scholarly journals Hierarchical multilevel optimization with multiple-leaders multiple-followers setting and nonseparable objectives

2021 ◽  
Vol 55 (5) ◽  
pp. 2915-2939
Author(s):  
Addis Belete Zewde ◽  
Semu Mitiku Kassa
Keyword(s):  
Decision Makers ◽  
Multilevel Optimization ◽  
Equal Status ◽  
Multiple Decision Makers ◽  
Decision Variables ◽  
Solution Methods ◽  
Upper Level ◽  
Parametric Algorithm ◽  
Multiple Followers ◽  
Hierarchical Multilevel Optimization

Hierarchical multilevel multi-leader multi-follower problems are non-cooperative decision problems in which multiple decision-makers of equal status in the upper-level and multiple decision-makers of equal status are involved at each of the lower-levels of the hierarchy. Much of solution methods proposed so far on the topic are either model specific which may work only for a particular sub-class of problems or are based on some strong assumptions and only for two level cases. In this paper, we have considered hierarchical multilevel multi-leader multi-follower problems in which the objective functions contain separable and non-separable terms (but the non-separable terms can be written as a factor of two functions, a function which depends on other level decision variables and a function which is common to all objectives across the same level) and shared constraint. We have proposed a solution algorithm to such problems by equivalent reformulation as a hierarchical multilevel problem involving single decision maker at all levels of the hierarchy. Then, we applied a multi-parametric algorithm to solve the resulting single leader single followers problem.

scholarly journals A Comprehensive Study on Metaheuristic Techniques Using Genetic Approach

2019 ◽  
Vol 7 (8) ◽  
pp. 23-31
Author(s):  
G. Kalyani ◽  
K. Krishna Jyothi ◽  
T. Pratyusha
Keyword(s):  
Pareto Front ◽  
Optimization Problems ◽  
Real Life ◽  
Decision Makers ◽  
Benchmark Problems ◽  
Multiple Decision Makers ◽  
Trade Offs ◽  
Solution Methods ◽  
Metaheuristic Techniques ◽  
Comprehensive Study

Most real-life optimization problems involve multiple objective functions. Finding  a  solution  that  satisfies  the  decision-maker  is  very  difficult  owing  to  conflict  between  the  objectives.  Furthermore,  the  solution  depends  on  the  decision-maker’s preference.  Metaheuristic solution methods have become common tools to solve these problems.  The  task  of  obtaining  solutions  that  take  account  of  a  decision-maker’s preference  is  at  the  forefront  of  current  research.  It  is  also  possible  to  have  multiple decision-makers with different preferences and with different  decision-making  powers. It may not be easy to express a preference using crisp numbers. In this study, the preferences of multiple decision-makers were simulated  and  a solution based on  a genetic  algorithm was  developed  to  solve  multi-objective  optimization  problems.  The  preferences  were collected  as  fuzzy  conditional  trade-offs  and  they  were  updated  while  running  the algorithm interactively with the decision-makers. The proposed method was tested using well-known benchmark problems.  The solutions were found to converge around the Pareto front of the problems.

FUZZY BILEVEL PROGRAMMING: MULTI-OBJECTIVE AND MULTI-FOLLOWER WITH SHARED VARIABLES

2008 ◽  
Vol 16 (supp02) ◽  
pp. 105-133 ◽  
Author(s):  
GUANGQUAN ZHANG ◽  
JIE LU ◽  
YA GAO
Keyword(s):  
Bilevel Programming ◽  
Optimization Problems ◽  
Programming Model ◽  
Hierarchical Optimization ◽  
Multi Objective ◽  
Decision Variables ◽  
Shared Variables ◽  
Upper Level ◽  
Bilevel Programming Model ◽  
Multiple Followers

Bilevel programming deals with hierarchical optimization problems in which the leader at the upper level attempts to optimize his or her objectives, but subject to a set of constraints and the follower's reactions. Typical bilevel programming considers one leader one follower situation and supposes each of them has only one objective. In real world situations, multiple followers may be involved and they may be with different relationships such as sharing decision variables or not, sharing objectives or not. Therefore, the leader's decision will be affected not only by those followers' reactions but also by their relationships. In addition, any of the leader and/or these followers may have multiple conflict objectives that should be optimized simultaneously. Furthermore, the parameters of a bilevel programming model may be described by uncertain values. This paper addresses all these three issues as a whole by particularly focusing on the situation of sharing decision variables among followers. It first proposes a set of fuzzy multi-objective multi-follower bilevel programming (FMMBP) models to describe the complex issue. It then presents an approximation branch-and-bound algorithm to solve the FMMBP problems. Finally, two examples illustrate the proposed models and algorithm.

