scholarly journals On the Construction of an Approximate Optimal Solution for Geometric Programming Problem

1984 ◽  
Vol 20 (2) ◽  
pp. 130-136
Author(s):  
Kaname YOSHIDA
Keyword(s):  
Programming Problem ◽  
Geometric Programming ◽  
Optimal Solution ◽  
Approximate Optimal Solution

scholarly journals A New Method to Optimize the Satisfaction Level of the Decision Maker in Fuzzy Geometric Programming Problems

Mathematics ◽  
2019 ◽  
Vol 7 (5) ◽  
pp. 464
Author(s):  
Armita Khorsandi ◽  
Bing-Yuan Cao ◽  
Hadi Nasseri
Keyword(s):  
Mathematical Modeling ◽  
Objective Function ◽  
Programming Problem ◽  
Decision Maker ◽  
Geometric Programming ◽  
Fuzzy Numbers ◽  
Optimal Solution ◽  
New Method ◽  
Satisfaction Level ◽  
Simple Parameter

Geometric programming problems are well-known in mathematical modeling. They are broadly used in diverse practical fields that are contemplated through an appropriate methodology. In this paper, a multi-parametric vector α is proposed for approaching the highest decision maker satisfaction. Hitherto, the simple parameter α , which has a scalar role, has been considered in the problem. The parameter α is a vector whose range is within the region of the satisfaction area. Conventionally, it is assumed that the decision maker is sure about the parameters, but, in reality, it is mostly hesitant about them, so the parameters are presented in fuzzy numbers. In this method, the decision maker can attain different satisfaction levels in each constraint, and even full satisfaction can be reached in some constraints. The goal is to find the highest satisfaction degree to maintain an optimal solution. Moreover, the objective function is turned into a constraint, i.e., one more dimension is added to n-dimensional multi-parametric α . Thus, the fuzzy geometric programming problem under this multi-parametric vector α ∈ ( 0 , 1 ] n + 1 gives a maximum satisfaction level to the decision maker. A numerical example is presented to illustrate the proposed method and the superiority of this multi-parametric α over the simple one.

scholarly journals The Magnetic Bead Computing Model of the 0-1 Integer Programming Problem Based on DNA Cycle Hybridization

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Rujie Xu ◽  
Zhixiang Yin ◽  
Zhen Tang ◽  
Jing Yang ◽  
Jianzhong Cui ◽  
...  
Keyword(s):  
Integer Programming ◽  
Programming Problem ◽  
Magnetic Beads ◽  
Specific Binding ◽  
Optimal Solution ◽  
High Sensitivity ◽  
Magnetic Bead ◽  
Integer Programming Problem ◽  
Computing Model ◽  
Dna Strands

Magnetic beads and magnetic Raman technology substrates have good magnetic response ability and surface-enhanced Raman technology (SERS) activity. Therefore, magnetic beads exhibit high sensitivity in SERS detection. In this paper, DNA cycle hybridization and magnetic bead models are combined to solve 0-1 integer programming problems. First, the model maps the variables to DNA strands with hairpin structures and weights them by the number of hairpin DNA strands. This result can be displayed by the specific binding of streptavidin and biotin. Second, the constraint condition of the 0-1 integer programming problem can be accomplished by detecting the signal intensity of the biological barcode to find the optimal solution. Finally, this model can be used to solve the general 0-1 integer programming problem and has more extensive applications than the previous DNA computing model.

scholarly journals Ranking Function Application for Optimal Solution of Fractional programming problem

2020 ◽  
Vol 25 (1) ◽  
Author(s):  
Rasha Jalal
Keyword(s):  
Linear Programming ◽  
Programming Problem ◽  
Fractional Programming ◽  
Linear Programming Problem ◽  
Fuzzy Numbers ◽  
Optimal Solution ◽  
Ranking Function ◽  
Linear Fractional Programming ◽  
Fractional Programming Problem ◽  
Linear Programming Problems

The aim of this paper is to suggest a solution procedure to fractional programming problem based on new ranking function (RF) with triangular fuzzy number (TFN) based on alpha cuts sets of fuzzy numbers. In the present procedure the linear fractional programming (LFP) problems is converted into linear programming problems. We concentrate on linear programming problem problems in which the coefficients of objective function are fuzzy numbers, the right- hand side are fuzzy numbers too, then solving these linear programming problems by using a new ranking function. The obtained linear programming problem can be solved using win QSB program (simplex method) which yields an optimal solution of the linear fractional programming problem. Illustrated examples and comparisons with previous approaches are included to evince the feasibility of the proposed approach.

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.

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