Can LIME Make Interactive Multiobjective Optimization Methods Explainable?

Real-world optimization problems often involve multiple (typically conflicting) objective functions that must be balanced since they cannot reach their optima simultaneously. Interactive multiobjective optimization methods are powerful in solving such problems because they incorporate the preference information of a domain expert, a decision maker (DM), in the solution process to find the most preferred trade-offs. However, the connection between the preferences and the solutions generated based on them may remain unclear, limiting a DM’s understanding and confidence in the solution process. Therefore, we propose a novel approach leveraging local interpretable model-agnostic explanations (LIME) to make interactive methods explainable.We generate local linear approximations of the set of solutions that reflect different trade-offs to provide a DM with insights into the behavior of objective functions near the solutions considered. We can explain how changes in one objective function value affect others, assisting a DM in adjusting their preferences during the interactive solution process to get more preferred solutions. We utilize Karush-Kuhn-Tucker multipliers to construct the linear model analogous to LIME. This is convenient since the multipliers can readily be obtained as a byproduct of applying an appropriate numerical optimization solver.To our knowledge, this is the first application of LIME-inspired ideas to the domain of interactive multiobjective optimization. The proposed approach can significantly enhance the transparency and trustworthiness of interactive methods, ultimately leading to better decisions.