Advances on Mathematical Modeling and Optimization with Its Applications

✍ Scribed by Gunjan Mukherjee, Biswadip Basu Mallik, Rahul Kar, Aryan Chaudhary

• Publisher: CRC Press
• Year: 2024
• Tongue: English
• Leaves: 279
• Category: Library

✦ Synopsis

Advances on Mathematical Modeling and Optimization with Its Applications discusses optimization, equality, and inequality constraints and their application in the versatile optimizing domain. It further covers non-linear optimization methods such as global optimization, and gradient-based non-linear optimization, and their applications.

• Discusses important topics including multi-component differential equations, geometric partial differential equations, and computational neural systems.

• Covers linear integer programming and network design problems, along with an application of the mixed integer problems.

• Discusses constrained and unconstrained optimization, equality, and inequality constraints, and their application in the versatile optimizing domain.

• Elucidates the application of statistical models, probability models, and transfer learning concepts.

• Showcases the importance of multi-attribute decision modeling in the domain of image processing and soft computing.

The text is primarily for senior undergraduate and graduate students, and academic researchers in the fields of mathematics, statistics, and computer science.

✦ Table of Contents

Cover
Half Title
Series Page
Title Page
Copyright Page
Table of Contents
Preface
Editors
Contributors
Chapter 1 Mathematical Modeling and Analysis of a Marine Ecosystem: A Deterministic and Stochastic Process
1.1 Introduction
1.2 The Mathematical Model
1.3 Some Preliminary Results
1.4 Optimal Harvesting Policy
1.5 The Stochastic Model
1.6 Numerical Simulations
1.7 Discussion
References
Chapter 2 Multi-Criteria Optimisation and Compromise Solution to Select Financially Efficient NIFTY IT Companies Pre and During COVID-19 Pandemic
2.1 Introduction
2.2 Literature Review
2.3 Research Objectives
2.4 Research Methodology
2.5 Data and Findings
2.6 Suggestions for Compromise Solution
2.7 Conclusions
2.8 Limitations
2.9 Future Scope of Study
References
Chapter 3 Conjoint Analysis: A Heuristic Decision-Making Model of Product Selection
3.1 Introduction
3.2 Historical Background of Conjoint Analysis
3.3 Statistical Modeling of Conjoint Analysis
3.4 Steps of Conjoint Analysis
3.5 Application of Conjoint Analysis for Market Researchers
3.6 An Illustration of Conjoint Analysis with the Application of Software
3.7 Merits and Demerits of Conjoint Analysis
3.8 Conclusion
References
Chapter 4 Ranking of Wear Behavior Characteristics in Al6061 Reinforced with Industrial Waste Materials Using PROMETHEE and MOORA Methods
4.1 Introduction
4.2 Material and Methods
4.3 Experimental Procedure
4.4 Result Analysis
4.5 Conclusion
References
Chapter 5 Aqueous Humor Flow in the Schlemm's Canal Via Rectangular Channel: Mathematical Modeling for Analytical Results, Numerical Experiments, and Implications for Treatments
5.1 Introduction
5.2 Model Description
5.3 Governing Equation
5.4 Boundary Conditions
5.5 Problem Formulation
5.6 Results and Discussion
5.7 Conclusion
References
Chapter 6 Solving Fuzzy Nonlinear Optimization Problems Using Evolutionary Algorithms
6.1 Introduction
6.2 Literature Review
6.3 Methodology
6.4 Discussion of Strengths and Limitations of Existing Approaches
6.5 EAs for Fuzzy Nonlinear Optimization
6.6 Case Studies
6.7 Comparison with Other Methods
6.8 Conclusion and Future Directions
References
Chapter 7 Mathematical Modelling Techniques and Applications of Wireless Communication Using Fuzzy Logic
