scholarly journals Multi-Objective Faculty Course Assignment Problem with Result and Feedback Based Uncertain Preferences

2021 ◽  
Vol 6 (4) ◽  
pp. 1055-1075
Author(s):  
Sunil B. Bhoi ◽  
Jayesh M Dhodiya
Keyword(s):  
Deterministic Model ◽  
Optimal Solution ◽  
Fuzzy Programming ◽  
Programming Technique ◽  
Feedback Analysis ◽  
Multi Objective ◽  
Ranking Criteria ◽  
Uncertain Preferences ◽  
Single Objective ◽  
Optimistic Value

In this paper, a multi-objective faculty course allocation problem with result analysis and feedback analysis based on uncertain preferences mathematical model is presented. To deal with an uncertain model, three different ranking criteria are being used to develop: a) Expected value, b) Optimistic value, c) Dependent optimistic value criterion. These mathematical models are transformed into their corresponding deterministic forms using the basic concepts of uncertainty theory. The deterministic model of DOCM consists of fractional objectives which are converted into their linear form using Charnes and Cooper’s transformation. These deterministic formulations MOFCAP are converted into a single objective problem by using the fuzzy programming technique with linear and exponential membership functions. Further, the single objective problem for all the defined models is solved in the Lingo 18.0 software to derive the Pareto-optimal solution. The sensitivity of the models is also performed to examine the variation in the objective function due to the variation in parameters. Finally, a numerical example is given to exhibit the application and algorithm of the models.

scholarly journals Multi-Objective Capacitated Solid Transportation Problem with Uncertain Variables

2021 ◽  
Vol 6 (5) ◽  
pp. 1406-1422
Author(s):  
Vandana Y. Kakran ◽  
Jayesh M. Dhodiya
Keyword(s):  
Transportation Problem ◽  
Optimal Solution ◽  
Fuzzy Programming ◽  
Solid Transportation Problem ◽  
Programming Technique ◽  
Distance Method ◽  
Multi Objective ◽  
Uncertain Variables ◽  
Value Model ◽  
Single Objective

This paper investigates a multi-objective capacitated solid transportation problem (MOCSTP) in an uncertain environment, where all the parameters are taken as zigzag uncertain variables. To deal with the uncertain MOCSTP model, the expected value model (EVM) and optimistic value model (OVM) are developed with the help of two different ranking criteria of uncertainty theory. Using the key fundamentals of uncertainty, these two models are transformed into their relevant deterministic forms which are further converted into a single-objective model using two solution approaches: minimizing distance method and fuzzy programming technique with linear membership function. Thereafter, the Lingo 18.0 optimization tool is used to solve the single-objective problem of both models to achieve the Pareto-optimal solution. Finally, numerical results are presented to demonstrate the application and algorithm of the models. To investigate the variation in the objective function, the sensitivity of the objective functions in the OVM model is also examined with respect to the confidence levels.

Multi-Objective Fixed-Charge Transportation Problem with Random Rough Variables

2018 ◽  
Vol 26 (06) ◽  
pp. 971-996 ◽  
Author(s):  
Sankar Kumar Roy ◽  
Sudipta Midya ◽  
Vincent F. Yu
Keyword(s):  
Transportation Problem ◽  
Deterministic Model ◽  
Real Life ◽  
Optimal Solution ◽  
Fuzzy Programming ◽  
Fixed Charge ◽  
Optimal Solutions ◽  
Multi Objective ◽  
Proposed Model ◽  
Fixed Charge Transportation Problem

This paper considers a multi-objective fixed-charge transportation problem (MOFCTP) in which the parameters of the objective functions are random rough variables, while the supply and the demand parameters are rough variables. In real-life situations, the parameters of a multi-objective fixed-charge transportation problem may not be defined precisely, because of globalization of the market, uncontrollable factors, etc. As such, the multi-objective fixed-charge transportation problem is proposed under rough and random rough environments. To tackle uncertain (rough and random rough) parameters, the proposed model employs an expected value operator. Furthermore, a procedure is developed for converting the uncertain multi-objective fixed-charge transportation problem into a deterministic form and then solving the deterministic model. Three different methods, namely, the fuzzy programming, global criterion, and ϵ-constrained methods, are used to derive the optimal compromise solutions of the suggested model. To provide the preferable optimal solution of the formulated problem, a comparison is drawn among the optimal solutions that are extracted from different methods. Herein, the ϵ-constrained method derives a set of optimal solutions and generates an exact Paretofront. Finally, in order to show the applicability and feasibility of the proposed model, the paper includes a real-life example of a multi-objective fixed-charge transportation problem. The main contribution of the paper is that it deals with MOFCTP using two types of uncertainties, thus making the decision making process more flexible.

