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1.
On Solution to an Optimal Shape Design Problem in 3-Dimensional Linear Magnetostatics 总被引:2,自引:0,他引:2
Dalibor Lukáš 《Applications of Mathematics》2004,49(5):441-464
In this paper we present theoretical, computational, and practical aspects concerning 3-dimensional shape optimization governed by linear magnetostatics. The state solution is approximated by the finite element method using Nédélec elements on tetrahedra. Concerning optimization, the shape controls the interface between the air and the ferromagnetic parts while the whole domain is fixed. We prove the existence of an optimal shape. Then we state a finite element approximation to the optimization problem and prove the convergence of the approximated solutions. In the end, we solve the problem for the optimal shape of an electromagnet that arises in the research on magnetooptic effects and that was manufactured afterwards. 相似文献
2.
S. Rangavajhala A. A. Mullur A. Messac 《Journal of Optimization Theory and Applications》2009,140(2):315-337
Robust design optimization (RDO) problems can generally be formulated by incorporating uncertainty into the corresponding
deterministic problems. In this context, a careful formulation of deterministic equality constraints into the robust domain
is necessary to avoid infeasible designs under uncertain conditions. The challenge of formulating equality constraints is
compounded in multiobjective RDO problems. Modeling the tradeoffs between the mean of the performance and the variation of
the performance for each design objective in a multiobjective RDO problem is itself a complex task. A judicious formulation
of equality constraints adds to this complexity because additional tradeoffs are introduced between constraint satisfaction
under uncertainty and multiobjective performance. Equality constraints under uncertainty in multiobjective problems can therefore
pose a complicated decision making problem. In this paper, we provide a new problem formulation that can be used as an effective
multiobjective decision making tool, with emphasis on equality constraints. We present two numerical examples to illustrate
our theoretical developments. 相似文献
3.
Computational Approach to Essential and Nonessential Objective Functions in Linear Multicriteria Optimization 总被引:2,自引:0,他引:2
A. B. Malinowska D. F. M. Torres 《Journal of Optimization Theory and Applications》2008,139(3):577-590
The question of obtaining well-defined criteria for multiple-criteria decision making problems is well known. One of the approaches
dealing with this question is the concept of nonessential objective functions. A certain objective function is called nonessential
if the set of efficient solutions is the same with or without that objective function. We present two methods for determining
nonessential objective functions. A computational implementation is done using a computer algebra system.
Portions of this paper were presented at the 23rd IFIP TC 7 International Conference on System Modelling and Optimization,
Cracow, Poland, July 23–27, 2007. This work was supported by KBN under Bialystok Technical University Grant S/WI/1/08 and
by the R&D unit CEOC of the University of Aveiro through FCT and FEDER/POCI 2010. 相似文献
4.
The rigorous and efficient determination of the global solution of a nonconvex MINLP problem arising from product portfolio
optimization introduced by Kallrath (2003) is addressed. The objective of the optimization problem is to determine the optimal
number and capacity of reactors satisfying the demand and leading to a minimal total cost. Based on the model developed by
Kallrath (2003), an improved formulation is proposed, which consists of a concave objective function and linear constraints
with binary and continuous variables. A variety of techniques are developed to tighten the model and accelerate the convergence
to the optimal solution. A customized branch and bound approach that exploits the special mathematical structure is proposed
to solve the model to global optimality. Computational results for two case studies are presented. In both case studies, the
global solutions are obtained and proved optimal very efficiently in contrast to available commercial MINLP solvers. 相似文献
5.
In this paper, we address a global optimization approach to a waterdistribution network design problem. Traditionally, a variety of localoptimization schemes have been developed for such problems, each new methoddiscovering improved solutions for some standard test problems, with noknown lower bound to test the quality of the solutions obtained. A notableexception is a recent paper by Eiger et al. (1994) who present a firstglobal optimization approach for a loop and path-based formulation of thisproblem, using a semi-infinite linear program to derive lower bounds. Incontrast, we employ an arc-based formulation that is linear except forcertain complicating head-loss constraints and develop a first globaloptimization scheme for this model. Our lower bounds are derived through thedesign of a suitable Reformulation-Linearization Technique (RLT) thatconstructs a tight linear programming relaxation for the given problem, andthis is embedded within a branch-and-bound algorithm. Convergence to anoptimal solution is induced by coordinating this process with an appropriatepartitioning scheme. Some preliminary computational experience is providedon two versions of a particular standard test problem for the literature forwhich an even further improved solution is discovered, but one that isverified for the first time to be an optimum, without any assumed boundson the flows. Two other variants of this problem are also solved exactly forillustrative purposes and to provide researchers with additional test caseshaving known optimal solutions. Suggestions on a more elaborate study involving several algorithmic enhancements are presented for futureresearch. 相似文献