Introduction to Scalarization Methods for Multi-objective Optimization

This video is part of the set of lectures for SE 413, an engineering design optimization course at UIUC. This video introduces scalarization methods for solving multi-objective optimization problems. This class of methods converts multi-objective optimization problems into a set of single-objective optimization problems. Each of these subproblems, if solved successfully, produces a non-dominated point. The set of all non-dominated points, or the Pareto set, is the solution to the multi-objective optimization problem. The popular and intuitive weighted sum method is introduced, but then demonstrated to have several critical shortcomings. The epsilon-constraint method is then detailed, which is shown to be a much more effective strategy for many cases. Both methods are demonstrated using a simple example implemented in MATLAB. The MATLAB code is available from: https://www.mathworks.com/matlabcentral/fileexchange/64787-demonstration-of-two-multi-objective-optimization-strategies This lecture is one of several on the topic of multi-objective optimization problems. Other lectures address the relationship between multi-objective optimization and practical engineering design optimization problems, other example problems, and decision analysis (especially, Arrow's impossibility theorem and the difficulty of defining an optimum to satisfy multiple decision makers). The following published Google doc lists the sequence of SE 413 lecture videos and provides links to those that are publically available: https://tinyurl.com/fg37hj77