A two-sided matching decision-making approach based on regret theory under intuitionistic fuzzy environment

2021 ◽  
pp. 1-18
Author(s):  
Xiang Jia ◽  
Xinfan Wang ◽  
Yuanfang Zhu ◽  
Lang Zhou ◽  
Huan Zhou
Keyword(s):  
Decision Making ◽  
Hamming Distance ◽  
Optimal Solution ◽  
Intuitionistic Fuzzy Sets ◽  
Regret Theory ◽  
Multi Objective ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Environment ◽  
Objective Model ◽  
Single Objective

This study proposes a two-sided matching decision-making (TSMDM) approach by combining the regret theory under the intuitionistic fuzzy environment. At first, according to the Hamming distance of intuitionistic fuzzy sets and regret theory, superior and inferior flows are defined to describe the comparative preference of subjects. Hereafter, the satisfaction degrees are obtained by integrating the superior and inferior flows of the subjects. The comprehensive satisfaction degrees are calculated by aggregating the satisfaction degrees, based on which, a multi-objective TSMDM model is built. Furthermore, the multi-objective TSMDM model is converted to a single-objective model, the optimal solution of the latter is derived. Finally, an illustrative example and several analyses are provided to verify the feasibility and the effectiveness of the proposed approach.

An Interactive Neural Network for Constrained Multi-Objective Optimization with Application to the Design of Digital Filters

2012 ◽  
Vol 433-440 ◽  
pp. 2808-2816
Author(s):  
Jian Jin Zheng ◽  
You Shen Xia
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Computational Complexity ◽  
Digital Filters ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Optimal Solution ◽  
Multi Objective Optimization ◽  
Multi Objective ◽  
Single Objective

This paper presents a new interactive neural network for solving constrained multi-objective optimization problems. The constrained multi-objective optimization problem is reformulated into two constrained single objective optimization problems and two neural networks are designed to obtain the optimal weight and the optimal solution of the two optimization problems respectively. The proposed algorithm has a low computational complexity and is easy to be implemented. Moreover, the proposed algorithm is well applied to the design of digital filters. Computed results illustrate the good performance of the proposed algorithm.

scholarly journals Geometric Mean Method to Solve Multi-Objective Transportation Problem Under Fuzzy Environment

2020 ◽  
Vol 9 (5) ◽  
pp. 1739-1744
Keyword(s):  
Transportation Problem ◽  
Geometric Mean ◽  
Method Comparison ◽  
Optimal Solution ◽  
Pareto Optimal Solution ◽  
Pareto Optimal ◽  
Numerical Examples ◽  
Multi Objective ◽  
Fuzzy Environment ◽  
Single Objective

Transportation problem is a very common problem for a businessman. Every businessman wants to reduce cost, time and distance of transportation. There are several methods available to solve the transportation problem with single objective but transportation problems are not always with single objective. To solve transportation problem with more than one objective is a typical task. In this paper we explored a new method to solve multi criteria transportation problem named as Geometric mean method to Solve Multi-objective Transportation Problem Under Fuzzy Environment. We took a problem of transportation with three objectives cost, time and distance. We converted objectives into membership values by using a membership function and then geometric mean of membership values is taken. We also used a procedure to find a pareto optimal solution. Our method gives the better values of objectives than other methods. Two numerical examples are given to illustrate the method comparison with some existing methods is also made.

