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.

Goal programming approach for solving multi-objective fractional transportation problem with fuzzy parameters

2019 ◽  
Vol 53 (1) ◽  
pp. 157-178 ◽  
Author(s):  
Paraman Anukokila ◽  
Bheeman Radhakrishnan ◽  
Antony Anju
Keyword(s):  
Goal Programming ◽  
Transportation Problem ◽  
Fuzzy Numbers ◽  
Decision Makers ◽  
Programming Approach ◽  
Multi Objective ◽  
Proposed Model ◽  
Fuzzy Goal ◽  
Fuzzy Parameters ◽  
Interval Valued

In this paper, authors studied a goal programming approach for solving multi-objective fractional transportation problem by representing the parameters (γ, δ) in terms of interval valued fuzzy numbers. Fuzzy goal programming problem with multiple objectives is difficult for the decision makers to determine the goal valued of each objective precisely. The proposed model presents a special type of non-linear (hyperbolic) membership functions to solve multi-objective fractional transportation problem with fuzzy parameters. To illustrate the proposed method numerical examples are solved.

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 A Method for Integration of Preferences to a Multi-Objective Evolutionary Algorithm Using Ordinal Multi-Criteria Classification

2021 ◽  
Vol 26 (2) ◽  
pp. 27
Author(s):  
Alejandro Castellanos-Alvarez ◽  
Laura Cruz-Reyes ◽  
Eduardo Fernandez ◽  
Nelson Rangel-Valdez ◽  
Claudia Gómez-Santillán ◽  
...  
Keyword(s):  
Genetic Algorithm ◽  
Selective Pressure ◽  
Optimization Problems ◽  
Region Of Interest ◽  
Decision Makers ◽  
Multiple Objective ◽  
Objective Functions ◽  
Multi Objective ◽  
Imperfect Knowledge ◽  
Real World Problems

Most real-world problems require the optimization of multiple objective functions simultaneously, which can conflict with each other. The environment of these problems usually involves imprecise information derived from inaccurate measurements or the variability in decision-makers’ (DMs’) judgments and beliefs, which can lead to unsatisfactory solutions. The imperfect knowledge can be present either in objective functions, restrictions, or decision-maker’s preferences. These optimization problems have been solved using various techniques such as multi-objective evolutionary algorithms (MOEAs). This paper proposes a new MOEA called NSGA-III-P (non-nominated sorting genetic algorithm III with preferences). The main characteristic of NSGA-III-P is an ordinal multi-criteria classification method for preference integration to guide the algorithm to the region of interest given by the decision-maker’s preferences. Besides, the use of interval analysis allows the expression of preferences with imprecision. The experiments contrasted several versions of the proposed method with the original NSGA-III to analyze different selective pressure induced by the DM’s preferences. In these experiments, the algorithms solved three-objectives instances of the DTLZ problem. The obtained results showed a better approximation to the region of interest for a DM when its preferences are considered.

A multi-objective optimization model for logistic planning in the crisis response phase

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Mohammad Mahdi Ershadi ◽  
Hossein Shams Shemirani
Keyword(s):  
Objective Function ◽  
Optimization Model ◽  
Crisis Response ◽  
Multi Objective Optimization ◽  
Content Type ◽  
Multi Objective ◽  
Proposed Model ◽  
Different Types ◽  
Response Phase ◽  
Logistic Planning

PurposeProper planning for the response phase of humanitarian relief can significantly prevent many financial and human losses. To this aim, a multi-objective optimization model is proposed in this paper that considers different types of injured people, different vehicles with determining capacities and multi-period logistic planning. This model can be updated based on new information about resources and newly identified injured people.Design/methodology/approachThe main objective function of the proposed model in this paper is minimizing the unsatisfied prioritized injured people in the network. Besides, the total transportation activities of different types of vehicles are considered as another objective function. Therefore, these objectives are optimized hierarchically in the proposed model using the Lexicographic method. This method finds the best value for the first objective function. Then, it tries to optimize transportation activities as the second objective function while maintaining the optimality of the first objective function.FindingsThe performances of the proposed model were analyzed in different cases and its robust approach for different problems was shown within the framework of a case study. Besides, the sensitivity analysis of results shows the logical behavior of the proposed model against various factors.Practical implicationsThe proposed methodology can be applied to find the best response plan for all crises.Originality/valueIn this paper, we have tried to use a multi-objective optimization model to guide and correct response programs to deal with the occurred crisis. This is important because it can help emergency managers to improve their plans.

