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>

Robust Design of Power Distribution Systems Using an Enhanced Multi-Objective Genetic Algorithm

2012 ◽  
pp. 179-200 ◽  
Author(s):  
Cristiane G. Taroco ◽  
Eduardo G. Carrano ◽  
Oriane M. Neto
Keyword(s):  
Power Distribution ◽  
Distribution Systems ◽  
Search Algorithm ◽  
Efficient Solutions ◽  
Optimization Techniques ◽  
Nsga Ii ◽  
Robust Solutions ◽  
Multi Objective ◽  
Multi Objective Genetic Algorithm ◽  
Reliability And Robustness

The growing importance of electric distribution systems justifies new investments in their expansion and evolution. It is well known in the literature that optimization techniques can provide better allocation of the financial resources available for such a task, reducing total installation costs and power losses. In this work, the NSGA-II algorithm is used for obtaining a set of efficient solutions with regard to three objective functions, that is cost, reliability, and robustness. Initially, a most likely load scenario is considered for simulation. Next, the performances of the solutions achieved by the NSGA-II are evaluated under different load scenarios, which are generated by means of Monte Carlo Simulations. A Multi-objective Sensitivity Analysis is performed for selecting the most robust solutions. Finally, those solutions are submitted to a local search algorithm to estimate a Pareto set composed of just robust solutions only.

scholarly journals Effect of Crossover Probability on Performance of Genetic Algorithm in Scheduling of Parallel Machines for BI- Criteria Objectives

2019 ◽  
Vol 9 (1) ◽  
pp. 2827-2831
Keyword(s):  
Genetic Algorithm ◽  
Objective Function ◽  
Parallel Machines ◽  
Optimization Techniques ◽  
Computational Time ◽  
Planning And Scheduling ◽  
Multi Objective ◽  
Mutation Operators ◽  
Crossover Probability ◽  
Wide Range

Optimization of multi objective function gain the importance in the scheduling process. Many classical techniques are available to address the multi objective functions but the solutions yield the unsatisfactory results when the problem becomes complex and large. Evolutionary algorithm would be the solution for such problems. Genetic algorithm is adaptive heuristic search algorithms and optimization techniques that mimic the process of natural evolution. Genetic algorithms are a very effective way of obtaining a reasonable solution quickly to a complex problem. The genetic algorithm operators such as selection method, crossover method, crossover probability, mutation operators and stopping criteria have an effect on obtaining the reasonably good solution and the computational time. Partially mapped crossover operators are used to solve the problem of the traveling salesman, planning and scheduling of the machines, etc., which are having a wide range of solutions. This paper presents the effect of crossover probability on the performance of the genetic algorithm for the bi-criteria objective function to obtain the best solution in a reasonable time. The simulation on a designed genetic algorithm was conducted with a crossover probability of 0.4 to 0.95 (with a step of 0.05) and 0.97, found that results were converging for the crossover probability of 0.6 with the computational time of 3.41 seconds.

Application of multi-objective optimization techniques to improve the aerodynamic performance of a tunnel ventilation jet fan

2014 ◽  
Vol 229 (1) ◽  
pp. 91-105 ◽  
Author(s):  
Joon-Hyung Kim ◽  
Jin-Hyuk Kim ◽  
Joon-Yong Yoon ◽  
Young-Seok Choi ◽  
Sang-Ho Yang
Keyword(s):  
Objective Function ◽  
Design Optimization ◽  
Optimization Model ◽  
Forward Direction ◽  
Aerodynamic Performance ◽  
Optimization Techniques ◽  
Multi Objective Optimization ◽  
Tunnel Ventilation ◽  
Multi Objective ◽  
Jet Fan

This paper describes the design optimization of a tunnel ventilation jet fan through multi-objective optimization techniques. Four design variables were selected for design optimization. To analyze the performance of the fan, numerical analyses were conducted, and three-dimensional Reynolds-averaged Navier–Stokes equations with a shear stress transport turbulence model were solved. Two objective functions, the total efficiency of the forward direction and the ratio of the reverse direction outlet velocity to the forward direction outlet velocity, were employed, and multi-objective optimization was carried out to improve the aerodynamic performance. A response surface approximation surrogate model was constructed for each objective function based on numerical solutions obtained at specified design points. The non-dominated sorting genetic algorithm with a local search procedure was used for multi-objective optimization. The tradeoff between the two objectives was determined and described with respect to the Pareto-optimal solutions. Based on the analysis of the optimization results, we propose an optimization model to satisfy the objective function. Finally, to verify the performance, experiments with the base model and the optimization model were carried out.

