Advances in Metaheuristics

1. Overview of Optimization

1.1 Introduction

1.2 Combinatorial Optimization

1.3 NP-hardness

1.4 NP-hardness in Combinatorial Optimization

1.5 General Framework of a Combinatorial Optimization Problem

1.6 Methods for Combinatorial Optimization Problems

1.7 A General Optimization Algorithm

1.8 Summary

2. The Master Problem

2.1 Introduction

2.2 The Problem Statement

2.3 The Space of Instances

2.4 The Space of Algorithms

2.5 The Space of Parameters

2.6 Simultaneous Parameter Optimization with AGA

2.7 Independent Parameter Optimization

2.8 The Algorithm Selection Problem

2.9 The No-Free-Lunch in AGA

2.10 Summary

3. Modeling Problems

3.1 The Modeling Process

3.2 Identifying Problems

3.3 Approaching Practical Problems in Operations Research

3.4 Fundamental Models in OR

3.5 Approaching Practical Problems via AI

3.6 Fundamental Models in AI

3.7 Approaching Practical Problems by AGA

3.8 A Fundamental AGA Model

3.9 Summary

4. AGA with Genetic Programming

4.1 Introduction

4.2 The Master Problem in AGA

4.3 Genetic Programming

4.3.1 The General Algorithmic Evolutionary Process

4.3.2 Genetic Operations in GP

4.4 GP as a Metaheuristic

4.5 Modeling the Master Problem with GP

4.5.1 Solution Representation as a Tree

4.5.2 The Fitness Function

4.6 The Evolution of Algorithms

4.7 Constructive and Refinement Algorithms

4.8 Robustness Versus Specialization

4.9 AGA for Population-Based Algorithms

4.10 Rediscovering Algorithms

4.11 AGA Specification Sheet

4.12 Summary

5. AGA and Machine Learning

5.1 Introduction

5.2 Schematic Overview of Machine Learning

5.2.1 Modeling a Practical Problem

5.2.2 Meaning of the Dataset

5.2.3 Hypothetical Model

5.2.4 The Optimization Problem

5.2.5 Algorithms for the Optimization Problem

5.3 Types of Problems in Machine Learning

5.4 Schematic Overview of the Automatic Generation of Algorithms

5.4.1 Problem Instances

5.4.2 Algorithmic Components

5.4.3 The Master Problem

5.4.4 The Resulting Algorithm

5.5 Symbolic Regression

5.6 Summary

6. Producing Metaheuristics Automatically

6.1 Metaheuristics and AGA

6.2 Types of Metaheuristics

6.3 Key Concepts in Metaheuristics

6.4 Solution Container Definition

6.5 Terminals Definition

6.6 Defining Terminals for AGM

6.7 Possible Combinations

6.8 Summary

7. AGA with Reinforcement Learning

7.1 Introduction

7.2 Dynamic Programming

7.3 Bellman's Principle of Optimality

7.4 Dynamic Programming Algorithms

7.5 Dynamic Programming Approaches

7.6 Deciding Agent Problem

7.7 AGA with Reinforcement Learning

7.7.1 Introduction

7.7.2 RL Algorithms

7.7.3 Modeling the Automatic Generation of Algorithms as a DAP

7.8 Summary

8.Conclusions and Future Trends

8.1 Introduction

8.2 Future Directions and Research Paths

8.3 Closing Thoughts