共查询到20条相似文献,搜索用时 15 毫秒
1.
E. A. Galperin 《Journal of Optimization Theory and Applications》1992,75(1):69-85
A new approach to multiobjective optimization is presented which is made possible due to our ability to obtain full global optimal solutions. A distinctive feature of this approach is that a vector cost function is nonscalarized. The method provides a means for the solution of vector optimization problems with nonreconcilable objectives.This work was supported by the Natural Sciences and Engineering Research Council of Canada, Grant No. A3492. 相似文献
2.
Multiobjective optimization deals with problems involving multiple measures of performance that should be optimized simultaneously.
In this paper we extend bucket elimination (BE), a well known dynamic programming generic algorithm, from mono-objective to
multiobjective optimization. We show that the resulting algorithm, MO-BE, can be applied to true multi-objective problems
as well as mono-objective problems with knapsack (or related) global constraints. We also extend mini-bucket elimination (MBE),
the approximation form of BE, to multiobjective optimization. The new algorithm MO-MBE can be used to obtain good quality
multi-objective lower bounds or it can be integrated into multi-objective branch and bound in order to increase its pruning efficiency. Its
accuracy is empirically evaluated in real scheduling problems, as well as in Max-SAT-ONE and biobjective weighted minimum
vertex cover problems. 相似文献
3.
A crucial step in global optimization algorithms based on random sampling in the search domain is decision about the achievement of a prescribed accuracy. In order to overcome the difficulties related to such a decision, the Bayesian Nonparametric Approach has been introduced. The aim of this paper is to show the effectiveness of the approach when an ad hoc clustering technique is used for obtaining promising starting points for a local search algorithm. Several test problems are considered. 相似文献
4.
In this paper we propose an algorithm using only the values of the objective function and constraints for solving one-dimensional global optimization problems where both the objective function and constraints are Lipschitzean and nonlinear. The constrained problem is reduced to an unconstrained one by the index scheme. To solve the reduced problem a new method with local tuning on the behavior of the objective function and constraints over different sectors of the search region is proposed. Sufficient conditions of global convergence are established. We also present results of some numerical experiments. 相似文献
5.
This paper concerns the study of the so-called super minimizers related to the concept of super efficiency in constrained
problems of multiobjective optimization, where cost mappings are generally set-valued. We derive necessary conditions for
super minimizers on the base of advanced tools of variational analysis and generalized differentiation that are new in both
finite-dimensional and infinite-dimensional settings for problems with single-valued and set-valued objectives.
相似文献
6.
Eliane R. Panier 《Mathematical Programming》1987,37(3):269-292
An algorithm for solving linearly constrained optimization problems is proposed. The search direction is computed by a bundle
principle and the constraints are treated through an active set strategy. Difficulties that arise when the objective function
is nonsmooth, require a clever choice of a constraint to relax. A certain nondegeneracy assumption is necessary to obtain
convergence.
Most of this research was performed when the author was with I.N.R.I.A. (Domaine de Voluceau-Rocquencourt, B.P. 105, 78153
Le Chesnay Cédex, France).
This research was supported in part by the National Science Foundation, Grants No. DMC-84-51515 and OIR-85-00108. 相似文献
7.
A generalized primal-relaxed dual algorithm for global optimization is proposed and its convergence is proved. The (GOP) algorithm of Floudas and Visweswaran (Refs. 1–2) is shown to be a special case of this general algorithm. Within the proposed framework, the algorithm of Floudas and Visweswaran (Refs. 1–2) is further extended to the nonsmooth case. A penalty implementation of the extended (GOP) algorithm is studied to improve its efficiency. 相似文献
8.
In this paper, a new global optimization method is proposed for an optimization problem with twice-differentiable objective
and constraint functions of a single variable. The method employs a difference of convex underestimator and a convex cut function,
where the former is a continuous piecewise concave quadratic function, and the latter is a convex quadratic function. The
main objectives of this research are to determine a quadratic concave underestimator that does not need an iterative local
optimizer to determine the lower bounding value of the objective function and to determine a convex cut function that effectively
detects infeasible regions for nonconvex constraints. The proposed method is proven to have a finite ε-convergence to locate
the global optimum point. The numerical experiments indicate that the proposed method competes with another covering method,
the index branch-and-bound algorithm, which uses the Lipschitz constant. 相似文献
9.
B. Betro 《Journal of Optimization Theory and Applications》1984,42(1):31-50
Random distribution functions are the basic tool for solving nonparametric decision-theoretic problems. In 1974, Doksum introduced the family of distributions neutral to the right, that is, distributions such thatF(t
1),[F(t
2)–F(t
1)]/[1 –F(t
1)],...,[F(t
k)–F(t
k – 1)]/[1 –F(t
k – 1)] are independent whenevert
1 < ... <t
kIn practice, application of distributions neutral to the right has been prevented by the lack of a manageable analytical expression for probabilities of the typeP(F(t)<q) for fixedt andq. A subclass of such distributions can be provided which allows for a close expression of the characteristic function of log[1–F(t)], given the sample. Then, thea posteriori distribution ofF(t) is obtained by numerical evaluation of a Fourier integral. As an application, the global optimization problem is formulated as a problem of inference about the quantiles of the distributionF(y) of the random variableY=f(X), wheref is the objective function andX is a random point in the search domain.The author thanks J. Koronacki and R. Zielinski of the Polish Academy of Sciences for their valuable criticism during the final draft of the paper. 相似文献
10.
