scholarly journals Multiobjective Quadratic Fractional Programming using Iterative Parametric Function

2019 ◽  
Vol 8 (11) ◽  
pp. 2116-2121
Keyword(s):  
Objective Function ◽  
Fractional Programming ◽  
Programming Model ◽  
Efficient Solutions ◽  
Objective Functions ◽  
Parametric Function ◽  
Quadratic Constraints ◽  
Quadratic Fractional Programming ◽  
Parametric Functions ◽  
Constraint Method

The paper proposed the Model of multiobjective quadratic fractional optimisation problem with a set of quadratic constraints and a methodology for obtaining a set of solutions based on the approach of using iterative parametric functions. Firstly, each fractional objective function is transformed into non-fractional parametric objective function by assigning a vector of parameters to each objective function. In this approach, the Decision Maker(DM) predecides the desired tolerance levels of the objective functions in the form of termination constants. Then, by using ε-constraint method, a set of efficient solutions is obtained and termination conditions are checked for each parametric objective function. Also, a comparative study of the proposed method and fuzzy approach is given to reveal the validity of the method. A numerical for Multiobjective quadratic fractional programming Model (MOQFPM) is given in the end to check the applicability of the approach.

Iterative Parametric Approach for Quadratically Constrained Bi-Level Multiobjective Quadratic Fractional Programming

2020 ◽  
Vol 17 (11) ◽  
pp. 5046-5051
Author(s):  
Vandana Goyal ◽  
Namrata Rani ◽  
Deepak Gupta
Keyword(s):  
Fractional Programming ◽  
Optimization Problem ◽  
Programming Model ◽  
Pareto Optimal Solutions ◽  
Parametric Approach ◽  
Second Stage ◽  
Quadratic Fractional Programming ◽  
Upper Level ◽  
Quadratically Constrained ◽  
Constraint Method

The paper proposed an iterative parametric approach procedure for solving Bi-level Multiobjective Quadratic Fractional Programming model. The Model is divided into two levels-upper and lower. In the first stage of the approach, a set of pareto optimal solutions of upper Level is obtained by converting the problem into equivalent single non-fractional parametric objective optimization problem by using parametric vector and ε-constraint method. Then for the second stage, the solution of upper level is followed by the lower level decision maker while finding solution with the proposed algorithm to obtain the best preferred solution. A numerical example is solved in the last to validate the feasibility of the approach.

scholarly journals ПАРАМЕТРИЧЕСКАЯ ОПТИМИЗАЦИЯ ПО КРИТЕРИЮ ОБЪЕМА ДВУХСТУПЕНЧАТОГО ПЛАНЕТАРНОГО МЕХАНИЗМА ТИПА AI–II

2019 ◽  
pp. 92-102
Author(s):  
Владимир Анатольевич Матусевич ◽  
Юрий Владимирович Шарабан ◽  
Александр Владимирович Шехов
Keyword(s):  
Objective Functions ◽  
Parametric Function ◽  
Planetary Gears ◽  
Optimization Task ◽  
Parametric Functions ◽  
Analysis Of Function ◽  
Differential Properties ◽  
The Mathematical Model ◽  
Optimal Designing ◽  
Planetary Mechanism

The task of parametric optimization on the criterion of total volume is considered for the two-stage planetary mechanism of type AI–II. The objective function of optimization is built as a sum of two dimensionless parametric functions of volume (analogs of volume) of the separate stages of planetary mechanism of type AI–II. Construction of analogs of volume of simple planetary mechanisms of type AI and II, corresponding the first and second to the stages of planetary mechanism of type AI–II, it is based on their presentation as conditional disks. Thus the volume of the conditional disk is equivalent to the volume of a simple planetary mechanism. The mathematical model of analogs of the volume is built taking into account the terms of the durability of the toothed hooking of the sun gear and planetary gears of simple planetary mechanism, and also taking into account an area possible his transmission relation. Considering terms of contact and bending durability of the toothed hooking, get the analogs of volume at a calculation on contact and bending to durability. Depending on the condition of durability (contact or bending) and type of simple planetary mechanism the analog of his volume appears as a parametric function of corresponding parameters of his kinematics diagram. As parameters transmission relation attitude of simple planetary mechanism, parameters of bringing a mechanism over, toward a conditional disk, and also the relation of reference diameters of planetary gears of the mechanism is chosen. An analysis over of influence of each is brought of parameters of the function of analog of volume on the pattern of behavior to it. On the basis of this analysis of function of analogs of volume of the stages of planetary mechanism of type AI–II appear as parametric functions of the guided parameters. For the simple planetary mechanism of type AI one guided parameter is chosen, namely transmission relation of mechanism. For the guided parameters of function of analog of volume for the simple planetary mechanism of type II a transmission relation and relation of reference diameters of planetary gears of mechanism are chosen, i.e. two guided parameters. Offered approach for the decision of optimization task, based on research of differential properties of objective functions of volume (analogs of volume) of the separate stages of planetary mechanism of type AI–II. It is given the example of the optimal designing of construction of minimum volume of planetary mechanism of type AI–II.

