共查询到20条相似文献,搜索用时 671 毫秒
1.
Tadeusz Antczak 《Journal of Global Optimization》2009,43(1):111-140
This paper represents the second part of a study concerning the so-called G-multiobjective programming. A new approach to duality in differentiable vector optimization problems is presented. The techniques
used are based on the results established in the paper: On G-invex multiobjective programming. Part I. Optimality by T.Antczak. In this work, we use a generalization of convexity, namely G-invexity, to prove new duality results for nonlinear differentiable multiobjective programming problems. For such vector
optimization problems, a number of new vector duality problems is introduced. The so-called G-Mond–Weir, G-Wolfe and G-mixed dual vector problems to the primal one are defined. Furthermore, various so-called G-duality theorems are proved between the considered differentiable multiobjective programming problem and its nonconvex vector
G-dual problems. Some previous duality results for differentiable multiobjective programming problems turn out to be special
cases of the results described in the paper. 相似文献
2.
A New Multiobjective Dynamic Routing Method for Multiservice Networks: Modelling and Performance 总被引:1,自引:0,他引:1
There are potential advantages in formulating the routing problems in modern multiservice networks as multiple objective problems. This paper presents a novel hierarchical bi-level multiobjective dynamic routing model for multiservice networks. It is based on a bi-objective shortest path algorithm, with dynamically adapted soft-constraints, to compute alternative paths for each node pair and on a heuristic to synchronously select alternative routing plans for the network in a dynamic alternative routing context. It is a routing method which periodically changes alternative paths as a function of periodic updates of certain QoS related parameters obtained from real-time measurements. The performance of the proposed routing method is compared with two reference dynamic routing methods namely RTNR and DAR by means of a discrete-event simulator.A previous short version of this work was presented at INOC’03 (International Network Optimisation Conference). Work partially supported by programme POSI of the III EC programme cosponsored by FEDER and national funds. 相似文献
3.
Altannar Chinchuluun Dehui Yuan Panos M. Pardalos 《Annals of Operations Research》2007,154(1):133-147
In this paper, we consider nondifferentiable multiobjective fractional programming problems. A concept of generalized convexity,
which is called (C,α,ρ,d)-convexity, is first discussed. Based on this generalized convexity, we obtain efficiency conditions for multiobjective fractional
programming (MFP). Furthermore, we establish duality results for three types of dual problems of (MFP) and present the corresponding
duality theorems. 相似文献
4.
We investigate one stage stochastic multiobjective optimization problems where the objectives are the expected values of random
functions. Assuming that the closed form of the expected values is difficult to obtain, we apply the well known Sample Average
Approximation (SAA) method to solve it. We propose a smoothing infinity norm scalarization approach to solve the SAA problem
and analyse the convergence of efficient solution of the SAA problem to the original problem as sample sizes increase. Under
some moderate conditions, we show that, with probability approaching one exponentially fast with the increase of sample size,
an ϵ-optimal solution to the SAA problem becomes an ϵ-optimal solution to its true counterpart. Moreover, under second order growth conditions, we show that an efficient point
of the smoothed problem approximates an efficient solution of the true problem at a linear rate. Finally, we describe some
numerical experiments on some stochastic multiobjective optimization problems and report preliminary results. 相似文献
5.
Recently Hachimi and Aghezzaf introduced the notion of (F,α,ρ,d)-type I functions, a new class of functions that unifies several concepts of generalized type I functions. Here, we extend
the concepts of (F,α,ρ,d)-type I and generalized (F,α,ρ, d)-type I functions to the continuous case and we use these concepts to establish various sufficient optimality conditions
and mixed duality results for multiobjective variational problems. Our results apparently generalize a fairly large number
of sufficient optimality conditions and duality results previously obtained for multiobjective variational problems. 相似文献
6.
X. J. Long 《Journal of Optimization Theory and Applications》2011,148(1):197-208
The purpose of this paper is to consider a class of nondifferentiable multiobjective fractional programming problems in which
every component of the objective function contains a term involving the support function of a compact convex set. Based on
the (C,α,ρ,d)-convexity, sufficient optimality conditions and duality results for weakly efficient solutions of the nondifferentiable
multiobjective fractional programming problem are established. The results extend and improve the corresponding results in
the literature. 相似文献
7.
