Heuristic Methods For Optimization

Content

Objective

This course aims to equip students with the ability to develop versatile and innovative solution strategies for complex and large-scale optimization problems. The primary goal is to introduce the theoretical foundations of heuristic and metaheuristic methods and demonstrate their advantages in various scenarios through concrete examples. The course covers a broad spectrum, from computational complexity to constructive and improvement heuristics, population-based approaches, and modern algorithms in the literature. By the end of the course, students will acquire the necessary knowledge to generate efficient solutions for various academic and industrial optimization problems.

Presentations and term projects play a central role in bridging theoretical knowledge with practical applications. Students will implement metaheuristic algorithms for specific optimization problems, quantitatively and qualitatively evaluate their results, and develop a critical perspective on the strengths and weaknesses of different methods. In this process, they will gain experience in algorithm design and performance analysis and learn how to develop new methods or hybridize existing ones. Thus, the course aims to prepare students for advanced academic research as well as the ability to provide effective solutions for complex industry problems.

Course Content

1. Week: Computational Complexity, Heuristic and Metaheuristic Methods
2. Week: Constructive Heuristics
3. Week: Improvement Heuristics
4. Week: Simulated Annealing, Tabu Search
5. Week: Genetic Algorithms, Differential Evolution Algorithm
6. Week: Particle Swarm Optimization, Ant Colony Optimization
7. Week: Whale Optimization Algorithm, Grey Wolf Optimization
8. Week: Flower Pollination Algorithm, Dragonfly Algorithm
9. Week: Harmony Search Algorithm, Gravitational Search Algorithm
10. Week: Hybridization of Metaheuristic Methods
11. Week: Constraint Handling Approaches
12. Week: Performance Evaluation of Heuristics
13. Week: Term Project Presentations
14. Week: Term Project Presentations

Course Learning Outcomes

Upon successful completion of this course, students will be able to:

1. Analyze the relationship between computational complexity and heuristic/metaheuristic methods, developing a strategic perspective on selecting appropriate approaches for solving large-scale and complex problems.

2. Understand the fundamental principles of constructive and improvement heuristics, applying these methods to various problem types and evaluating their advantages and disadvantages through concrete examples.

3. Comprehend the working mechanisms of population-based algorithms such as Simulated Annealing, Tabu Search, Genetic Algorithms, Particle Swarm Optimization, and Ant Colony Optimization; interpret algorithm variations and literature applications and adapt them to different solutions.

4. Gain proficiency in hybridizing metaheuristic methods, handling constraints, and performance evaluation techniques; implement different algorithms, analyze their results experimentally, and make necessary improvements.

5. Apply a metaheuristic algorithm to a unique optimization problem; compare the algorithm’s performance across multiple test cases and systematically present the results through reports and presentations, improving research, discussion, and reporting skills.

References

1. Gendreau, M., & Potvin, J.-Y. (Eds.). (2019). Handbook of Metaheuristics (3rd ed.). Springer International Publishing.

2. Martí, R., Pardalos, P. M., & Resende, M. G. C. (Eds.). (2018). Handbook of Heuristics. Springer International Publishing.

3. Maniezzo, V., Boschetti, M. A., & Stützle, T. (2021). Matheuristics: Algorithms and Implementations. Springer International Publishing.

4. Talbi, E.-G. (2009). Metaheuristics: From design to implementation. John Wiley & Sons.

5. Blum, C., & Raidl, G. R. (2016). Hybrid metaheuristics: Powerful tools for optimization. Springer International Publishing.

6. Kulkarni, A. J., Mezura-Montes, E., Wang, Y., Gandomi, A. H., & Krishnasamy, G. (Eds.). (2021). Constraint handling in metaheuristics and applications. Springer.

7. Michalewicz, Z., & Fogel, D. B. (2004). How to solve it: Modern heuristics. Springer.

8. Kaveh, A., & Bakhshpoori, T. (2019). Metaheuristics: Outlines, MATLAB codes and examples. Springer Nature Switzerland.

9. Taillard, É. D. (2023). Design of heuristic algorithms for hard optimization: With Python codes for the traveling salesman problem. Springer Nature.

Weekly Contents

Assessment System

ECTS