A solution procedure for multi-objective fully quadratic fractional optimization model

2021 ◽  
Author(s):  
Namrata Rani ◽  
Vandana Goyal ◽  
Deepak Gupta
Keyword(s):  
Optimization Model ◽  
Solution Procedure ◽  
Multi Objective ◽  
Fractional Optimization

scholarly journals On Solving Bi-level Multi-Objective Fully Quadratic Fractional Optimization Model with Fuzzy Demands

2021 ◽  
Vol 6 (6) ◽  
pp. 1612-1628
Author(s):  
Namrata Rani ◽  
Vandana Goyal ◽  
Deepak Gupta
Keyword(s):  
Optimization Model ◽  
Decision Makers ◽  
Quadratic Functions ◽  
Objective Functions ◽  
Quadratic Constraints ◽  
Non Linear Programming ◽  
Multi Objective ◽  
Fractional Optimization ◽  
Proposed Model ◽  
Fuzzy Goal

This paper has been designed to introduce the method for solving the Bi-level Multi-objective (BL-MO) Fully Quadratic Fractional Optimization Model through Fuzzy Goal Programming (FGP) approach by utilising non-linear programming. In Fully Quadratic Fractional Optimization Model, the objective functions are in fractional form, having quadratic functions in both numerator and denominator subject to quadratic constraints set. The motive behind this paper is to provide a solution to solve the BL-MO optimization model in which number of decision-makers (DM) exists at two levels in the hierarchy. First, the fractional functions with fuzzy demand, which are in the form of fuzzy numbers, are converted into crisp models by applying the concept of α-cuts. After that, membership functions are developed which are corresponding to each decision-maker’s objective and converted into simpler form to avoid complications due to calculations. Finally, the model is simplified by applying FGP approach, and a compromised solution to the initial model is obtained. An algorithm, flowchart and example are also given at the end to explain the study of the proposed model.

Using NSGA-II to solve multi-objective competitive location problem with cooperative coverage for distance-based attractiveness

2021 ◽  
pp. 1-12
Author(s):  
Sheng-Chuan Wang ◽  
Ta-Cheng Chen
Keyword(s):  
Genetic Algorithms ◽  
Optimization Model ◽  
Location Problem ◽  
Solution Procedure ◽  
Competitive Location ◽  
Multi Objective Optimization ◽  
Demand Point ◽  
Nsga Ii ◽  
Solution Sets ◽  
Multi Objective

Multi-objective competitive location problem with cooperative coverage for distance-based attractiveness is introduced in this paper. The potential facilities compete to be selected to serve all demand points which are determined by maximizing total collective attractiveness of all demand points from assigned facilities and minimizing the fixed and distance costs between all demand points and selected facilities. Facility attractiveness is represented as a coverage of the facility with full, partial and none coverage corresponding to maximum full and partial coverage radii. Cooperative coverage, which the demand point is covered by at least one facility, is also considered. The problem is formulated as a multi-objective optimization model and solution procedure based on elitist non-dominated sorting genetic algorithms (NSGA-II) is developed. Experimental example demonstrates the best non-dominated solution sets obtained by developed solution procedure. Contributions of this paper include introducing competitive location problem with facility attractiveness as a distance-based coverage of the facility, re-categorizing facility coverage classification and developing solution procedure base upon NSGA-II.

scholarly journals FGP in Multi-objective Non-Linear Fractional Optimization Model including Triangular Fuzzy Numbers

2019 ◽  
Vol 8 (11) ◽  
pp. 2122-2130
Keyword(s):  
Optimization Model ◽  
Fuzzy Numbers ◽  
Fuzzy Model ◽  
Objective Functions ◽  
Triangular Fuzzy Numbers ◽  
Multi Objective ◽  
Fractional Optimization ◽  
Non Linear ◽  
Multi Level

The motivation behind this paper is to propose method to obtain compromized solution of Non-Linear fractional Optimization Model. In this paper, Multi-level multi-objective fully quadratic fractional optimization model (ML-MOFQFOM) is studied in which various objective functions are involved, generally have conflicting nature. FGP approach is being used to solve ML-MOFQFOM involving triangular fuzzy numbers. This paper deals with the ML-MOFQFOM in which fuzzy model converted into deterministic form through the help of  -cuts where  is the combined choice of all objective functions. An algorithm and examples are also presented to validate the proposed method.

scholarly journals Research on Blank Optimization Design Based on Low-Carbon and Low-Cost Blank Process Route Optimization Model

2021 ◽  
Vol 13 (4) ◽  
pp. 1929
Author(s):  
Yongmao Xiao ◽  
Wei Yan ◽  
Ruping Wang ◽  
Zhigang Jiang ◽  
Ying Liu
Keyword(s):  
Optimization Model ◽  
Optimization Design ◽  
Design Method ◽  
Low Cost ◽  
Route Optimization ◽  
Low Carbon ◽  
Multi Objective Optimization ◽  
Multi Objective ◽  
Blank Design ◽  
Process Route

The optimization of blank design is the key to the implementation of a green innovation strategy. The process of blank design determines more than 80% of resource consumption and environmental emissions during the blank processing. Unfortunately, the traditional blank design method based on function and quality is not suitable for today’s sustainable development concept. In order to solve this problem, a research method of blank design optimization based on a low-carbon and low-cost process route optimization is proposed. Aiming at the processing characteristics of complex box type blank parts, the concept of the workstep element is proposed to represent the characteristics of machining parts, a low-carbon and low-cost multi-objective optimization model is established, and relevant constraints are set up. In addition, an intelligent generation algorithm of a working step chain is proposed, and combined with a particle swarm optimization algorithm to solve the optimization model. Finally, the feasibility and practicability of the method are verified by taking the processing of the blank of an emulsion box as an example. The data comparison shows that the comprehensive performance of the low-carbon and low-cost multi-objective optimization is the best, which meets the requirements of low-carbon processing, low-cost, and sustainable production.

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