Pioneering Techniques to Tackle Challenges of Interactive Multiobjective Optimization

Abstract

Decision-makers (DMs) must often consider several, potentially conflicting objective functions simultaneously before making a decision. Such problems do not usually have a single optimal solution. Instead, they typically have (even infinitely) many so-called Pareto optimal solutions representing different trade-offs between the objectives. One of the ways to solve these multiobjective optimization problems (MOPs) is to use interactive methods that incorporate the DM’s preferences during the solution process. Interactive multiobjective optimization has various challenges. The process of formulating an MOP can itself be challenging. How to decide which objectives to consider or which method to use to solve the MOP? The implementations of many published methods are not openly available, which introduces additional challenges. In certain MOPs, objectives can only be evaluated by experimentation or conducting lengthy computer simulations introducing a need to replace the objectives with less costly machine learning models trained on data. However, this introduces further complications, including choosing the best models for the MOP and model management. Finally, there is also the issue of visualizing the solutions to the DM and enabling them to interact with the method intuitively. This thesis tackles the aforementioned problems and more. We propose the so-called SMTS algorithm, which predicts the best machine learning model for MOPs. With the so-called IOPIS algorithm, we introduce a completely new paradigm for interactive multiobjective optimization, enabling modular creation of interactive methods and supporting various ways of incorporating preferences. We propose the O-NAUTILUS algorithm to tackle problems with costly function evaluations in a way that allows a DM to conduct targeted evaluations in their region of interest. We introduce a novel visualization technique, SCORE bands, which can simultaneously visualize thousands of solutions with up to a dozen objectives. The DESDEO framework provides free access to the algorithms mentioned above (and many others). The framework enables its users to utilize the implemented algorithms and easily combine parts of them to create whole new ones. Finally, we put the above into practice with a case study: solving a complex data-driven metallurgical problem using the tools provided by DESDEO. Keywords: preference-based optimization, surrogate modelling, evolutionary algorithms, visualization, decision making, open-source software