New Approach for Solving Multi – Objective Problems

2012 ◽  
Vol 18 (67) ◽  
pp. 1
Author(s):  
علاء الدين نوري احمد ◽  
نذير عباس ابراهيم
Keyword(s):  
Mathematical Model ◽  
Objective Function ◽  
Efficient Solutions ◽  
Real Problem ◽  
New Approach ◽  
Multi Objective ◽  
Application Problem

  There are many researches deals with constructing an efficient solutions for real problem having Multi - objective confronted with each others. In this paper we construct a decision for Multi – objectives based on building a mathematical model formulating a unique objective function by combining the confronted objectives functions. Also we are presented some theories concerning this problem. Areal application problem has been presented to show the efficiency of the performance of our model and the method. Finally we obtained some results by randomly generating some problems.

scholarly journals Solving Multi-Objective Probabilistic Factional Programming Problem

2019 ◽  
Vol 8 (6S3) ◽  
pp. 897-903
Keyword(s):  
Genetic Algorithm ◽  
Objective Function ◽  
Programming Problem ◽  
Stochastic Simulation ◽  
Fractional Programming ◽  
Linear Fractional Programming ◽  
Multi Objective ◽  
Fractional Programming Problem ◽  
Simulation Based ◽  
Linear Fractional Programming Problem

This paper presents the solution methodology of a multiobjective probabilistic fractional programming problem. In the proposed model the parameters in the constraints coefficient and the right-hand sides of the constraints follow continuous random variables having known distribution. Since the programming problem consists of random variables, multi-objective function and fractional objective function, it is lengthy, time-consuming and clumsy to solve the proposed programming problem using analytical methods. Stochastic simulation-based genetic algorithm approach is directly applied to solve multi-objective probabilistic non-linear fractional programming problem involving beta distribution and chi-square distribution. In the proposed method, it is not necessary to find the deterministic equivalent of a probabilistic programming problem and applying any traditional methods of fractional programming problem. The stochastic simulation-based genetic algorithm is coded by Code block C++ 16.01 compiler. A set of Pareto optimal solutions are generated for a multi objective probabilistic non-linear fractional programming problem. A numerical example and case study on inventory problem are presented to validate the proposed method.

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.

Flexible Genetic Algorithm Based Optimal Power Flow of Power Systems

2018 ◽  
Vol 24 (3) ◽  
pp. 84
Author(s):  
Hassan Abdullah Kubba ◽  
Mounir Thamer Esmieel
Keyword(s):  
Genetic Algorithm ◽  
Objective Function ◽  
Power Flow ◽  
Optimal Power Flow ◽  
Reactive Power ◽  
Test System ◽  
Multi Objective ◽  
Optimal Power ◽  
Blending Method ◽  
Real Coded Genetic Algorithm

Nowadays, the power plant is changing the power industry from a centralized and vertically integrated form into regional, competitive and functionally separate units. This is done with the future aims of increasing efficiency by better management and better employment of existing equipment and lower price of electricity to all types of customers while retaining a reliable system. This research is aimed to solve the optimal power flow (OPF) problem. The OPF is used to minimize the total generations fuel cost function. Optimal power flow may be single objective or multi objective function. In this thesis, an attempt is made to minimize the objective function with keeping the voltages magnitudes of all load buses, real output power of each generator bus and reactive power of each generator bus within their limits. The proposed method in this thesis is the Flexible Continuous Genetic Algorithm or in other words the Flexible Real-Coded Genetic Algorithm (RCGA) using the efficient GA's operators such as Rank Assignment (Weighted) Roulette Wheel Selection, Blending Method Recombination operator and Mutation Operator as well as Multi-Objective Minimization technique (MOM). This method has been tested and checked on the IEEE 30 buses test system and implemented on the 35-bus Super Iraqi National Grid (SING) system (400 KV). The results of OPF problem using IEEE 30 buses typical system has been compared with other researches.     

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