Mathematical Modelling and Optimization of Engineering Problems (Nonlinear Systems and Complexity, 30)

Preface
Contents
1 Heuristic Techniques for Real-Time Order Acceptance and Scheduling in Metal Additive Manufacturing
	1.1 Introduction
	1.2 Literature Review
	1.3 Problem Statement
		1.3.1 Assumptions
		1.3.2 Notation
			Decision Variables
			Indicators
		1.3.3 Basic Formulations
		1.3.4 Objective Function
		1.3.5 Constraints
	1.4 Meta-heuristic Procedures
		1.4.1 Generation of Feasible Solutions
			1.4.1.1 Single Machine
			1.4.1.2 Multiple Machines
		1.4.2 Selection Rules
			1.4.2.1 Stochastic Selection
			1.4.2.2 Profit-Time Based Selection
			1.4.2.3 Cost Benefit Based Selection
	1.5 Computational Experiments
		1.5.1 Data Generation
		1.5.2 Experimental Results and Discussions
			1.5.2.1 The Difference of Stochastic Results
			1.5.2.2 Performance of Non-random Selection Rules
	1.6 Conclusions and Future Research
	References
2 Developing a Nationwide Energy Storage Policy by Optimal Size and Site Selection
	2.1 Introduction
	2.2 Optimization Models in Energy Economics
		2.2.1 Economic Dispatch Model
		2.2.2 Unit Commitment Model
		2.2.3 Energy Storage System Modeling in UC
		2.2.4 AC Optimal Power Flow Model
		2.2.5 DC Optimal Power Flow Model
		2.2.6 Optimal Energy Storage System Placement and Sizing Model
	2.3 Optimization of the Nationwide Energy Storage System
		2.3.1 The Maximum Sizing of Energy Storage Systems
		2.3.2 Distribution of Energy Storage Systems Within the Network
		2.3.3 The Proposed Bi-level Optimization for Sizing and Siting of Storage Units
	2.4 Case Study: Power Systems in Turkey
	2.5 Discussion on a Nationwide Energy Policy
	2.6 Conclusion
	Nomenclature
	References
3 Pontryagin\'s Principle for a Class of Discrete Time Infinite Horizon Optimal Growth Problems
	3.1 Introduction
	3.2 One-Sector Optimal Growth Model
		3.2.1 Social Planner\'s Problem of E
		3.2.2 Necessary and Sufficient Conditions of Optimality
	3.3 Optimal Growth Model with an Natural Exhaustible Resource
		3.3.1 Management Problem of Eenr
		3.3.2 Necessary and Sufficient Conditions of an Optimal Management of a Natural Resource
	3.4 Optimal Growth Model of a Forest: An Optimal Management Model of Forestry
		3.4.1 Planner\'s Management Problem
		3.4.2 Necessary Conditions of Optimality
	3.5 Conclusion
	References
4 A Medical Modelling Using Multiple Linear Regression
	4.1 Introduction
	4.2 Materials and Methods
		4.2.1 Study Samples
		4.2.2 Multiple Linear Regression Analysis
		4.2.3 Test for the Model
		4.2.4 Residual Analysis
	4.3 Building Regression Analysis Model
	4.4 Discussion and Analysis
	4.5 Conclusions and Recommendations
	References
5 Lie Group Method Solution for Two-Dimensional Heat and Viscous Flow Driven by Injection Through a Deformable Rectangular Channel with Porous Walls
	5.1 Introduction
	5.2 Mathematical Modelling of the Problem
		5.2.1 Problem Statement
		5.2.2 Flow Configuration
		5.2.3 Forces Affecting the Dynamics of the Flow
			5.2.3.1 Surface Force
			5.2.3.2 Body Forces
		5.2.4 Derivation of Governing Equations
			5.2.4.1 Conservation of Mass
			5.2.4.2 Conservation of Momentum
			5.2.4.3 Conservation of Energy
			5.2.4.4 Boundary Conditions
	5.3 Mathematical Representation of Problem
		5.3.1 Governing Equations and Boundary Conditions
	5.4 Solution of the Problem
		5.4.1 Lie Group Analysis
		5.4.2 Semi-Analytical Solution
	5.5 Results and Discussion
		5.5.1 Effects of Wall Dilation
		5.5.2 Effects of Reynolds number inside the Filtration Chamber
		5.5.3 Effects of Porosity Variable Inside the Filtration Chamber
		5.5.4 Effects of Stuart Number Inside the Filtration Chamber
		5.5.5 Temperature Distribution Inside the Chamber
	5.6 Concluding Remarks
	References
6 Optimal Siting of Wind Turbines in a Wind Farm
	6.1 Introduction
	6.2 Numerical Methods of the Present Study
		6.2.1 Wake Model
		6.2.2 Power Model
	6.3 Methodology
		6.3.1 Problem Formulation
		6.3.2 Initial Population Based on Elevation Values
		6.3.3 Genetic Algorithm for Optimization
			6.3.3.1 Population Formation
			6.3.3.2 Selection
			6.3.3.3 Crossover
			6.3.3.4 Mutation
			6.3.3.5 Genetic Algorithm Parameters
	6.4 Results and Discussion
	6.5 Conclusion
	References
7 RSM-Based Optimization of Excitation Capacitance and Speed for a Self-Excited Induction Generator
	7.1 Introduction
	7.2 Modelling of SEIG
	7.3 Voltage Build-up process
	7.4 Analysis
	7.5 Response Surface Method
	7.6 Results and Discussions
	7.7 Conclusion
	References
8 Distance-Constrained Vehicle Routing Problems: A Case Study Using Artificial Bee Colony Algorithm
	8.1 Introduction
	8.2 Research Background
	8.3 Artificial Bee Colony (ABC) Algorithm
		8.3.1 Initialization of the Population
		8.3.2 Initialization of the Bee Phase
		8.3.3 Onlooker Bee Phase
		8.3.4 Scout Bee Phase
		8.3.5 Stopping Phase
	8.4 Case Study
	8.5 Results and Discussion
	8.6 Conclusion
	References
9 Fractional Model for Type 1 Diabetes
	9.1 Introduction
		9.1.1 Some Concepts of Fractional Calculus
	9.2 Description of the Model
	9.3 Model Analysis
	9.4 Global Stability of the Disease-Free Equilibrium
	9.5 Numerical Results
	9.6 Conclusion
	References
10 Mathematical Modelling and Additive Manufacturingof a Gyroid
	10.1 Infinite Periodic Minimal Surfaces (IPMS) Without Self-intersections: Gyroid
	10.2 Additive Manufacturing Technology
	10.3 3D Printing Process of an IPMS Gyroid
		10.3.1 Creating the 3D Mathematical Model of the IPMS Gyroid with K3DSurf Program
		10.3.2 Converting the CAD Model Data to ``.obj\'\' or ``.stl\'\' File Format
		10.3.3 Generating a Solid, Thickened Shell or Hollow CAD Model
		10.3.4 Slice the Model into Layers, Generate the Travel Movements and Support Structure
		10.3.5 3D Printing of the Model
			10.3.5.1 Fused Deposition Modelling
			10.3.5.2 3D Printing of the IPMS Gyroid
		10.3.6 Removing the Support Material If Any and Apply Finishing Process
	10.4 Conclusion
	References
Index