TIEJ6002 COM2: Beyond Conventional Optimisation: Data-Driven Multi-Objective Bayesian Optimisation (JSS33) (2–4 op)

Many real-world optimisation problems involve computationally (or financially) expensive evaluations. For example, the shape design of a component in an air intake ventilation system [1] and the stator design in a hydrodynamic pump [2], involve computationally expensive fluid dynamics simulations. Another example of a computationally expensive problem involving a hydrogeological simulation model is the management of hydraulic barriers in coastal aquifers [3]. All these problems are black boxes without any information on gradients and closed-form expressions of objectives. Bayesian optimisation is an efficient tool for solving such kinds of problems. The course will bridge the gap between traditional optimisation limitations and the demands of modern decision-making. By exploring advanced Bayesian techniques integrated with data-driven approaches, the course will cover different approaches for solving complex multi-objective optimisation problems [4] and provide methods to make informed decisions efficiently. The potential of Bayesian optimisation will be shown by providing examples of real-world applications. The course aims to provide a comprehensive understanding of cutting-edge optimisation methodologies and their potential in solving real-world optimisation problems. The following topics will be covered in the course:

• Introduction to (multi-objective) Optimisation:
  - Definition of multi-objective optimisation problems (MOPs) and challenges in solving MOPs
  - Pareto dominance and Pareto optimality
  - Introduction to multi-objective evolutionary algorithms
  - Quality indicators
• Multiple Criteria Decision Making:
  - Role of decision maker
  - Scalarising functions in multi-objective optimisation
  - A priori, a posteriori and interactive methods
• Bayesian Optimisation
  - Understanding Bayesian optimisation principles
  - Gaussian Processes as probabilistic machine learning models
  - Acquisition functions and their role in Bayesian optimisation
  - Mono- and multi-surrogate approaches
  - Exploitation and exploration trade-off in multi-objective Bayesian optimisation
• Future Trends and Challenges:
  - Challenges and open research questions in the field
  - Potential avenues for further exploration

References:

[1] T. Chugh, T. Kratky, K. Miettinen, Y. Jin, P. Makkonen P. (2019) Multiobjective Shape Design in a Ventilation System with a Preference-driven Surrogate-assisted Evolutionary Algorithm, In the proceedings of The Genetic and Evolutionary Computation Conference, Pages 1147–1155, 2019

[2] T. Kratky. Shape optimization of hydraulic surfaces of the impeller and stator parts of hydrodynamic pumps, 2021. Available from: https://theses.cz/id/6ihxiw/. Doctoral theses, Dissertations. Palacky University Olomouc, Faculty of Science.

By the end of this module, students will be able to:

• Understand theoretical and practical challenges in solving black-box computationally expensive optimisation problems.
• Understand the principles of traditional optimisation techniques and recognise their limitations in handling computationally expensive optimisation problems.
• Grasp the fundamentals of probabilistic machine learning and its applications in solving optimisation problems.
• Apply and implement data-driven Bayesian optimisation techniques in optimising multiple conflicting objectives on case studies.

Basics of programming language (preferably Python), Calculus, basic concepts of statistics (random variables, what is a normal distribution, correlation)