E. Miglierina 《Rendiconti del Circolo Matematico di Palermo》2001,50(1):153-164
A characterization of weakly efficient, efficient and properly efficient solutions of multiobjective optimization problems
is given in terms of a scalar optimization problem by using a special “distance” function. The concept of the well-posedness
for this special scalar problem is then linked with the properly efficient solutions of the multiobjective problem. 相似文献
8.
9.
Tadeusz Antczak 《Journal of Global Optimization》2009,43(1):97-109
In this paper, a generalization of convexity, namely G-invexity, is considered in the case of nonlinear multiobjective programming problems where the functions constituting vector
optimization problems are differentiable. The modified Karush-Kuhn-Tucker necessary optimality conditions for a certain class
of multiobjective programming problems are established. To prove this result, the Kuhn-Tucker constraint qualification and
the definition of the Bouligand tangent cone for a set are used. The assumptions on (weak) Pareto optimal solutions are relaxed
by means of vector-valued G-invex functions. 相似文献
10.
The concept of a K-gradient, introduced in Ref. 1 in order to generalize the concept of a derived convex cone defined by Hestenes, is extended to weak multiobjective optimization problems including not only a state variable, but also a control variable. The new concept is employed to state multiplier rules for the local solutions of such dynamic multiobjective optimization problems. An application of these multiplier rules to the local solutions of an abstract multiobjective optimal control problem yields general necessary optimality conditions that can be used to derive concrete maximum principles for multiobjective optimal control problems, e.g., problems described by integral equations with additional functional constraints. 相似文献
11.
Arnaud Liefooghe 《4OR: A Quarterly Journal of Operations Research》2011,9(2):219-222
This is a summary of the author’s PhD thesis supervised by Laetitia Jourdan and El-Ghazali Talbi and defended on 8 December
2009 at the Université Lille 1. The thesis is written in French and is available from . This work deals with the design, implementation and experimental analysis of metaheuristics for solving multiobjective optimisation
problems, with a particular interest on hard and large combinatorial problems from the field of logistics. After focusing
on a unified view of multiobjective metaheuristics, we propose new cooperative, adaptive and parallel approaches. The performance
of these methods are experimented on a scheduling and a routing problem involving two or three objective functions. We finally
discuss how to adapt such metaheuristics during the search process in order to handle uncertainty that may occur from many
different sources. 相似文献
12.
Erin K. Doolittle Hervé L. M. Kerivin Margaret M. Wiecek 《Annals of Operations Research》2018,271(2):487-525
Robust optimization addressing decision making under uncertainty has been very well developed for problems with a single objective function and applied to areas of human activity such as portfolio selection, investment decisions, signal processing, and telecommunication-network planning. As these decision problems typically have several decisions or goals, we extend robust single objective optimization to the multiobjective case. The column-wise uncertainty model can be carried over to the multiobjective case without any additional assumptions. For the row-wise uncertainty model, we show under additional assumptions that robust efficient solutions are efficient to specific instance problems and can be found as the efficient solutions of another deterministic problem. Being motivated by the fact that Internet traffic must be maintained in a reliable yet affordable manner in situations of complex and dynamic usage, we apply the row-wise model to an intradomain multiobjective routing problem with polyhedral traffic uncertainty. We consider traditional objective functions corresponding to link utilizations and implement the biobjective case using the parametric simplex algorithm to compute robust efficient routings. We also present computational results for the Abilene network and analyze their meaning in the context of the application. 相似文献
13.
Based upon Ben-Tal’s generalized algebraic operations, new classes of functions, namely (h,φ)-type-I, quasi (h,φ)-type-I, and pseudo (h,φ)-type-I, are defined for a multi-objective programming problem. Sufficient optimality conditions are obtained for a feasible
solution to be a Pareto efficient solution for this problem. Some duality results are established by utilizing the above defined
classes of functions, considering the concept of a Pareto efficient solution.
This research is supported by National Science Foundation of China under Grant No. 69972036. 相似文献
14.
S. Nobakhtian 《Journal of Optimization Theory and Applications》2006,130(2):361-367
In this paper, we consider a generalization of convexity for nonsmooth multiobjective programming problems. We obtain sufficient optimality conditions under generalized (Fρ)-convexity.This work was supported by Project 821134 and by the Center of Excellence for Mathematics, University of Isfahan, Isfahan, Iran.Communicated by F. Giannessi 相似文献
15.
