scholarly journals Exact Penalization and Necessary Optimality Conditions for Multiobjective Optimization Problems with Equilibrium Constraints

2014 ◽  
Vol 2014 ◽  
pp. 1-13
Author(s):  
Shengkun Zhu ◽  
Shengjie Li
Keyword(s):  
Multiobjective Optimization ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Necessary Optimality Conditions ◽  
Inequality Constraints ◽  
Multiobjective Optimization Problem ◽  
Equilibrium Constraints ◽  
Exact Penalization ◽  
Multiobjective Optimization Problems ◽  
Weak Vector

A calmness condition for a general multiobjective optimization problem with equilibrium constraints is proposed. Some exact penalization properties for two classes of multiobjective penalty problems are established and shown to be equivalent to the calmness condition. Subsequently, a Mordukhovich stationary necessary optimality condition based on the exact penalization results is obtained. Moreover, some applications to a multiobjective optimization problem with complementarity constraints and a multiobjective optimization problem with weak vector variational inequality constraints are given.

scholarly journals MultiObjective Genetic Modified Algorithm (MOGMA)

2012 ◽  
Vol 12 (2) ◽  
pp. 23-33
Author(s):  
Elica Vandeva
Keyword(s):  
Genetic Algorithms ◽  
Multiobjective Optimization ◽  
Pareto Front ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Multiobjective Optimization Problem ◽  
Multiobjective Optimization Problems ◽  
Modified Algorithm

Abstract Multiobjective optimization based on genetic algorithms and Pareto based approaches in solving multiobjective optimization problems is discussed in the paper. A Pareto based fitness assignment is used − non-dominated ranking and movement of a population towards the Pareto front in a multiobjective optimization problem. A MultiObjective Genetic Modified Algorithm (MOGMA) is proposed, which is an improvement of the existing algorithm.

scholarly journals Nonemptiness and Compactness of Solutions Set for Nondifferentiable Multiobjective Optimization Problems

2011 ◽  
Vol 2011 ◽  
pp. 1-16 ◽  
Author(s):  
Xin-kun Wu ◽  
Jia-wei Chen ◽  
Yun-zhi Zou
Keyword(s):  
Fixed Point ◽  
Multiobjective Optimization ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Efficient Solutions ◽  
Multiobjective Optimization Problem ◽  
Weakly Efficient Solutions ◽  
Set Constraints ◽  
Multiobjective Optimization Problems ◽  
Problems And Solutions

A nondifferentiable multiobjective optimization problem with nonempty set constraints is considered, and the equivalence of weakly efficient solutions, the critical points for the nondifferentiable multiobjective optimization problems, and solutions for vector variational-like inequalities is established under some suitable conditions. Nonemptiness and compactness of the solutions set for the nondifferentiable multiobjective optimization problems are proved by using the FKKM theorem and a fixed-point theorem.

scholarly journals Necessary optimality conditions for a fractional multiobjective optimization problem

2020 ◽  
Author(s):  
Nazih Abderrazzak Gadhi ◽  
khadija hamdaoui ◽  
mohammed El idrissi ◽  
Fatima zahra Rahou
Keyword(s):  
Multiobjective Optimization ◽  
Optimality Conditions ◽  
Optimization Problem ◽  
Constraint Qualification ◽  
Optimization Problems ◽  
Necessary Optimality Conditions ◽  
Multiobjective Optimization Problem ◽  
Support Functions

In this paper, we are concerned with a fractional multiobjective optimization problem (P). Using support functions together with a generalized Guignard constraint qualification, we give necessary optimality conditions in terms of convexificators and the Karush-Kuhn-Tucker multipliers. Several intermediate optimization problems have been introduced to help us in our investigation.

scholarly journals A Novel Hybrid Algorithm for Solving Multiobjective Optimization Problems with Engineering Applications

2018 ◽  
Vol 2018 ◽  
pp. 1-15 ◽  
Author(s):  
Lulu Fan ◽  
Tatsuo Yoshino ◽  
Tao Xu ◽  
Ye Lin ◽  
Huan Liu
Keyword(s):  
Multiobjective Optimization ◽  
Hybrid Algorithm ◽  
Optimization Problems ◽  
Inequality Constraints ◽  
Primary Energy ◽  
Engineering Practice ◽  
Optimization Strategy ◽  
Frontal Collision ◽  
Multiobjective Optimization Problems ◽  
Crashworthiness Design

An effective hybrid algorithm is proposed for solving multiobjective optimization engineering problems with inequality constraints. The weighted sum technique and BFGS quasi-Newton’s method are combined to determine a descent search direction for solving multiobjective optimization problems. To improve the computational efficiency and maintain rapid convergence, a cautious BFGS iterative format is utilized to approximate the Hessian matrices of the objective functions instead of evaluating them exactly. The effectiveness of the proposed algorithm is demonstrated through a comparison study, which is based on numerical examples. Meanwhile, we propose an effective multiobjective optimization strategy based on the algorithm in conjunction with the surrogate model method. This proposed strategy has been applied to the crashworthiness design of the primary energy absorption device’s crash box structure and front rail under low-speed frontal collision. The optimal results demonstrate that the proposed methodology is promising in solving multiobjective optimization problems in engineering practice.