7.1 Introduction
7.2 Fuzzy Logic Control Overview and Classification
7.3 The Benefits and Capabilities of Fuzzy Logic Techniques
7.4 Wireless Sensor Network's Features (WSN)
7.5 Wireless Sensor Network Difficulties
7.6 List of Various Techniques and Applications of Wireless Communication Using Fuzzy Logic
7.7 Key Findings and Results of the Research Chapter
7.8 Summary and Future Study
7.9 Conclusion
References
Chapter 8 Availability Optimization of Poly-Ethylene Terephthalate Bottle Hot Drink Filling System Using Particle Swarm and Grey Wolf Optimizers
8.1 Introduction
8.2 System Description, Notations, and Assumptions
8.3 Mathematical Modeling of the System in Steady State
8.4 Evolutionary Algorithms
8.5 Results and Discussion
8.6 Conclusion
References
Chapter 9 Optimisation of Drilling Parameters on Glass Fibre Reinforced Polymer Composites with Stainless Steel Mesh Using Taguchi and Grey Fuzzy Relation Method
9.1 Introduction
9.2 Experimental Method
9.3 Results and Discussion
9.4 Conclusion
References
Chapter 10 A Comprehensive Mathematical Framework for Diabetes and its Complications in Crisp and Fuzzy Settings
10.1 Introduction
10.2 Fuzzy Differential Equations
10.3 Basic Concepts
10.4 Predictive Mathematical Model of Diabetes in a Crisp Environment
10.5 Mathematical Modelling of Diabetes in Fuzzy Environment
10.6 Stability Analysis
10.7 Numerical Illustration
10.8 Results and Discussion
10.9 Conclusion
References
Chapter 11 Applications of Mathematical Techniques to Artificial Intelligence: Mathematical Methods, Algorithms, Computer Programming and Applications
11.1 Introduction: Background and Driving Forces
11.2 Linear Algebra
11.3 Applications of Statistics in Data Science Through Machine Learning Algorithms
11.4 Some Other Statistical Methods
11.5 Calculus
11.6 Optimization or Operation Research
11.7 Computer Programs
11.8 AI Applications
11.9 Concluding Remarks
References
Chapter 12 Prediction of Winning Team in Soccer Game: A Supervised Machine Learning-Based Approach
12.1 Introduction
12.2 Literature Survey
12.3 Background
12.4 Result Analysis
12.5 Conclusions and Future Works
Conflict of Interest
Funding
References
Chapter 13 Asset Liability Management Model Based on Duration and Convexity for Commercial Banks
13.1 Introduction
13.2 Prerequisite Terms
13.3 Mathematical Model
13.4 Mathematical Analysis
13.5 Numerical Illustrations
13.6 Conclusions
References
Chapter 14 A Qualitative Mathematical Analysis of Pandemic SARS-Cov-2 with Special Emphasis on Uncertain Environments
14.1 Introduction
14.2 Model of SARS-Cov-2 with Time Delay
14.3 Mathematical Analysis of System (14.2) Without Time Delay
14.4 Investigation of the Ideal's Stability at Steadiness Without Time Delay
14.5 Analysis of the Delayed NVIR Model
14.6 Numerical Simulations
14.7 Discussion and Concluding Remarks
Contributions of Authors
Conflict of Interest
Acknowledgment
References
Chapter 15 A Game Theory Model to Analyze Business Strategies for Increasing Profits: Analytical and Computational Approaches
15.1 Introduction: Background and Driving Forces
15.2 The Company Context
15.3 Game Theory as an Analytica Approach
15.4 The Game Model
15.5 Value of Fuels and Lignocellulose as Raw Material
15.6 Recommendations
15.7 Implications and Conclusion
Acknowledgment
References
Chapter 16 An Efficient Course Assignment Technique Based on Teachers Rating to Support Higher Education Systems
16.1 Introduction
16.2 Related Works
16.3 Materials and Methods
16.4 Proposed Method of Assignment for Course Assignment
16.5 Case Study
16.6 Results
16.7 Conclusion
References
Index