This book discusses the basic ideas, underlying principles, mathematical formulations, analysis and applications of the different combinatorial problems under uncertainty and attempts to provide solutions for the same. Uncertainty influences the behaviour of the market to a great extent. Global pandemics and calamities are other factors which affect and augment unpredictability in the market. The intent of this book is to develop mathematical structures for different aspects of allocation problems depicting real life scenarios. The novel methods which are incorporated in practical scenarios under uncertain circumstances include the STAR heuristic approach, Matrix geometric method, Ranking function and Pythagorean fuzzy numbers, to name a few. Distinct problems which are considered in this book under uncertainty include scheduling, cyclic bottleneck assignment problem, bilevel transportation problem, multi-index transportation problem, retrial queuing, uncertain matrix games, optimal production evaluation of cotton in different soil and water conditions, the healthcare sector, intuitionistic fuzzy quadratic programming problem, and multi-objective optimization problem. This book may serve as a valuable reference for researchers working in the domain of optimization for solving combinatorial problems under uncertainty. The contributions of this book may further help to explore new avenues leading toward multidisciplinary research discussions.
Author(s): Ritu Arora, Shalini Arora, Anand Kulkarni, Patrick Siarry
Series: Advances in Metaheuristics
Publisher: CRC Press
Year: 2023
Language: English
Pages: 220
City: Boca Raton
Cover
Half Title
Series Information
Title Page
Copyright Page
Table of Contents
Preface
About the Editors
1 Estimation of Uncertainties for Multiserver Queuing Systems with Bernoulli Feedback
Introduction
Portrayal of Model
Matrix Geometric Method
System Performance Measures
Illustration
Application Example
Conclusion
References
2 Optimality for Fuzzy Transportation Problem under Ranking Method
Introduction
Classic Set
Fuzzy Set
Membership Function
Motivation
Network Flow Programming
Shortest Path Problem
Mines and Factories
Moving Books (The Importance of the Cost Function)
Abstract Formulation (Monge and Kantorovich Formulations)
Methods
North-West Corner Rule
Vogel's Approximation Method
uv-Method
Ranking Method
Problem Formulation
Preliminaries
Fuzzy Transportation Problem
Robust Ranking Transportation Problem
Application
Least Time Fuzzy Transportation Model
Numerical Examples
Conclusion
Acknowledgements
Conflict of Interest
References
3 Solution of Bilevel Linear Fractional Transportation Problem with Pythagorean Fuzzy Numbers
Introduction
Literature Review
Bilevel Linear Fractional Transportation Problem
Basic Definitions
Bilevel Fractional Transportation Problem with Pythagorean Fuzzy Parameters
Solution Methodology for BFTPPFN
Fuzzy Programming Approach
Goal Programming Approach
Application of BLFTP with Pythagorean Fuzzy Parameters
Conclusions and Prospective Work
Acknowledgements
Conflict of Interest
References
4 Optimal Production Evaluation of Cotton in Different Soil and Water Conditions in Sundarban of West Bengal under Hesitant Interval Fuzzy Environment Using Projection Measures
Introduction
Cotton Production Problem
MCDM and Uncertainty
Literature Review
Mathematical Preliminaries
Hesitant Interval-Valued Fuzzy Linguistic Element (HIFLE)
Projection Measure in HIFLE
Fuzzy MCDM Problem
MCDM Method Based on HIFLE Using Projection
Case Studies: Cotton Production in Sundarban
Results and Discussion
Conclusion
Conflict of Interest
References
5 A Novel Approach for Feature Detection in Vector Graphics
Introduction
Mathematical Formulation
Analysis of Results
Dataset Description
Experimental Setup
Results
Conclusion and Future Scope
Acknowledgements
Appendix 5A: An Example of Mathematical Processing of XML of a SVG Image
References
6 On Uncertain Matrix Games Involving Linguistic Pythagorean Fuzzy Sets
Introduction
Inspiration and Significance for Suggested Methodology
Definitions and Properties
Linguistic Pythagorean Fuzzy Set (LPFS)
Matrix Games with Uncertain Information
Solution Technique for Matrix Games Characterized by LPFVs
Numerical Illustration
Comparative Study
Concluding Note
References
7 Cyclic Surgery Scheduling using Variations of Cohort Intelligence
Introduction
Variations of CI
Real-World Application of Healthcare Assignment Problem
Results and Discussion
Conclusion
References
8 Cone Method for Uncertain Multiobjective Optimization Problems with Minmax Robustness
Introduction
Prerequisite
(Deterministic) MOP and Cone Method
UOPs and Minmax Robustness
Robust Counterparts for Uncertain MOPs
Cone Method for Uncertain MOPs
Conclusion
Pros and Cons of Minmax Robustness
Future Directions
Acknowledgements
References
9 Solving Multi-Index Transportation Problem with Axial Constraints Having Impaired Flow
Introduction
Theoretical Development
Impaired Flow
Numerical Examples
Additional Computational Results
Conclusion
References
10 STAR Heuristic Method: A Novel Approach and Its Comparative Analysis with CI Algorithm to Solve CBAP in Healthcare
Introduction
Cyclic Bottleneck Assignment Problem (CBAP)
STAR Heuristic Method
Cohort Intelligence (CI)
Comparison with CI
Literature Review
Dataset
STAR Heuristic Algorithm
Flowchart
Implementation Results
Result Discussion
Boundary Case
Conclusions and Future Scope
References
11 Development and Optimization of Quadratic Programming Problems with Intuitionistic Fuzzy Parameters
Introduction
Preliminaries
Intuitionistic Fuzzy Quadratic Programming Problem
Model Formulation
Proposed Solution Methodology
Numerical Illustration
Conclusion
Acknowledgements
References
Index
