Search results for "Mathematical optimization"
showing 10 items of 1300 documents
New Geometric Constraint Solving Formulation: Application to the 3D Pentahedron
2014
Geometric Constraint Solving Problems (GCSP) are nowadays routinely investigated in geometric modeling. The 3D Pentahedron problem is a GCSP defined by the lengths of its edges and the planarity of its quadrilateral faces, yielding to an under-constrained system of twelve equations in eighteen unknowns. In this work, we focus on solving the 3D Pentahedron problem in a more robust and efficient way, through a new formulation that reduces the underlying algebraic formulation to a well-constrained system of three equations in three unknowns, and avoids at the same time the use of placement rules that resolve the under-constrained original formulation. We show that geometric constraints can be …
Solution isolation strategies for the Bernstein polytopes-based solver
2013
The Bernstein polytopes-based solver is a new method developed to solve systems of nonlinear equations, which often occur in Geometric Constraint Solving Problems. The principle of this solver is to linearize nonlinear monomials and then to solve the resulting linear programming problems, through linear programming. However, without any strategy for the isolation of the many solutions of multiple-solution systems, this solver is slow in practice. To overcome this problem, we propose in this work, a study of several strategies for solution isolation, through the split of solution boxes into several subboxes, according to three main steps answering the questions: when, where, and how to perfo…
Partial spatial equilibria with fuzzy constraints
1981
It is implicitly accepted by spatial economic analysis that the economic behaviour of agents located in given spaces (market areas, regions, etc.) is precise, that is to say, their behaviour is such that a possible action (consumption, production) is, or is not, preferable to another. In otherwords, economic agents are assumed to make accurate economic calculations and optimise the objective functions under strict constraints of resource limitation. These objective functions have clearly defined arguments and well-controlled parameters.
mplicit Identification of Contact Parameters in a Continuous Chain Model
2011
Accurate contact modeling is of great importance in the field of dynamic chain simulations. In this paper emphasis is on contact dynamics for a time-domain simulation model of large chains guided in a closed loop track. The chain model is based on theory for unconstrained rigid multibody dynamics where contact within the chain and with the track is defined through continuous point contacts using the contact indentation and rate as means. This paper presents an implicit method to determine contact parameters of the chain model through the use of none gradient optimization methods. The set of model parameters are estimated by minimizing the residual between simulated and measured results. The…
Nonsmooth Penalty Techniques in Control of the Continuous Casting Process
1991
We introduce a mathematical model which is used to simulate the continuous casting process and to control the secondary cooling water sprays. The main object is to minimize the defects in the final products. The problem is formulated as an optimal control problem where the cost function is constructed according to certain metallurgical criteria and constraints. The temperature distribution of the strand is calculated by solving a nonlinear heat equation with free boundaries between solid and liquid phases.
An Adaptive Metamodel-Based Optimization Approach for Vehicle Suspension System Design
2014
Published version of an article in the journal: Mathematical Problems in Engineering. Also available from the publisher at: http://dx.doi.org/10.1155/2014/965157 The performance index of a suspension system is a function of the maximum and minimum values over the parameter interval. Thus metamodel-based techniques can be used for designing suspension system hardpoints locations. In this study, an adaptive metamodel-based optimization approach is used to find the proper locations of the hardpoints, with the objectives considering the kinematic performance of the suspension. The adaptive optimization method helps to find the optimum locations of the hardpoints efficiently as it may be unachie…
Partial Discharges analysis and parameters identification by continuous Ant Colony Optimization
2008
The technique of ant colony optimization has been employed in this paper to efficiently deal with the problem of parameters identification in partial discharge, PD, analysis. The latter is a continuous optimization problem. From the technical point of view the identification of these parameters allows the modeling of the phenomenon of Partial Discharges in dielectrics. In this way it is possible the early diagnosis of defects in Medium Voltage cable lines and components and thus it is possible to prevent possible outages and service interruptions. Analytically, the problem consists of finding the Weibull parameters of the Pulse Amplitude Distribution (PAD) distributions allowing the identif…
An evolutionary method for complex-process optimization
2010
10 páginas, 7 figuras, 7 tablas
Black box scatter search for general classes of binary optimization problems
2010
The purpose of this paper is to apply the scatter search methodology to general classes of binary problems. We focus on optimization problems for which the solutions are represented as binary vectors and that may or may not include constraints. Binary problems arise in a variety of settings, including engineering design and statistical mechanics (e.g., the spin glass problem). A distinction is made between two sets of general constraint types that are handled directly by the solver and other constraints that are addressed via penalty functions. In both cases, however, the heuristic treats the objective function evaluation as a black box. We perform computational experiments with four well-k…
SSPMO: A Scatter Tabu Search Procedure for Non-Linear Multiobjective Optimization
2007
We describe the development and testing of a metaheuristic procedure, based on the scatter-search methodology, for the problem of approximating the efficient frontier of nonlinear multiobjective optimization problems with continuous variables. Recent applications of scatter search have shown its merit as a global optimization technique for single-objective problems. However, the application of scatter search to multiobjective optimization problems has not been fully explored in the literature. We test the proposed procedure on a suite of problems that have been used extensively in multiobjective optimization. Additional tests are performed on instances that are an extension of those consid…