A nonsmooth multiobjective optimization problem involving generalized (F, α, ρ, d)-type I function is considered. Karush–Kuhn–Tucker type necessary and sufficient optimality conditions are obtained for a
feasible point to be an efficient or properly efficient solution. Duality results are obtained for mixed type dual under the
aforesaid assumptions. 相似文献
16.
Douglas A. G. Vieira Ricardo H. C. Takahashi Rodney R. Saldanha 《Mathematical Programming》2012,131(1-2):131-161
This work presents an algorithm for multiobjective optimization that is structured as: (i) a descent direction is calculated, within the cone of descent and feasible directions, and (ii) a multiobjective line search is conducted over such direction, with a new multiobjective golden section segment partitioning scheme that directly finds line-constrained efficient points that dominate the current one. This multiobjective line search procedure exploits the structure of the line-constrained efficient set, presenting a faster compression rate of the search segment than single-objective golden section line search. The proposed multiobjective optimization algorithm converges to points that satisfy the Kuhn-Tucker first-order necessary conditions for efficiency (the Pareto-critical points). Numerical results on two antenna design problems support the conclusion that the proposed method can solve robustly difficult nonlinear multiobjective problems defined in terms of computationally expensive black-box objective functions. 相似文献
17.
对于线性型多目标半定规划问题,引进加权中心路径的概念,并利用单目标半定规划的中心路径法,提出了求解多目标半定规划问题的加权中心路径法,先得型对一个叔向量的有效解,然后在此基础上,提出了通过一次迭代得到对应一定范围内其他任意权向量的有效解的一步修正方法. 相似文献
18.
M. Arana-Jiménez A. Rufián-Lizana R. Osuna-Gómez G. Ruiz-Garzón 《Nonlinear Analysis: Theory, Methods & Applications》2008
In this paper, we establish characterizations for efficient solutions to multiobjective programming problems, which generalize the characterization of established results for optimal solutions to scalar programming problems. So, we prove that in order for Kuhn–Tucker points to be efficient solutions it is necessary and sufficient that the multiobjective problem functions belong to a new class of functions, which we introduce. Similarly, we obtain characterizations for efficient solutions by using Fritz–John optimality conditions. Some examples are proposed to illustrate these classes of functions and optimality results. We study the dual problem and establish weak, strong and converse duality results. 相似文献
19.
The effect of managing aircraft movements on the airport’s ground is an important tool that can alleviate the delays of flights,
specially in peak hours or congested situations. Although some strategic design decisions regarding aeronautical and safety
aspects have a main impact on the airport’s topology, there exists a number of other additional factors that must be evaluated
according to the on ground operations, i.e. previous to the taking-off or after landing. Among these factors one can consider
capacities at waiting points and directions of some corridors. These factors are related to the demand situation of a given
period and influence the aircraft’s routing on the ground or short term Taxi Planning problem (or TP-S). While the TP-S problem studies the aircraft routing and scheduling on the airport’s ground under a dynamic point of view, this paper presents
a Taxi Planning network design model (or TPND), attending to these additional factors of the airport’s topology and the conflicting movements of the aircraft on them with
the same modelling approach used in the TP-S problem. The TPND model is formulated as a binary multicommodity network flow problem with additional side constraints under a multiobjective
approach. The side constraints included are the classical limitations due to capacity and also as a distinctive approach,
constraints that restrict the interference of aircraft in order to decrease the intervention of human controllers during the
operations or increase their safety margins. The multiobjective approach adopted for the TPND model balances conflicting objectives: airport’s throughput, travel times, safety of operations and costs. In the paper computational
results are included on two test airports solving the TPND model by “Branch and Bound” showing the effect of the conflicting objectives in the design decisions.
Research supported under Research Project TRA-2005-09068-C03-01/MODAL from the “Ministerio de Educación y Ciencia”. 相似文献
20.
In this paper, a new class of second-order (F, α, ρ, d)-V-type I functions is introduced that generalizes the notion of (F, α, ρ, θ)-V-convex functions introduced by Zalmai (Computers Math. Appl. 2002; 43:1489–1520) and (F, α, ρ, p, d)-type I functions defined by Hachimi and Aghezzaf (Numer. Funct. Anal. Optim. 2004; 25:725–736). Based on these functions, weak, strong, and strict converse duality theorems are derived for Wolfe and Mond–Weir type multiobjective dual programs in order to relate the efficient and weak efficient solutions of primal and dual problems. 相似文献