scholarly journals A Survey of Multi-Objective Sequential Decision-Making

2013 ◽  
Vol 48 ◽  
pp. 67-113 ◽  
Author(s):  
D. M. Roijers ◽  
P. Vamplew ◽  
S. Whiteson ◽  
R. Dazeley
Keyword(s):  
Decision Making ◽  
Pareto Front ◽  
Optimal Solution ◽  
Multiple Objectives ◽  
Sequential Decision Making ◽  
Sequential Decision ◽  
Multi Objective ◽  
Scalarization Function ◽  
Future Work ◽  
Single Objective

Sequential decision-making problems with multiple objectives arise naturally in practice and pose unique challenges for research in decision-theoretic planning and learning, which has largely focused on single-objective settings. This article surveys algorithms designed for sequential decision-making problems with multiple objectives. Though there is a growing body of literature on this subject, little of it makes explicit under what circumstances special methods are needed to solve multi-objective problems. Therefore, we identify three distinct scenarios in which converting such a problem to a single-objective one is impossible, infeasible, or undesirable. Furthermore, we propose a taxonomy that classifies multi-objective methods according to the applicable scenario, the nature of the scalarization function (which projects multi-objective values to scalar ones), and the type of policies considered. We show how these factors determine the nature of an optimal solution, which can be a single policy, a convex hull, or a Pareto front. Using this taxonomy, we survey the literature on multi-objective methods for planning and learning. Finally, we discuss key applications of such methods and outline opportunities for future work.

Multi-Objective Generation Scheduling Using Genetic-Based Fuzzy Mathematical Programming Technique

2014 ◽  
pp. 450-474 ◽  
Author(s):  
Abdellah Derghal ◽  
Noureddine Goléa
Keyword(s):  
Mathematical Programming ◽  
Optimal Power Flow ◽  
Optimal Solution ◽  
Fuzzy Mathematical Programming ◽  
Programming Technique ◽  
Solution Approach ◽  
Physical Constraints ◽  
Multi Objective ◽  
Generation Scheduling ◽  
Mathematical Programming Problems

This chapter presents a solution for multi-objective Optimal Power Flow (OPF) problem via a genetic fuzzy formulation algorithm (GA-FMOPF). The OPF problem is formulated as a multiple objective problem subject to physical constraints. The objectives and constraints are modelled as fuzzy mathematical programming problems involving the minimization of the objective function with fuzzy parameters and uncertainties in set of constraints. So the method is capable of representing practical situations in power system operation where the limits on specific variables are soft and the small violations of these limits may be tolerable. Then, genetic algorithm is used in order to seek a feasible optimal solution to the environmental/economic dispatch problem. Illustrative examples are given to clarify the proposed method developed in this manuscript and the performance of this solution approach is evaluated by comparing its results with that of their existing methods.

scholarly journals Stability of multi-objective bi-level linear programming problems under fuzziness

2013 ◽  
Vol 23 (3) ◽  
pp. 343-354
Author(s):  
Mahmoud Abo-Sinna
Keyword(s):  
Linear Programming ◽  
Electronic Commerce ◽  
Partial Information ◽  
Information Service ◽  
Optimal Solution ◽  
Programming Technique ◽  
Multi Objective ◽  
Linear Programming Problems ◽  
Primary Focus ◽  
The Individual

This paper deals with multi-objective bi-level linear programming problems under fuzzy environment. In the proposed method, tentative solutions are obtained and evaluated by using the partial information on preference of the decision-makers at each level. The existing results concerning the qualitative analysis of some basic notions in parametric linear programming problems are reformulated to study the stability of multi-objective bi-level linear programming problems. An algorithm for obtaining any subset of the parametric space, which has the same corresponding Pareto optimal solution, is presented. Also, this paper established the model for the supply-demand interaction in the age of electronic commerce (EC). First of all, the study uses the individual objectives of both parties as the foundation of the supply-demand interaction. Subsequently, it divides the interaction, in the age of electronic commerce, into the following two classifications: (i) Market transactions, with the primary focus on the supply demand relationship in the marketplace; and (ii) Information service, with the primary focus on the provider and the user of information service. By applying the bi-level programming technique of interaction process, the study will develop an analytical process to explain how supply-demand interaction achieves a compromise or why the process fails. Finally, a numerical example of information service is provided for the sake of illustration.

Sign in / Sign up

Export Citation Format

Share Document