scholarly journals Multi-objective geometric programming problem and its applications

2010 ◽  
Vol 20 (2) ◽  
pp. 213-227 ◽  
Author(s):  
Sahidul Islam
Keyword(s):  
Programming Problem ◽  
Geometric Programming ◽  
Optimization Technique ◽  
Real Life ◽  
Fuzzy Optimization ◽  
Solution Procedure ◽  
Programming Technique ◽  
Multi Objective ◽  
Numerical Example ◽  
Multiobjective Problem

In this paper, we have discussed constrained posynomial Multi-Objective Geometric Programming Problem. Here we shall describe the fuzzy optimization technique (through Geometric Programming technique) In order to solve the above multiobjective problem. The solution procedure of the fuzzy technique is illustrated by a numerical example and real life applications.

Solving the multi-objective stochastic interval-valued linear fractional integer programming problem

2021 ◽  
pp. 2250022
Author(s):  
Leila Younsi-Abbaci ◽  
Mustapha Moulaï
Keyword(s):  
Integer Programming ◽  
Programming Problem ◽  
Probabilistic Constraints ◽  
Chance Constrained Programming ◽  
Integer Programming Problem ◽  
Objective Functions ◽  
Programming Technique ◽  
Multi Objective ◽  
Weighted Sum Method ◽  
Interval Valued

In this paper, we consider a Multi-Objective Stochastic Interval-Valued Linear Fractional Integer Programming problem (MOSIVLFIP). We especially deal with a multi-objective stochastic fractional problem involving an inequality type of constraints, where all quantities on the right side are log-normal random variables, and the objective functions coefficients are fractional intervals. The proposed solving procedure is divided in three steps. In the first one, the probabilistic constraints are converted into deterministic ones by using the chance constrained programming technique. Then, the second step consists of transforming the studied problem objectives on an optimization problem with an interval-valued objective functions. Finally, by introducing the concept of weighted sum method, the equivalent converted problem obtained from the two first steps is transformed into a single objective deterministic fractional problem. The effectiveness of the proposed procedure is illustrated through a numerical example.

scholarly journals MULTI-OBJECTIVE PROBABILISTIC FRACTIONAL PROGRAMMING PROBLEM INVOLVING TWO PARAMETERS CAUCHY DISTRIBUTION

2019 ◽  
Vol 24 (3) ◽  
pp. 385-403
Author(s):  
Srikumar Acharya ◽  
Berhanu Belay ◽  
Rajashree Mishra
Keyword(s):  
Mathematical Model ◽  
Mathematical Programming ◽  
Programming Problem ◽  
Fractional Programming ◽  
Cauchy Distribution ◽  
Solution Procedure ◽  
Mathematical Programming Problem ◽  
Multi Objective ◽  
Fractional Programming Problem ◽  
Two Parameters

The paper presents the solution methodology of a multi-objective probabilistic fractional programming problem, where the parameters of the right hand side constraints follow Cauchy distribution. The proposed mathematical model can not be solved directly. The solution procedure is completed in three steps. In first step, multi-objective probabilistic fractional programming problem is converted to deterministic multi-objective fractional mathematical programming problem. In the second step, it is converted to its equivalent multi-objective mathematical programming problem. Finally, ε -constraint method is applied to find the best compromise solution. A numerical example and application are presented to demonstrate the procedure of proposed mathematical model.

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.

scholarly journals Goal Programming Models with Linear and Exponential Fuzzy Preference Relations

Symmetry ◽  
2020 ◽  
Vol 12 (6) ◽  
pp. 934
Author(s):  
Mohammad Faisal Khan ◽  
Md. Gulzarul Hasan ◽  
Abdul Quddoos ◽  
Armin Fügenschuh ◽  
Syed Suhaib Hasan
Keyword(s):  
Membership Function ◽  
Goal Programming ◽  
Real Life ◽  
Programming Models ◽  
Membership Functions ◽  
Preference Relations ◽  
Multi Objective ◽  
Numerical Example ◽  
Fuzzy Preference Relations ◽  
Fuzzy Preference

Goal programming (GP) is a powerful method to solve multi-objective programming problems. In GP the preferential weights are incorporated in different ways into the achievement function. The problem becomes more complicated if the preferences are imprecise in nature, for example ‘Goal A is slightly or moderately or significantly important than Goal B’. Considering such type of problems, this paper proposes standard goal programming models for multi-objective decision-making, where fuzzy linguistic preference relations are incorporated to model the relative importance of the goals. In the existing literature, only methods with linear preference relations are available. As per our knowledge, nonlinearity was not considered previously in preference relations. We formulated fuzzy preference relations as exponential membership functions. The grades or achievement function is described as an exponential membership function and is used for grading levels of preference toward uncertainty. A nonlinear membership function may lead to a better representation of the achievement level than a linear one. Our proposed models can be a useful tool for different types of real life applications, where exponential nonlinearity in goal preferences exists. Finally, a numerical example is presented and analyzed through multiple cases to validate and compare the proposed models. A distance measure function is also developed and used to compare proposed models. It is found that, for the numerical example, models with exponential membership functions perform better than models with linear membership functions. The proposed models will help decision makers analyze and plan real life problems more realistically.

scholarly journals Optimizing Painting Sequence Scheduling Based on Adaptive Partheno-Genetic Algorithm

Processes ◽  
2021 ◽  
Vol 9 (10) ◽  
pp. 1714
Author(s):  
Jun Yang ◽  
Tong Sun ◽  
Xiuxiang Huang ◽  
Ke Peng ◽  
Zhongxiang Chen ◽  
...  
Keyword(s):  
Genetic Algorithm ◽  
Programming Problem ◽  
Large Scale ◽  
Scheduling Algorithm ◽  
Real Life ◽  
Optimal Solution ◽  
Mixed Integer ◽  
Rule Based ◽  
Multi Objective ◽  
Color Changes

In this paper, we formulate and solve a novel real-life large-scale automotive parts paint shop scheduling problem, which contains color arrangement restrictions, part arrangement restrictions, bracket restrictions, and multi-objectives. Based on these restrictions, we construct exact constraints and two objective functions to form a large-scale multi-objective mixed-integer linear programming problem. To reduce this scheduling problem’s complexity, we converted the multi-objective model into a multi-level objective programming problem by combining the rule-based scheduling algorithm and the adaptive Partheno-Genetic algorithm. The rule-based scheduling algorithm is adopted to optimize color changes horizontally and bracket replacements vertically. The adaptive Partheno-Genetic algorithm is designed to optimize production based on the rule-based scheduling algorithm. Finally, we apply the model to the actual optimization problem that contained 829,684 variables and 137,319 constraints, and solved this problem by Python. The proposed method solves the optimal solution, consuming 575 s.

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