Search results for "linear programming"
showing 10 items of 137 documents
V I G — A Visual and Dynamic Decision Support System for Multiple Objective Linear Programming
1989
In this paper we describe the principles of VIG (Visual Interactive Goal Programming), a Multiple Criteria Decision Support System, recently developed by Korhonen. PARETO RACE is a corner-stone of this system, which is designed to support both the modelling and solving of a multiple objective linear programming problem. The interface is based on one main menu, spreadsheets, and interactive use of computer graphics. VIG provides the decision-maker with the possibility to approach his/her decision problem by using an “evolutionary approach”. This means that the decision-maker does not have to specify the model precisely prior to solving the problem. In fact, the model evolves progressively. W…
Optimal placement of 3D sensors considering range and field of view
2017
This paper describes a novel approach to the problem of optimal placement of 3D sensors in a specified volume of interest. The coverage area of the sensors is modelled as a cone having limited field of view and range. The volume of interest is divided into many, smaller cubes each having a set of associated Boolean and continuous variables. The proposed method could be easily extended to handle the case where certain sub-volumes must be covered by several sensors (redundancy), for example ex-zones, regions where humans are not allowed to enter or regions where machine movement may obstruct the view of a single sensor. The optimisation problem is formulated as a Mixed-Integer Linear Program …
Optimum plastic design for multiple sets of loads
1974
We study optimum plastic design of structures made up, or conceived as assemblies of finite elements, each having an elemental piece-wise linear rigid-plastic behaviour. Since cost function linearly dependent on design variables are considered, optimization problems in linear programming are encountered. Allowance is made for design dependent mass forces, and for some technological constraints. The design growing process is studied in the case of various sets of alternative applied loads, and the optimality conditions are written in a proper geometrical form which leads to a generalization of the concept of Foulkes mechanism.
A fuzzy method to repair infeasibility in linearly constrained problems
2001
Abstract In this paper we introduce a fuzzy method to deal with infeasibility in linearly constrained programs. Given an infeasible instance, we determine how much we should perturb the right-hand side coefficients in order to attain feasibility and propose a ‘feasible reformulation’ of the problem. Although we prove that our algorithm always finds such a reformulation the convenience of using it can be decided by the analyst. By this, we mean that the method also provides a simple way to compute lower bounds on the changes on every right-hand side coefficient, and if the decision maker considers that some of the magnitudes are unacceptable, he or she simply stops at this step. We think tha…
Path relinking and GRG for artificial neural networks
2006
Artificial neural networks (ANN) have been widely used for both classification and prediction. This paper is focused on the prediction problem in which an unknown function is approximated. ANNs can be viewed as models of real systems, built by tuning parameters known as weights. In training the net, the problem is to find the weights that optimize its performance (i.e., to minimize the error over the training set). Although the most popular method for training these networks is back propagation, other optimization methods such as tabu search or scatter search have been successfully applied to solve this problem. In this paper we propose a path relinking implementation to solve the neural ne…
SIOPRED performance in a Forecasting Blind Competition
2012
In this paper we present the results obtained by applying our automatic forecasting support system, named SIOPRED, over a data set of time series in a Forecasting Blind Competition. In order to apply our procedure for providing point forecasts it has been necessary to develop an interactive strategy for the choice of the suitable length of the seasonal cycle and the seasonality form for a generalized exponential smoothing method, which have been obtained using SIOPRED. For the choice of those essential characteristics of forecasting methods, also a certain multi-objective formulation which minimizes several measures of fitting is used. Once these specifications are established, the model pa…
Optimal Impulse Control Problems and Linear Programming
2009
Optimal impulse control problems are, in general, difficult to solve. A current research goal is to isolate those problems that lead to tractable solutions. In this paper, we identify a special class of optimal impulse control problems which are easy to solve. Easy to solve means that solution algorithms are polynomial in time and therefore suitable to the on-line implementation in real-time problems. We do this by using a paradigm borrowed from the Operations Research field. As main result, we present a solution algorithm that converges to the exact solution in polynomial time. Our approach consists in approximating the optimal impulse control problem via a binary linear programming proble…
The Tax Justice Network-Africa v Cabinet Secretary for National Treasury & 2 Others: A Big Win for Tax Justice Activism?
2019
This paper develops an optimization model for selecting a large subsample that improves the representativeness of a simple random sample previously obtained from a population larger than the population of interest. The problem formulation involves convex mixed-integer nonlinear programming (convex MINLP) and is therefore NP-hard. However, the solution is found by maximizing the “constant of proportionality” – in other words, maximizing the size of the subsample taken from a stratified random sample with proportional allocation – and restricting it to a p-value high enough to achieve a good fit to the population of interest using Pearson’s chi-square goodness-of-fit test. The beauty of the m…
Optimization under Uncertainty and Linear Semi-Infinite Programming: A Survey
2001
This paper deals with the relationship between semi-infinite linear programming and decision making under uncertainty in imprecise environments. Actually, we have reviewed several set-inclusive constrained models and some fuzzy programming problems in order to see if they can be solved by means of a linear semi-infinite program. Finally, we present some numerical examples obtained by using a primal semi-infinite programming method.
Determining the best shipper sizes for sending products to customers
2014
A distribution company has to send products, packed into shippers, from the warehouse to retail shops. The number of different shipper types is regarded as a parameter given by the user, who is looking for a balance between transportation costs and stock and procurement costs. The problem is to decide the sizes of the shipper types to keep at the warehouse so as to minimize the cost of meeting the forecasted demand over the planning horizon. In this paper, we describe an integer linear programming formulation for the problem and obtaining feasible solutions. Other models, based on multiknapsack and p-median and facility location models, are for obtaining lower bounds. We study several ways …