  To address the interpretability challenge in machine learning (ML) systems,
counterfactual explanations (CEs) have emerged as a promising solution. CEs are
unique as they provide workable suggestions to users, in addition to explaining
why a certain outcome was predicted. The application of CEs encounters two main
challenges: general user preferences and variable ML systems. User preferences
tend to be general rather than specific, and CEs need to be adaptable to
variable ML models while maintaining robustness even as these models change.
Facing these challenges, we present a solution rooted in validated general user
preferences, which are derived from thorough user research. We map these
preferences to the properties of CEs. Additionally, we introduce a novel
method, \uline{T}ree-based \uline{C}onditions \uline{O}ptional \uline{L}inks
(T-COL), which incorporates two optional structures and multiple condition
groups for generating CEs adaptable to general user preferences. Meanwhile, we
employ T-COL to enhance the robustness of CEs with specific conditions, making
them more valid even when the ML model is replaced. Our experimental
comparisons under different user preferences show that T-COL outperforms all
baselines, including Large Language Models which are shown to be able to
generate counterfactuals.