scholarly journals On robust weakly $ \varepsilon $-efficient solutions for multi-objective fractional programming problems under data uncertainty

2021 ◽  
Vol 7 (2) ◽  
pp. 2331-2347
Author(s):  
Shima Soleimani Manesh ◽  
◽  
Mansour Saraj ◽  
Mahmood Alizadeh ◽  
Maryam Momeni ◽  
...  
Keyword(s):  
Objective Function ◽  
Fractional Programming ◽  
Uncertain Data ◽  
Positive Function ◽  
Efficient Solutions ◽  
Optimization Techniques ◽  
Data Uncertainty ◽  
Multi Objective ◽  
Negative Function ◽  
Function Vector

<abstract><p>In this study, we use the robust optimization techniques to consider a class of multi-objective fractional programming problems in the presence of uncertain data in both of the objective function and the constraint functions. The components of the objective function vector are reported as ratios involving a convex non-negative function and a concave positive function. In addition, on applying a parametric approach, we establish $ \varepsilon $-optimality conditions for robust weakly $ \varepsilon $-efficient solution. Furthermore, we present some theorems to obtain a robust $ \varepsilon $-saddle point for uncertain multi-objective fractional problem.</p></abstract>

scholarly journals An Exact Method for a Discrete Multiobjective Linear Fractional Optimization

2008 ◽  
Vol 2008 ◽  
pp. 1-12 ◽  
Author(s):  
Mohamed El-Amine Chergui ◽  
Mustapha Moulaï
Keyword(s):  
Fractional Programming ◽  
Feasible Solution ◽  
Efficient Solutions ◽  
Branch And Cut ◽  
Multiple Objective ◽  
Objective Functions ◽  
Linear Fractional Programming ◽  
Fractional Optimization ◽  
Important Field ◽  
Linear Fractional Programming Problem

Integer linear fractional programming problem with multiple objective (MOILFP) is an important field of research and has not received as much attention as did multiple objective linear fractional programming. In this work, we develop a branch and cut algorithm based on continuous fractional optimization, for generating the whole integer efficient solutions of the MOILFP problem. The basic idea of the computation phase of the algorithm is to optimize one of the fractional objective functions, then generate an integer feasible solution. Using the reduced gradients of the objective functions, an efficient cut is built and a part of the feasible domain not containing efficient solutions is truncated by adding this cut. A sample problem is solved using this algorithm, and the main practical advantages of the algorithm are indicated.

Power Generation for India with Higher Efficiency

2018 ◽  
Vol 6 (7) ◽  
pp. 267
Author(s):  
Umeshkannan P ◽  
Muthurajan KG
Keyword(s):  
Power Generation ◽  
Objective Function ◽  
Fossil Fuels ◽  
Programming Model ◽  
Developed Countries ◽  
Power Requirement ◽  
Average Efficiency ◽  
Potential Demand ◽  
The Developed Countries ◽  
Developed Nations