scholarly journals Sailing Speed Optimization Model for Slow Steaming Considering Loss Aversion Mechanism

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Yuzhe Zhao ◽  
Jingmiao Zhou ◽  
Yujun Fan ◽  
Haibo Kuang
Keyword(s):  
Loss Aversion ◽  
Optimization Model ◽  
Value Function ◽  
Fitness Function ◽  
Decision Makers ◽  
Value Functions ◽  
Delivery Delay ◽  
Slow Steaming ◽  
Proposed Model ◽  
Speed Optimization

This paper analyses loss aversion mechanism (LAM) of the shipping company’s decision-makers about the risk-based decision (RBD) for slow steaming and generalizes a novel optimization model for the sailing speed through the trade-off between fuel consumption, SOx emissions and delivery delay. The value functions against the benchmark speed were constructed based on physiological expected utility (PEU) to reveal the features of loss aversion, and the objective function was derived from these value functions with the aim to optimize the sailing speed. After that, a Genetic Algorithm (GA) solution with fitness function and special operators was built to solve the proposed model. Finally, the model was applied to pinpoint the PEU for the optimal sailing speed against the benchmark speed, and the sensitivity of the model was discussed with different benchmark speeds, value function weights and input parameters. The analysis shows that the proposed model can assist the slow steaming RBD based on the inner feelings of the shipping company’s decision-makers, offering a novel tool for sailing speed optimization.

scholarly journals Multi-Objective Optimization Model for P + R and K + R Facilities’ Collaborative Layout Decision

2020 ◽  
Vol 12 (21) ◽  
pp. 8833
Author(s):  
Wei Wang ◽  
Zhentian Sun ◽  
Zhiyuan Wang ◽  
Yue Liu ◽  
Jun Chen
Keyword(s):  
Optimization Model ◽  
Road Traffic ◽  
Supply And Demand ◽  
Optimal Decision ◽  
Multi Objective Optimization ◽  
Service Capacity ◽  
Location Selection ◽  
Multi Objective ◽  
Proposed Model ◽  
Collaborative Decision

In order to reduce the pressure on urban road traffic, multi-modal travel is gradually replacing single-modal travel. Park and ride (P + R) and kiss and ride (K + R) are effective methods to integrate car transportation and rail transit. However, there is often an imbalance between supply and demand in existing car occupant transfer facilities, which include both P + R and K + R facilities. Therefore, we aim to conduct a research on P + R and K + R facilities’ collaborative decision. It first classifies car occupant transfer facilities into types and levels and sets the service capacity of each category. On the premise of ensuring the occupancy of parking spaces, our model aims to maximize the intercepted vehicle mileage and transfer utility and establishes an optimal decision model for car occupant transfer facilities. The model collaboratively decides the facilities in terms of location selection, layout arrangement, and overflow demand conversion to balance the supply and demand. We choose Chengdu as an example, apply the multi-objective optimization model of car occupant transfer facilities, give improved schemes, and further explore the influence of the quantity of facilities on the optimization objectives. The results show that the scheme obtained by the proposed model is significantly better than the existing scheme.

scholarly journals Genetic Algorithm Based Solution of Fuzzy Multi-Objective Transportation Problem

2020 ◽  
Vol 5 (6) ◽  
pp. 1452-1467
Author(s):  
Jaydeepkumar M. Sosa ◽  
Jayesh M. Dhodiya
Keyword(s):  
Genetic Algorithm ◽  
Transportation Problem ◽  
Shape Parameter ◽  
Optimization Problems ◽  
Decision Makers ◽  
Objective Functions ◽  
Full Data ◽  
Multi Objective ◽  
Life Problems ◽  
Modern Era

Optimizing problems in the modern era, the single objective optimization problems are insufficient to hold the full data of the problem. Therefore, multi-objective optimization problems come to the rescue. Similarly, in daily life problems, the parameters used in the optimization problem are not always fixed but there may be some uncertainty and it can characterize by fuzzy number. This work underlines the genetic algorithm (GA) based solution of fuzzy transportation problem with more than one objective. With a view to providing the multifaceted choices to decision-maker (DM), the exponential membership function is used with the decision-makers desired number of cases which consisted of shape parameter and aspiration level. Here, we consider the objective functions which are non-commensurable and conflict with each other. To interpret, evaluate and exhibit the usefulness of the proposed method, a numerical example is given.

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