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1.
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
2.
G. J. Zalmai 《Journal of Optimization Theory and Applications》1996,90(2):435-456
We establish necessary and sufficient conditions for properly efficient solutions of a class of nonsmooth nonconvex optimal control problems with multiple fractional objective functions, linear dynamics, and nonlinear inequality constraints on both the state and control variables. Subsequently, we utilize these proper efficiency criteria to construct two multiobjective dual problems and prove appropriate duality theorems. Also, we specialize and discuss these results for a particular case of our principal problem which contains square roots of positivesemidefinite quadratic forms. As special cases of the main proper efficiency and duality results, this paper also contains similar results for control problems with multiple, fractional, and ordinary objective functions. 相似文献
3.
In this paper, a graphical characterization, in the decision space, of the properly efficient solutions of a convex multiobjective
problem is derived. This characterization takes into account the relative position of the gradients of the objective functions
and the active constraints at the given feasible solution. The unconstrained case with two objective functions and with any
number of functions and the general constrained case are studied separately. In some cases, these results can provide a visualization
of the efficient set, for problems with two or three variables. Besides, a proper efficiency test for general convex multiobjective
problems is derived, which consists of solving a single linear optimization problem. 相似文献
4.
Tradeoff directions in multiobjective optimization problems 总被引:2,自引:0,他引:2
Multiobjective optimization problems (MOP) typically have conflicting objectives wherein a gain in one objective is at the
expense of another. Tradeoff directions, which measure the change in some objectives relative to changes in others, provide
important information as to the best direction of improvement from the current solution. In this paper we present a general
definition of tradeoffs as a cone of directions and provide a general method of calculating tradeoffs at every Pareto optimal
point of a convex MOP. This extends current definitions of tradeoffs which assume certain conditions on the feasible set and
the objective functions. Two comprehensive numerical examples are provided to illustrate the tradeoff directions and the methods
used to calculate them. 相似文献
5.
Radu Ioan Boţ Sorin-Mihai Grad Gert Wanka 《Mathematical Methods of Operations Research》2007,65(3):417-444
A general duality framework in convex multiobjective optimization is established using the scalarization with K-strongly increasing functions and the conjugate duality for composed convex cone-constrained optimization problems. Other
scalarizations used in the literature arise as particular cases and the general duality is specialized for some of them, namely
linear scalarization, maximum (-linear) scalarization, set scalarization, (semi)norm scalarization and quadratic scalarization.
相似文献
6.
MAJOR-EFFICIENT SOLUTIONS AND WEAKLY MAJOR-EFFICIENT SOLUTIONS OF MULTIOBJECTIVE PROGRAMMING 总被引:10,自引:0,他引:10
HU YUDA 《高校应用数学学报(英文版)》1994,9(1):85-94
MAJOR-EFFICIENTSOLUTIONSANDWEAKLYMAJOR-EFFICIENTSOLUTIONSOFMULTIOBJECTIVEPROGRAMMING¥HUYUDA(Dept.ofAppl.Math.,ShanghaiJiaoTon... 相似文献
7.
Recent literatures have suggested that multiobjective evolutionary algorithms (MOEAs) can serve as a more exploratory and effective tool in solving multiobjective optimization problems (MOPs) than traditional optimizers. In order to contain a good approximation of Pareto optimal set with wide diversity associated with the inherent characters and variability of MOPs, this paper proposes a new evolutionary approach—(μ, λ) multiobjective evolution strategy ((μ, λ)-MOES). Following the highlight of how to balance proximity and diversity of individuals in exploration and exploitation stages respectively, some cooperative techniques are devised. Firstly, a novel combinatorial exploration operator that develops strong points from Gaussian mutation of proximity exploration and from Cauchy mutation of diversity preservation is elaborately designed. Additionally, we employ a complete nondominance selection so as to ensure maximal pressure for proximity exploitation while a fitness assignment determined by dominance and population diversity information is simultaneous used to ensure maximal diversity preservation. Moreover, a dynamic external archive is introduced to store elitist individuals as well as relatively better individuals and exchange information with the current population when performing archive increase scheme and archive decrease scheme. By graphical presentation and examination of selected performance metrics on three prominent benchmark test functions, (μ, λ)-MOES is found to outperform SPEA-II to some extent in terms of finding a near-optimal, well-extended and uniformly diversified Pareto optimal front. 相似文献
8.
A fast Pareto genetic algorithm approach for solving expensive multiobjective optimization problems 总被引:1,自引:0,他引:1
We present a new multiobjective evolutionary algorithm (MOEA), called fast Pareto genetic algorithm (FastPGA), for the simultaneous
optimization of multiple objectives where each solution evaluation is computationally- and/or financially-expensive. This
is often the case when there are time or resource constraints involved in finding a solution. FastPGA utilizes a new ranking
strategy that utilizes more information about Pareto dominance among solutions and niching relations. New genetic operators
are employed to enhance the proposed algorithm’s performance in terms of convergence behavior and computational effort as
rapid convergence is of utmost concern and highly desired when solving expensive multiobjective optimization problems (MOPs).
Computational results for a number of test problems indicate that FastPGA is a promising approach. FastPGA yields similar
performance to that of the improved nondominated sorting genetic algorithm (NSGA-II), a widely-accepted benchmark in the MOEA
research community. However, FastPGA outperforms NSGA-II when only a small number of solution evaluations are permitted, as
would be the case when solving expensive MOPs. 相似文献
9.
In this paper, we introduce a vector-valued Tikhonov-type regularization algorithm for an extended-valued multiobjective optimization problem. Under some mild conditions, we prove that any sequence generated by this algorithm converges to a weak Pareto optimal solution of the multiobjective optimization problem. Our results improve and generalize some known results. 相似文献
10.