The developed countries are consuming more amount of energy in all forms including electricity continuously with advanced technologies.  Developing  nation’s  energy usage trend rises quickly but very less in comparison with their population and  their  method of generating power is not  seems  to  be  as  advanced  as  developed  nations. The   objective   function   of   this   linear   programming model is to maximize the average efficiency of power generation inIndia for 2020 by giving preference to energy efficient technologies. This model is subjected to various constraints like potential, demand, running cost and Hydrogen / Carbon ratio, isolated load, emission and already installed capacities. Tora package is used to solve this linear program. Coal,  Gas,  Hydro  and  Nuclear  sources can are  supply around 87 %  of  power  requirement .  It’s concluded that we can produce power  at  overall  efficiency  of  37%  while  meeting  a  huge demand  of  13,00,000  GWh  of  electricity.  The objective function shows the scenario of highaverage efficiency with presence of 9% renewables. Maximum value   is   restricted   by   low   renewable   source’s efficiencies, emission constraints on fossil fuels and cost restriction on some of efficient technologies. This    model    shows    that    maximum    18%    of    total requirement   can   be   met   by   renewable itself which reduces average efficiency to 35.8%.   Improving technologies  of  renewable  sources  and  necessary  capacity addition  to  them in  regular  interval  will  enhance  their  role and existence against fossil fuels in future. The work involves conceptualizing, modeling, gathering information for data’s to be used in model for problem solving and presenting different scenarios for same objective.

Scalable Computing Architecture for Time-Dependent Transportation Optimization Problems Based on High-Performance Computing Techniques

2019 ◽  
Vol 2673 (4) ◽  
pp. 205-216 ◽  
Author(s):  
Pengfei (Taylor) Li ◽  
Peirong (Slade) Wang ◽  
Farzana Chowdhury ◽  
Li Zhang
Keyword(s):  
Objective Function ◽  
High Performance Computing ◽  
High Performance ◽  
Optimization Problems ◽  
Dynamic Network ◽  
Alternative Formulation ◽  
High Fidelity ◽  
Objective Functions ◽  
Performance Computing ◽  
Transportation Optimization

Traditional formulations for transportation optimization problems mostly build complicating attributes into constraints while keeping the succinctness of objective functions. A popular solution is the Lagrangian decomposition by relaxing complicating constraints and then solving iteratively. Although this approach is effective for many problems, it generates intractability in other problems. To address this issue, this paper presents an alternative formulation for transportation optimization problems in which the complicating attributes of target problems are partially or entirely built into the objective function instead of into the constraints. Many mathematical complicating constraints in transportation problems can be efficiently modeled in dynamic network loading (DNL) models based on the demand–supply equilibrium, such as the various road or vehicle capacity constraints or “IF–THEN” type constraints. After “pre-building” complicating constraints into the objective functions, the objective function can be approximated well with customized high-fidelity DNL models. Three types of computing benefits can be achieved in the alternative formulation: ( a) the original problem will be kept the same; ( b) computing complexity of the new formulation may be significantly reduced because of the disappearance of hard constraints; ( c) efficiency loss on the objective function side can be mitigated via multiple high-performance computing techniques. Under this new framework, high-fidelity and problem-specific DNL models will be critical to maintain the attributes of original problems. Therefore, the authors’ recent efforts in enhancing the DNL’s fidelity and computing efficiency are also described in the second part of this paper. Finally, a demonstration case study is conducted to validate the new approach.

scholarly journals Optimal Placement and Sizing of D-STATCOM in Radial and Meshed Distribution Networks Using a Discrete-Continuous Version of the Genetic Algorithm

Electronics ◽  
2021 ◽  
Vol 10 (12) ◽  
pp. 1452
Author(s):  
Cristian Mateo Castiblanco-Pérez ◽  
David Esteban Toro-Rodríguez ◽  
Oscar Danilo Montoya ◽  
Diego Armando Giral-Ramírez
Keyword(s):  
Genetic Algorithm ◽  
Objective Function ◽  
Programming Model ◽  
Distribution Networks ◽  
Optimization Method ◽  
Optimal Placement ◽  
Mixed Integer ◽  
Power Balance ◽  
Continuous Version ◽  
Discrete Part

In this paper, we propose a new discrete-continuous codification of the Chu–Beasley genetic algorithm to address the optimal placement and sizing problem of the distribution static compensators (D-STATCOM) in electrical distribution grids. The discrete part of the codification determines the nodes where D-STATCOM will be installed. The continuous part of the codification regulates their sizes. The objective function considered in this study is the minimization of the annual operative costs regarding energy losses and installation investments in D-STATCOM. This objective function is subject to the classical power balance constraints and devices’ capabilities. The proposed discrete-continuous version of the genetic algorithm solves the mixed-integer non-linear programming model that the classical power balance generates. Numerical validations in the 33 test feeder with radial and meshed configurations show that the proposed approach effectively minimizes the annual operating costs of the grid. In addition, the GAMS software compares the results of the proposed optimization method, which allows demonstrating its efficiency and robustness.

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