scholarly journals ALGORITMA FUZZY GOAL PROGRAMMING UNTUK MASALAH PEMROGRAMAN BILEVEL MULTIOBJEKTIF

2018 ◽  
Vol 10 (1) ◽  
pp. 1
Author(s):  
Syarifah Inayati
Keyword(s):  
Membership Function ◽  
Goal Programming ◽  
Fuzzy Goal Programming ◽  
Hierarchical Organization ◽  
Decision Makers ◽  
Decision Variables ◽  
Fuzzy Goals ◽  
Fuzzy Goal ◽  
Upper Level ◽  
The Membership Function

Bilevel multiobjective programming problems are mathematical programming that solves the problem of planning with two decision makers (DM) in two level or hierarchical organization with the objective function of each organization can be more than one. In this paper, we discussed the special case of this problem with single decision maker at the upper level and multiple decision makers at the lower level. This problem can be solved using fuzzy goal programming (FGP) approach. In this approach, the membership function for the defined fuzzy goals of all objective functions of DMs at the two levels was developed first in the model formulation of the problem. Thus the membership function for vector of fuzzy goals of the decision variables controlled by the leader. Then FGP approach requires the leader to set goals for each objective that he/she wishes to attain. A preferred solution is then defined for minimizes the deviations from the set of goals. Numerical example is provided to illustrate the approach.

Linear Quadratic Nash Game of Stochastic Singular Time-Delay Systems with Multiple Decision Makers

2015 ◽  
Vol 3 (5) ◽  
pp. 472-480
Author(s):  
Huainian Zhu ◽  
Guangyu Zhang ◽  
Chengke Zhang ◽  
Ying Zhu ◽  
Haiying Zhou
Keyword(s):  
Time Delay ◽  
Decision Makers ◽  
Delay Systems ◽  
Linear Matrix ◽  
Time Delay Systems ◽  
Linear Quadratic ◽  
Nash Game ◽  
Multiple Decision Makers ◽  
Nash Strategies ◽  
Singular Time

AbstractThis paper discusses linear quadratic Nash game of stochastic singular time-delay systems governed by Itô’s differential equation. Sufficient condition for the existence of Nash strategies is given by means of linear matrix inequality for the first time. Moreover, in order to demonstrate the usefulness of the proposed theory, stochastic H2∕H∞control with multiple decision makers is discussed as an immediate application.

Method for Selecting Storage Enterprises Based on IFHA

2015 ◽  
Vol 713-715 ◽  
pp. 1769-1772
Author(s):  
Jie Wu ◽  
Lei Na Zheng ◽  
Tie Jun Pan
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Group Decision ◽  
Decision Makers ◽  
Decision Problems ◽  
Decision Making Process ◽  
Final Decision ◽  
Multiple Decision Makers ◽  
Intuitionistic Fuzzy ◽  
Averaging Operator

In order to reflect the decision-making more scientific and democratic, modern decision problems often require the participation of multiple decision makers. In group decision making process,require the use of intuitionistic fuzzy hybrid averaging operator (IFHA) to get the final decision result.

scholarly journals Identification of reverse logistics decision types from mathematical models

2018 ◽  
Vol 11 (2) ◽  
pp. 239 ◽  
Author(s):  
Pascual Cortés Pellicer ◽  
Faustino Alarcón Valero
Keyword(s):  
Decision Making ◽  
Mathematical Models ◽  
Reverse Logistics ◽  
Business Processes ◽  
Raw Materials ◽  
Decision Makers ◽  
Social Awareness ◽  
Decision Variables ◽  
Object Of Study ◽  
Aid Decision

Purpose: The increase in social awareness, politics and environmental regulation, the scarcity of raw materials and the desired “green” image, are some of the reasons that lead companies to decide for implement processes of Reverse Logistics (RL). At the time when incorporate new RL processes as key business processes, new and important decisions need to be made. Identification and knowledge of these decisions, including the information available and the implications for the company or supply chain, will be fundamental for decision-makers to achieve the best results. In the present work, the main types of RL decisions are identified.Design/methodology/approach: This paper is based on the analysis of mathematical models designed as tools to aid decision making in the field of RL. Once the types of interest work to be analyzed are defined, those studies that really deal about the object of study are searched and analyzed. The decision variables that are taken at work are identified and grouped according to the type of decision and, finally, are showed the main types of decisions used in mathematical models developed in the field of RL.    Findings: The principal conclusion of the research is that the most commonly addressed decisions with mathematical models in the field of RL are those related to the network’s configuration, followed by tactical/operative decisions such as the selections of product’s treatments to realize and the policy of returns or prices, among other decisions.Originality/value: The identification of the main decisions types of the reverse logistics will allow the managers of these processes to know and understand them better, while offer an integrated vision of them, favoring the achievement of better results. 

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