Explicit gradient information in multiobjective optimization 总被引:1,自引:0,他引:1
This work presents an algorithm that converges to points that satisfy a first-order necessary condition of weakly Pareto solutions of multiobjective optimization problems. Hints on how to include second-order information are given. Preliminary numerical results are encouraging. 相似文献
11.
Ivan Ginchev Angelo Guerraggio 《Journal of Mathematical Analysis and Applications》2007,328(2):780-788
We consider the constrained vector optimization problem minCf(x), x∈A, where X and Y are normed spaces, A⊂X0⊂X are given sets, C⊂Y, C≠Y, is a closed convex cone, and is a given function. We recall the notion of a properly efficient point (p-minimizer) for the considered problem and in terms of the so-called oriented distance we define also the notion of a properly efficient point of order n (p-minimizers of order n). We show that the p-minimizers of higher order generalize the usual notion of a properly efficient point. The main result is the characterization of the p-minimizers of higher order in terms of “trade-offs.” In such a way we generalize the result of A.M. Geoffrion [A.M. Geoffrion, Proper efficiency and the theory of vector maximization, J. Math. Anal. Appl. 22 (3) (1968) 618-630] in two directions, namely for properly efficient points of higher order in infinite dimensional spaces, and for arbitrary closed convex ordering cones. 相似文献
12.
Davinder Bhatia 《Journal of Mathematical Analysis and Applications》2003,287(2):415-429
A class of BF-type I functions and its extensions are introduced in the continuous case, an example is presented in support. Utilizing these new concepts, sufficient optimality conditions and duality results are presented for multiobjective variational problems involving arbitrary norms. 相似文献
13.
Mario Villalobos-Arias Carlos A. Coello Coello Onésimo Hernández-Lerma 《Mathematical Methods of Operations Research》2006,64(2):353-362
In this paper we consider a simulated annealing algorithm for multiobjective optimization problems. With a suitable choice of the acceptance probabilities, the algorithm is shown to converge asymptotically, that is, the Markov chain that describes the algorithm converges with probability one to the Pareto optimal set. 相似文献
14.
Constraint qualifications in multiobjective optimization problems: Differentiable case 总被引:7,自引:0,他引:7
T. Maeda 《Journal of Optimization Theory and Applications》1994,80(3):483-500
In this paper, we are concerned with a multiobjective optimization problem with inequality constraints. We introduce a constraint qualification and derive the Kuhn-Tucker type necessary conditions for efficiency. Moreover, we give conditions which ensure the constraint qualification.This work was done while the author was visiting the University of California, Berkeley, California. 相似文献
15.
A survey of recent developments in multiobjective optimization 总被引:2,自引:0,他引:2
Multiobjective Optimization (MO) has many applications in such fields as the Internet, finance, biomedicine, management science,
game theory and engineering. However, solving MO problems is not an easy task. Searching for all Pareto optimal solutions
is expensive and a time consuming process because there are usually exponentially large (or infinite) Pareto optimal solutions.
Even for simple problems determining whether a point belongs to the Pareto set is
-hard. In this paper, we discuss recent developments in MO. These include optimality conditions, applications, global optimization
techniques, the new concept of epsilon Pareto optimal solution, and heuristics. 相似文献
16.
Manuel Arana-Jiménez Gabriel Ruiz-Garzón 《Nonlinear Analysis: Theory, Methods & Applications》2010,73(6):1792-1801
In this paper, we introduce new pseudoinvexity conditions on functionals involved in a multiobjective control problem, called W-KT-pseudoinvexity and W-FJ-pseudoinvexity. We prove that all Kuhn-Tucker or Fritz-John points are weakly efficient solutions if and only if these conditions are fulfilled. We relate weakly efficient solutions to optimal solutions of weighting control problems. We generalize recently obtained optimality results of known mathematical programming problems and control problems. We illustrate these results with an example. 相似文献
17.
Using the notion of invexity, we give sufficient conditions of optimality for properly efficient solutions of a vector infinite
programming problem and show that the set of properly efficient solutions coincides with the set of optimal solutions of a
related scalar problem. 相似文献
18.
A new approach, based on indifference band, for analyzing problems with multiple objectives is described. The relations of this approach to some previous results are given. Methods for generating nondominated solutions are supplied. 相似文献
19.
This paper introduces a new class of non-convex vector functions strictly larger than that of P-quasiconvexity, with P m being the underlying ordering cone, called semistrictly ( m\ –int P)-quasiconvex functions. This notion allows us to unify various results on existence of weakly efficient (weakly Pareto) optima. By imposing a coercivity condition we establish also the compactness of the set of weakly Pareto solutions. In addition, we provide various characterizations for the non-emptiness, convexity and compactness of the solution set for a subclass of quasiconvex vector optimization problems on the real-line. Finally, it is also introduced the notion of explicit ( m\ –int P)-quasiconvexity (equivalently explicit (int P)-quasiconvexity) which plays the role of explicit quasiconvexity (quasiconvexity and semistrict quasiconvexity) of real-valued functions.Acknowldegements.The author wishes to thank both referees for their careful reading of the paper, their comments, remarks, helped to improve the presentation of some results. One of the referee provided the references [5, 6] and indirectly [20]. 相似文献
20.
《Optimization》2012,61(4):333-347
Necessary and sufficient conditions are established for properly efficient solutions of a class of nonsmooth nonconvex variational problems with multiple fractional objective functions and nonlinear inequality constraints. Based on these proper efficiency criteria. two multiobjective dual problems are constructed and appropriate duality theorems are proved. These proper efficiency and duality results also contain as special cases similar rcsults fer constrained variational problems with multiplei fractional. and conventional objective functions, which are particular cases of the main variational problem considered in this paper 相似文献