TIES5990 COM1: Evolutionary Multi-Objective Optimization (JSS35) (2 op)

In general, real-world optimization problems include multiple objectives. Thus, they can be formulated as multi-objective optimization problems. Those problems do not have a single optimal solution but multiple tradeoff solutions since multiple objectives cannot be simultaneously optimized by a single solution. However, multi-objective optimization problems are usually handled as single-objective optimization problems to find a single solution by focusing only on a main objective or combining multiple objectives into a scalarizing function. In this course, students will learn how to handle multiple objectives to find multiple candidate solutions by considering the tradeoff relation among the objectives. Emphasis will be given on the evolutionary multi-objective optimization (EMO) approach where a variety of solutions with different tradeoffs are evolved as a population to search for the entire tradeoff front of a multi-objective optimization problem. This course will address the following topics:

- Formulations of single-objective and multi-objective optimization problems with some examples

- Pareto optimality and its relation to the objective space dimensionality

- Scalarizing functions and their contour lines

- Decision maker's role and preference information

- EMO approach, MCDM approach and their hybrid approach

- Basic framework of single-objective evolutionary algorithms

- Basic framework of multi-objective evolutionary algorithms

- Search behavior analysis of NSGA-II and its modifications

- Related websites: PlatEMO and Pymoo

- Search behavior analysis of MOEA/D and its modifications

- Search behavior analysis of SMS-EMOA and its modifications

- Search behavior analysis of NSGA-III and its modifications

- Difficulties in performance comparison of EMO algorithms

- Performance indicators: Uniformity, s-energy, GD, IGD, IGD+ and HV

- Anytime performance analysis

- Population size specification for performance comparison

- Artificial test problems and real-world problems

- Performance improvement of EMO algorithms: Archiving and initialization

- Constraint handling in EMO algorithms

- Special multi-objective problems: Many-objective, large-scale, and sparse problems

- Use of machine learning techniques for EMO algorithms

After completing the course, students will have clear ideas about evolutionary algorithms and evolutionary multi-objective optimizations. They will be familiar with basic concepts in multi-objective optimization such as Pareto dominance and Pareto fronts, representative multi-objective evolutionary algorithms such as NSGA-II, MOEA/D and SMS-EMOA, performance indicators such as GD, IGD and hypervolume, and some hot topics such as archiving and Pareto set learning. They will also understand the importance of fair performance comparison.

Participants are expected to have prior knowledge of the following concepts:

- Basics of probability theory