scholarly journals Approaches for Solving Fully Fuzzy Rough Multi-Objective Nonlinear Programming Problems

2021 ◽  
pp. 113-128
Author(s):  
E. Ammar ◽  
A. Al-Asfar
Keyword(s):  
Nonlinear Programming ◽  
Programming Problem ◽  
Nonlinear Problems ◽  
Nonlinear Programming Problem ◽  
Multi Objective ◽  
Weighted Sum Method ◽  
Interval Variables ◽  
Triangular Numbers ◽  
Rough Interval ◽  
Α Level

Practical nonlinear programming problem often encounters uncertainty and indecision due to various factors that cannot be controlled. To overcome these limitations, fully fuzzy rough approaches are applied to such a problem. In this paper, an effective two approaches are proposed to solve fully fuzzy rough multi-objective nonlinear programming problems (FFRMONLP) where all the variables and parameters are fuzzy rough triangular numbers. The first, based on a slice sum technique, a fully fuzzy rough multi-objective nonlinear problem has turned into five equivalent multi-objective nonlinear programming (FFMONLP) problems. The second proposed method for solving FFRMONLP problems is α-cut approach, where the triangular fuzzy rough variables and parameters of the FFRMONLP problem are converted into rough interval variables and parameters by α-level cut, moreover the rough MONLP problem turns into four MONLP problems. Furthermore, the weighted sum method is used in both proposed approaches to convert multi-objective nonlinear problems into an equivalent nonlinear programming problem. Finally, the effectiveness of the proposed procedure is demonstrated by numerical examples.

Study on multi-objective nonlinear programming problem with rough parameters

2021 ◽  
pp. 1-14
Author(s):  
Harish Garg ◽  
Sultan S. Alodhaibi ◽  
Hamiden Abd El-Wahed Khalifa
Keyword(s):  
Nonlinear Programming ◽  
Programming Problem ◽  
Rough Set Theory ◽  
Real Life ◽  
Boundary Region ◽  
Efficient Solutions ◽  
Weighted Averaging ◽  
Nonlinear Programming Problem ◽  
Multi Objective ◽  
Constraint Set

Rough set theory, introduced by Pawlak in 1981, is one of the important theories to express the vagueness not by means of membership but employing a boundary region of a set, i.e., an object is approximately determined based on some knowledge. In our real-life, there exists several parameters which impact simultaneously on each other and hence dealing with such different parameters and their conflictness create a multi-objective nonlinear programming problem (MONLPP). The objective of the paper is to deal with a MONLPP with rough parameters in the constraint set. The considered MONLPP with rough parameters are converted into the two-single objective problems namely, lower and upper approximate problems by using the weighted averaging and the ɛ- constraints methods and hence discussed their efficient solutions. The Karush-Kuhn-Tucker’s optimality conditions are applied to solve these two lower and upper approximate problems. In addition, the rough weights and the rough parameter ɛ are determined by the lower and upper the approximations corresponding each efficient solution. Finally, two numerical examples are considered to demonstrate the stated approach and discuss their advantages over the existing ones.

A study of uncertain multi-objective nonlinear programming problems for rough intervals

2022 ◽  
pp. 1-15
Author(s):  
E. Ammar ◽  
A. Al-Asfar
Keyword(s):  
Nonlinear Programming ◽  
Nonlinear Problems ◽  
Optimal Solutions ◽  
Objective Functions ◽  
Weighting Method ◽  
Upper Approximation ◽  
Multi Objective ◽  
Inaccurate Data ◽  
Decision Variables ◽  
Rough Interval

In real conditions, the parameters of multi-objective nonlinear programming (MONLP) problem models can’t be determined exactly. Hence in this paper, we concerned with studying the uncertainty of MONLP problems. We propose algorithms to solve rough and fully-rough-interval multi-objective nonlinear programming (RIMONLP and FRIMONLP) problems, to determine optimal rough solutions value and rough decision variables, where all coefficients and decision variables in the objective functions and constraints are rough intervals (RIs). For the RIMONLP and FRIMONLP problems solving methodology are presented using the weighting method and slice-sum method with Kuhn-Tucker conditions, We will structure two nonlinear programming (NLP) problems. In the first one of this NLP problem, all of its variables and coefficients are the lower approximation (LAI) it’s RIs. The second NLP problems are upper approximation intervals (UAI) of RIs. Subsequently, both NLP problems are sliced into two crisp nonlinear problems. NLP is utilized because numerous real systems are inherently nonlinear. Also, rough intervals are so important for dealing with uncertainty and inaccurate data in decision-making (DM) problems. The suggested algorithms enable us to the optimal solutions in the largest range of possible solution. Finally, Illustrative examples of the results are given.

scholarly journals Trust-Region Based Penalty Barrier Algorithm for Constrained Nonlinear Programming Problems: An Application of Design of Minimum Cost Canal Sections

Mathematics ◽  
2021 ◽  
Vol 9 (13) ◽  
pp. 1551
Author(s):  
Bothina El-Sobky ◽  
Yousria Abo-Elnaga ◽  
Abd Allah A. Mousa ◽  
Mohamed A. El-Shorbagy
Keyword(s):  
Nonlinear Programming ◽  
Global Convergence ◽  
Programming Problem ◽  
Trust Region ◽  
Convergence Theory ◽  
Benchmark Problems ◽  
Nonlinear Programming Problem ◽  
Barrier Method ◽  
Starting Point ◽  
Constrained Nonlinear Programming

In this paper, a penalty method is used together with a barrier method to transform a constrained nonlinear programming problem into an unconstrained nonlinear programming problem. In the proposed approach, Newton’s method is applied to the barrier Karush–Kuhn–Tucker conditions. To ensure global convergence from any starting point, a trust-region globalization strategy is used. A global convergence theory of the penalty–barrier trust-region (PBTR) algorithm is studied under four standard assumptions. The PBTR has new features; it is simpler, has rapid convergerce, and is easy to implement. Numerical simulation was performed on some benchmark problems. The proposed algorithm was implemented to find the optimal design of a canal section for minimum water loss for a triangle cross-section application. The results are promising when compared with well-known algorithms.

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