By far the most efficient methods for global optimization are based on starting a local optimization routine from an appropriate
subset of uniformly distributed starting points. As the number of local optima is frequently unknown in advance, it is a crucial
problem when to stop the sequence of sampling and searching. By viewing a set of observed minima as a sample from a generalized
multinomial distribution whose cells correspond to the local optima of the objective function, we obtain the posterior distribution
of the number of local optima and of the relative size of their regions of attraction. This information is used to construct
sequential Bayesian stopping rules which find the optimal trade off between reliability and computational effort. 相似文献
11.
Zhe Chen 《Applicable analysis》2013,92(12):2457-2467
In this article, we investigate the nonemptiness and compactness of the weak Pareto optimal solution set of a multiobjective optimization problem with functional constraints via asymptotic analysis. We then employ the obtained results to derive the necessary and sufficient conditions of the weak Pareto optimal solution set of a parametric multiobjective optimization problem. Our results improve and generalize some known results. 相似文献
12.
A branch-and-reduce approach to global optimization 总被引:4,自引:0,他引:4
This paper presents valid inequalities and range contraction techniques that can be used to reduce the size of the search space of global optimization problems. To demonstrate the algorithmic usefulness of these techniques, we incorporate them within the branch-and-bound framework. This results in a branch-and-reduce global optimization algorithm. A detailed discussion of the algorithm components and theoretical properties are provided. Specialized algorithms for polynomial and multiplicative programs are developed. Extensive computational results are presented for engineering design problems, standard global optimization test problems, univariate polynomial programs, linear multiplicative programs, mixed-integer nonlinear programs and concave quadratic programs. For the problems solved, the computer implementation of the proposed algorithm provides very accurate solutions in modest computational time. 相似文献
13.
In this paper, we propose two kinds of robustness concepts by virtue of the scalarization techniques (Benson’s method and elastic constraint method) in multiobjective optimization, which can be characterized as special cases of a general non-linear scalarizing approach. Moreover, we introduce both constrained and unconstrained multiobjective optimization problems and discuss their relations to scalar robust optimization problems. Particularly, optimal solutions of scalar robust optimization problems are weakly efficient solutions for the unconstrained multiobjective optimization problem, and these solutions are efficient under uniqueness assumptions. Two examples are employed to illustrate those results. Finally, the connections between robustness concepts and risk measures in investment decision problems are also revealed. 相似文献
14.
Global optimization problems with a few variables and constraints arise in numerous applications but are seldom solved exactly. Most often only a local optimum is found, or if a global optimum is detected no proof is provided that it is one. We study here the extent to which such global optimization problems can be solved exactly using analytical methods. To this effect, we propose a series of tests, similar to those of combinatorial optimization, organized in a branch-and-bound framework. The first complete solution of two difficult test problems illustrates the efficiency of the resulting algorithm. Computational experience with the programbagop, which uses the computer algebra systemmacsyma, is reported on. Many test problems from the compendiums of Hock and Schittkowski and others sources have been solved.The research of the first and the third authors has been supported by AFOSR grants #0271 and #0066 to Rutgers University. Research of the second author has been supported by NSERC grant #GP0036426 and FCAR grants #89EQ4144 and #90NC0305. 相似文献
15.
Silvia Vogel 《Mathematical Programming》1992,56(1-3):91-119
In this paper we assume that a deterministic multiobjective programming problem is approximated by surrogate problems based on estimations for the objective functions and the constraints. Making use of a large deviations approach, we investigate the behaviour of the constraint sets, the sets of efficient points and the solution sets if the size of the underlying sample tends to infinity. The results are illustrated by applying them to stochastic programming with chance constraints, where (i) the distribution function of the random variable is estimated by the empirical distribution function, (ii) certain parameters have to be estimated. 相似文献
16.
In this paper we develop, analyze, and test a new algorithm for the global minimization of a function subject to simple bounds
without the use of derivatives. The underlying algorithm is a pattern search method, more specifically a coordinate search
method, which guarantees convergence to stationary points from arbitrary starting points. In the optional search phase of
pattern search we apply a particle swarm scheme to globally explore the possible nonconvexity of the objective function. Our
extensive numerical experiments showed that the resulting algorithm is highly competitive with other global optimization methods
also based on function values.
Support for Luís N. Vicente was provided by Centro de Matemática da Universidade de Coimbra and by FCT under grant POCI/MAT/59442/2004. 相似文献
17.
In this paper we consider a global optimization method for space trajectory design problems. The method, which actually aims
at finding not only the global minimizer but a whole set of low-lying local minimizers (corresponding to a set of different
design options), is based on a domain decomposition technique where each subdomain is evaluated through a procedure based
on the evolution of a population of agents. The method is applied to two space trajectory design problems and compared with
existing deterministic and stochastic global optimization methods. 相似文献
18.
研究了多目标优化问题的近似解. 首先证明了多面体集是 co-radiant集,并证明了一些性质. 随后研究了多面体集下多目标优化问题近似解的特殊性质. 相似文献
19.
Unconstrained and constrained global optimization of polynomial functions in one variable 总被引:1,自引:0,他引:1
In Floudas and Visweswaran (1990), a new global optimization algorithm (GOP) was proposed for solving constrained nonconvex problems involving quadratic and polynomial functions in the objective function and/or constraints. In this paper, the application of this algorithm to the special case of polynomial functions of one variable is discussed. The special nature of polynomial functions enables considerable simplification of the GOP algorithm. The primal problem is shown to reduce to a simple function evaluation, while the relaxed dual problem is equivalent to the simultaneous solution of two linear equations in two variables. In addition, the one-to-one correspondence between the x and y variables in the problem enables the iterative improvement of the bounds used in the relaxed dual problem. The simplified approach is illustrated through a simple example that shows the significant improvement in the underestimating function obtained from the application of the modified algorithm. The application of the algorithm to several unconstrained and constrained polynomial function problems is demonstrated. 相似文献