scholarly journals A Better Approach for Solving a Fuzzy Multiobjective Programming Problem by Level Sets

2021 ◽  
Author(s):  
Beatriz Hernández-Jiménez ◽  
Gabriel Ruiz-Garzón ◽  
Antonio Beato-Moreno ◽  
Rafaela Osuna-Gómez
Keyword(s):  
Programming Problem ◽  
Level Sets ◽  
Multiobjective Programming ◽  
Optimal Solutions ◽  
Multiobjective Programming Problem ◽  
Pareto Efficient

In this paper we deal with the resolution of a fuzzy multiobjective programming problem using the level sets optimization. We compare it to other optimization strategies studied until now and we propose an algorithm to identify possible Pareto efficient optimal solutions.

scholarly journals A Better Approach for Solving a Fuzzy Multiobjective Programming Problem by Level Sets

Mathematics ◽  
2021 ◽  
Vol 9 (9) ◽  
pp. 992
Author(s):  
Beatriz Hernández-Jiménez ◽  
Gabriel Ruiz-Garzón ◽  
Antonio Beato-Moreno ◽  
Rafaela Osuna-Gómez
Keyword(s):  
Programming Problem ◽  
Level Sets ◽  
Multiobjective Programming ◽  
Optimal Solutions ◽  
Multiobjective Programming Problem ◽  
Pareto Efficient

In this paper, we deal with the resolution of a fuzzy multiobjective programming problem using the level sets optimization. We compare it to other optimization strategies studied until now and we propose an algorithm to identify possible Pareto efficient optimal solutions.

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.

The Application of Stochastic Order to Stochastic Multiobjective Programming Problems

2014 ◽  
Vol 505-506 ◽  
pp. 524-527
Author(s):  
Ming Fa Zheng ◽  
Qi Hang He ◽  
Zu Tong Wang ◽  
Dong Qing Su
Keyword(s):  
Programming Problem ◽  
Theoretical Basis ◽  
Efficient Solution ◽  
Multiobjective Programming ◽  
Stochastic Order ◽  
Stochastic Approach ◽  
Stochastic Problems ◽  
Multiobjective Programming Problem ◽  
Pareto Efficient ◽  
Multiobjective Programming Problems

This paper is devoted to the application of stochastic order to the with stochastic multiobjective programming problem. A new method, called stochastic approach, is originally presented based on stochastic order. The partial Pareto efficient solution is defined first, and then several types of stochastic order from the viewpoint of practical problems are proposed. The results obtained can provide theoretical basis for dealing with the stochastic problems in field of civil engineering and transportation.

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 Multiobjective duality with ρ−(η,θ)-invexity

2005 ◽  
Vol 2005 (2) ◽  
pp. 175-180 ◽  
Author(s):  
C. Nahak ◽  
S. Nanda
Keyword(s):  
Programming Problem ◽  
Multiobjective Programming ◽  
Efficient Solutions ◽  
Duality Theorems ◽  
Converse Duality ◽  
Dual Problems ◽  
Properly Efficient Solutions ◽  
Multiobjective Programming Problem ◽  
Primal And Dual Problems ◽  
Primal And Dual

Under ρ−(η,θ)-invexity assumptions on the functions involved, weak, strong, and converse duality theorems are proved to relate properly efficient solutions of the primal and dual problems for a multiobjective programming problem.

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