A Dimensional Diversity Based Hybrid Multiobjective Evolutionary Algorithm for Optimization Problem

2016 ◽  
Vol 30 (07) ◽  
pp. 1659020 ◽  
Author(s):  
Peng Wang ◽  
Changsheng Zhang ◽  
Bin Zhang ◽  
Tingting Liu ◽  
Jiaxuan Wu
Keyword(s):  
Multiobjective Optimization ◽  
Evolutionary Algorithm ◽  
Optimization Problem ◽  
Optimization Problems ◽  
State Of The Art ◽  
Experimental Results ◽  
Selection Scheme ◽  
Genetic Operator ◽  
Hybrid Evolutionary Algorithm ◽  
Multiobjective Optimization Problems

Multiobjective density driven evolutionary algorithm (MODdEA) has been quite successful in solving multiobjective optimization problems (MOPs). To further improve its performance and address its deficiencies, this paper proposes a hybrid evolutionary algorithm based on dimensional diversity (DD) and firework explosion (FE). DD is defined to reflect the diversity degree of population dimension. Based on DD, a selection scheme is designed to balance diversity and convergence. A hybrid variation based on FE and genetic operator is designed to facilitate diversity of population. The proposed algorithm is tested on 14 tests problems with diverse characteristics and compared with three state-of-the-art designs. Experimental results show that the proposed design is better or at par with the chosen state-of-the-art algorithms for multiobjective optimization.

scholarly journals Synthesis of Phase-Only Reconfigurable Linear Arrays Using Multiobjective Invasive Weed Optimization Based on Decomposition

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Yan Liu ◽  
Yong-Chang Jiao ◽  
Ya-Ming Zhang ◽  
Yan-Yan Tan
Keyword(s):  
Multiobjective Optimization ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Amplitude Distribution ◽  
Invasive Weed Optimization ◽  
Invasive Weed ◽  
Linear Arrays ◽  
Reconfigurable Array ◽  
Multiobjective Optimization Problems ◽  
Antenna Array Synthesis

Synthesis of phase-only reconfigurable array aims at finding a common amplitude distribution and different phase distributions for the array to form different patterns. In this paper, the synthesis problem is formulated as a multiobjective optimization problem and solved by a new proposed algorithm MOEA/D-IWO. First, novel strategies are introduced in invasive weed optimization (IWO) to make original IWO fit for solving multiobjective optimization problems; then, the modified IWO is integrated into the framework of the recently well proved competitive multiobjective optimization algorithm MOEA/D to form a new competitive MOEA/D-IWO algorithm. At last, two sets of experiments are carried out to illustrate the effectiveness of MOEA/D-IWO. In addition, MOEA/D-IWO is compared with MOEA/D-DE, a new version of MOEA/D. The comparing results show the superiority of MOEA/D-IWO and indicate its potential for solving the antenna array synthesis problems.

scholarly journals Approximate proper efficiency for multiobjective optimization problems

Filomat ◽  
2019 ◽  
Vol 33 (18) ◽  
pp. 6091-6101
Author(s):  
Ying Gao ◽  
Zhihui Xu
Keyword(s):  
Multiobjective Optimization ◽  
Optimization Problem ◽  
Normal Cone ◽  
Generalized Convexity ◽  
Optimization Problems ◽  
Proper Efficiency ◽  
Proximal Normal Cone ◽  
Radiant Set ◽  
Benson Proper Efficiency ◽  
Multiobjective Optimization Problems

This paper is devoted to the study of a new kind of approximate proper efficiency in terms of proximal normal cone and co-radiant set for multiobjective optimization problem. We derive some properties of the new approximate proper efficiency and discuss the relations with the existing approximate concepts, such as approximate efficiency and approximate Benson proper efficiency. At last, we study the linear scalarizations for the new approximate proper efficiency under the generalized convexity assumption and give some examples to illustrate the main results.

scholarly journals A novel approach for the solution of multiobjective optimization problem using hesitant fuzzy aggregation operator

2022 ◽  
Author(s):  
Firoz Ahmad ◽  
Ahmad Yusuf Adhami ◽  
Boby John ◽  
Amit Reza
Keyword(s):  
Decision Making ◽  
Multiobjective Optimization ◽  
Decision Maker ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Aggregation Operator ◽  
Decision Making Process ◽  
Mathematical Framework ◽  
Multiobjective Optimization Problem ◽  
Fuzzy Aggregation

Many decision-making problems can solve successfully by traditional optimization methods with a well-defined configuration.  The formulation of such optimization problems depends on crisply objective functions and a specific system of constraints.  Nevertheless, in reality, in any decision-making process, it is often observed that due to some doubt or hesitation, it is pretty tricky for decision-maker(s) to specify the precise/crisp value of any parameters and compelled to take opinions from different experts which leads towards a set of conflicting values regarding satisfaction level of decision-maker(s). Therefore the real decision-making problem cannot always be deterministic. Various types of uncertainties in parameters make it fuzzy.  This paper presents a practical mathematical framework to reflect the reality involved in any decision-making process. The proposed method has taken advantage of the hesitant fuzzy aggregation operator and presents a particular way to emerge in a decision-making process. For this purpose,  we have discussed a couple of different hesitant fuzzy aggregation operators and developed linear and hyperbolic membership functions under hesitant fuzziness, which contains the concept of hesitant degrees for different objectives.  Finally, an example based on a multiobjective optimization problem is presented to illustrate the validity and applicability of our proposed models.

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