case where all facilities are fixed points, and also the case when metric constraints are added.Examples are solved to show the impact of assuming area demands, the conflicting nature of the minimax and minisum criteria and to illustrate the solutions techniques developed.A minimax objective function constrained by a bound on the total average cost of servicing all existing facilities (minisum function) is then discussed. Using duality properties, this problem is shown to be equivalent to another model which minimizes the minisum function subject to a bound on the same minimax function. This last problem proves to be easier to solve, and a specialized solution technique is developed. The resulting solutions are nondominated solutions in relation to the two criteria involved. Another way to generate nondominated solutions is by combining the two functions into a weighted sum. The constrained criterion method is shown to be superior both analytically and practically.Most probabilistic facility location problems investigated to date were variations of the generalized Weber formulation. In this research, several single facility minimax location models are analyzed, where both the weights and the locations of the existing facilities are random variables. The demand points are uniformly distributed over rectangular areas, the rectilinear metric is used and the weights are assumed to be independently distributed random variables. Two unconstrained probabilistic models are analyzed and compared to the centroid formulation, it is seen that the probabilistic models are sensitive to deviations from optimal solutions. An expected value criterion formulation is also presented along with lower and upper bound approximating functions
On minimax-regret Huff location models
We address the following single-facility location problem: a firm is entering into a market by locating one facility in a region of the plane. The demand captured from each user by the facility will be proportional to the users buying power and inversely proportional to a function of the user-facility distance. Uncertainty exists on the buying power (weight) of the users. This is modeled by assuming that a set of scenarios exists, each scenario
corresponding to a weight realization. The objective is to locate the facility following the Savage criterion, i.e., the minimax-regret location is sought. The problem is formulated as a global optimization problem with objective written as difference of two convex monotonic functions. The numerical results obtained show that a branch and bound using this new method for obtaining bounds clearly outperforms benchmark procedures.Ministerio de Educaci贸n y CienciaJunta de Andaluc铆
Solution Methods for the \u3cem\u3ep\u3c/em\u3e-Median Problem: An Annotated Bibliography
The p-median problem is a graph theory problem that was originally designed for, and has been extensively applied to, facility location. In this bibliography, we summarize the literature on solution methods for the uncapacitated and capacitated p-median problem on a graph or network
Task-Robust Pre-Training for Worst-Case Downstream Adaptation
Pre-training has achieved remarkable success when transferred to downstream
tasks. In machine learning, we care about not only the good performance of a
model but also its behavior under reasonable shifts of condition. The same
philosophy holds when pre-training a foundation model. However, the foundation
model may not uniformly behave well for a series of related downstream tasks.
This happens, for example, when conducting mask recovery regression where the
recovery ability or the training instances diverge like pattern features are
extracted dominantly on pre-training, but semantic features are also required
on a downstream task. This paper considers pre-training a model that guarantees
a uniformly good performance over the downstream tasks. We call this goal as
. Our method first separates the upstream
task into several representative ones and applies a simple minimax loss for
pre-training. We then design an efficient algorithm to solve the minimax loss
and prove its convergence in the convex setting. In the experiments, we show
both on large-scale natural language processing and computer vision datasets
our method increases the metrics on worse-case downstream tasks. Additionally,
some theoretical explanations for why our loss is beneficial are provided.
Specifically, we show fewer samples are inherently required for the most
challenging downstream task in some cases
Dynamic and Robust Capacitated Facility Location in Time Varying Demand Environments
This dissertation studies models for locating facilities in time varying demand
environments. We describe the characteristics of the time varying demand that motivate
the analysis of our location models in terms of total demand and the change
in value and location of the demand of each customer. The first part of the dissertation
is devoted to the dynamic location model, which determines the optimal
time and location for establishing capacitated facilities when demand and cost parameters
are time varying. This model minimizes the total cost over a discrete and
finite time horizon for establishing, operating, and closing facilities, including the
transportation costs for shipping demand from facilities to customers. The model
is solved using Lagrangian relaxation and Benders? decomposition. Computational
results from different time varying total demand structures demonstrate, empirically,
the performance of these solution methods.
The second part of the dissertation studies two location models where relocation
of facilities is not allowed and the objective is to determine the optimal location
of capacitated facilities that will have a good performance when demand and cost
parameters are time varying. The first model minimizes the total cost for opening
and operating facilities and the associated transportation costs when demand and
cost parameters are time varying. The model is solved using Benders? decomposition. We show that in the presence of high relocation costs of facilities (opening and closing
costs), this model can be solved as a special case by the dynamic location model. The
second model minimizes the maximum regret or opportunity loss between a robust
configuration of facilities and the optimal configuration for each time period. We
implement local search and simulated annealing metaheuristics to efficiently obtain
near optimal solutions for this model
Bibliography on Nondifferentiable Optimization
This is a research bibliography with all the advantages and shortcomings that this implies. The author has used it as a bibliographical data base when writing papers, and it is therefore largely a reflection of his own personal research interests. However, it is hoped that this bibliography will nevertheless be of use to others interested in nondifferentiable optimization
Facility Location Problems: Models, Techniques, and Applications in Waste Management
This paper presents a brief description of some existing models of facility location problems
(FLPs) in solid waste management. The study provides salient information on commonly used
distance functions in location models along with their corresponding mathematical formulation. Some
of the optimization techniques that have been applied to location problems are also presented along
with an appropriate pseudocode algorithm for their implementation. Concerning the models and
solution techniques, the survey concludes by summarizing some recent studies on the applications
of FLPs to waste collection and disposal. It is expected that this paper will contribute in no small
measure to an integrated solid waste management system with specific emphasis on issues associated
with waste collection, thereby boosting the drive for e锟絜ctive and e锟絚ient waste collection systems.
The content will also provide early career researchers with some necessary starting information
required to formulate and solve problems relating to FLP
A review of network location theory and models
Cataloged from PDF version of article.In this study, we review the existing literature on network location problems.
The study has a broad scope that includes problems featuring desirable and
undesirable facilities, point facilities and extensive facilities, monopolistic and
competitive markets, and single or multiple objectives. Deterministic and
stochastic models as well as robust models are covered. Demand data
aggregation is also discussed. More than 500 papers in this area are reviewed
and critical issues, research directions, and problem extensions are emphasized.Erdo臒an, Damla SelinM.S