Study on Multiobjective Programming Problem under Bifuzzy Environment

2011 ◽  
Vol 204-210 ◽  
pp. 502-507
Author(s):  
Ming Fa Zheng ◽  
Bing Jie Li ◽  
Guang Xing Kou
Keyword(s):  
Decision Making ◽  
Programming Problem ◽  
Solution Method ◽  
Multiobjective Programming ◽  
Expected Value ◽  
Decision Making Process ◽  
Multiobjective Problem ◽  
Expected Value Model ◽  
Multiobjective Programming Problem ◽  
Value Model

In this paper, based on bifuzzy theory, we have studied the multiobjective programming problem under bifuzzy environment, and presented the expected-value model which is a deterministic multiobjective problem. To the expected value model, the concepts of non-inferior solution are defined, and their relations are also discussed. According to practical decision-making process, a solution method, called the method of main objective function, has been studied, whose results can facilitate us to design algorithms to solve the bifuzzy multiobjective programming problem.

scholarly journals A New Hybrid Intelligent Algorithm for Fuzzy Multiobjective Programming Problem Based on Credibility Theory

2014 ◽  
Vol 2014 ◽  
pp. 1-11
Author(s):  
Zu-Tong Wang ◽  
Jian-Sheng Guo ◽  
Ming-Fa Zheng ◽  
Ying Wang
Keyword(s):  
Programming Problem ◽  
Multiobjective Programming ◽  
Expected Value ◽  
Credibility Theory ◽  
Support Vector ◽  
Intelligent Algorithm ◽  
Hybrid Intelligent Algorithm ◽  
Expected Value Model ◽  
Multiobjective Programming Problem ◽  
Value Model

Based on the credibility theory, this paper is devoted to the fuzzy multiobjective programming problem. Firstly, the expected-value model of fuzzy multiobjective programming problem is provided based on credibility theory; then two new approaches for obtaining efficient solutions are proposed on the basis of the expected-value model, whose validity has been proven. For solving the fuzzy MOP problem efficiently, Latin hypercube sampling, fuzzy simulation, support vector machine, and artificial bee colony algorithm are integrated to build a hybrid intelligent algorithm. An application case study on availability allocation optimization problem in repairable parallel-series system design is documented. The results suggest that the proposed method has excellent consistency and efficiency in solving fuzzy multiobjective programming problem and is particularly useful for expensive systems.

Multiobjective Programming

2014 ◽  
pp. 1585-1604
Author(s):  
Minghe Sun
Keyword(s):  
Programming Problem ◽  
Multiobjective Programming ◽  
Optimization Problems ◽  
Optimal Solution ◽  
Objective Functions ◽  
Solution Quality ◽  
Solution Methods ◽  
Multiobjective Programming Problem ◽  
Feasible Solutions ◽  
Multiobjective Programming Problems

Optimization problems with multiple criteria measuring solution quality can be modeled as multiobjective programming problems. Because the objective functions are usually in conflict, there is not a single feasible solution that can optimize all objective functions simultaneously. An optimal solution is one that is most preferred by the decision maker (DM) among all feasible solutions. An optimal solution must be nondominated but a multiobjective programming problem may have, possibly infinitely, many nondominated solutions. Therefore, tradeoffs must be made in searching for an optimal solution. Hence, the DM's preference information is elicited and used when a multiobjective programming problem is solved. The model, concepts and definitions of multiobjective programming are presented and solution methods are briefly discussed. Examples are used to demonstrate the concepts and solution methods. Graphics are used in these examples to facilitate understanding.

AN η-APPROXIMATION APPROACH IN NONLINEAR VECTOR OPTIMIZATION WITH UNIVEX FUNCTIONS

2006 ◽  
Vol 23 (04) ◽  
pp. 525-542 ◽  
Author(s):  
TADEUSZ ANTCZAK
Keyword(s):  
Programming Problem ◽  
Vector Optimization ◽  
Optimization Problem ◽  
Multiobjective Programming ◽  
Sufficient Conditions ◽  
Vector Optimization Problem ◽  
Approximation Approach ◽  
Nonlinear Vector Optimization ◽  
Multiobjective Programming Problem ◽  
Nonlinear Vector

In this paper, the so-called η-approximation approach is used to obtain the sufficient conditions for a nonlinear multiobjective programming problem with univex functions with respect to the same function η. In this method, an equivalent η-approximated vector optimization problem is constructed by a modification of both the objective and the constraint functions in the original multiobjective programming problem at the given feasible point. Moreover, to find the optimal solutions of the original multiobjective problem, it sufficies to solve its associated η-approximated vector optimization problem. Finally, the description of the η-approximation algorithm for solving a nonlinear multiobjective programming problem involving univex functions is presented.

scholarly journals An Improved Particle Swarm Optimization for Solving Bilevel Multiobjective Programming Problem

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
Tao Zhang ◽  
Tiesong Hu ◽  
Yue Zheng ◽  
Xuning Guo
Keyword(s):  
Particle Swarm Optimization ◽  
Programming Problem ◽  
Multiobjective Programming ◽  
Particle Swarm ◽  
Pareto Optimal ◽  
Pareto Optimal Solutions ◽  
Optimal Solutions ◽  
Swarm Optimization ◽  
Improved Particle Swarm Optimization ◽  
Multiobjective Programming Problem

An improved particle swarm optimization (PSO) algorithm is proposed for solving bilevel multiobjective programming problem (BLMPP). For such problems, the proposed algorithm directly simulates the decision process of bilevel programming, which is different from most traditional algorithms designed for specific versions or based on specific assumptions. The BLMPP is transformed to solve multiobjective optimization problems in the upper level and the lower level interactively by an improved PSO. And a set of approximate Pareto optimal solutions for BLMPP is obtained using the elite strategy. This interactive procedure is repeated until the accurate Pareto optimal solutions of the original problem are found. Finally, some numerical examples are given to illustrate the feasibility of the proposed algorithm.

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