Explanation Framework for Optimization-Based Scheduling: Evaluating Contributions of Constraints and Parameters by Shapley Values

Yuta Tsuchiya, Masaki Hamamoto

Keywords: Constraint, Explainable AI, Human-aware scheduling, Mathematical optimization, Shapley value, XAIP

TL;DR: We propose a general explanation framework to quantitatively evaluate the effect of constraints and parameters on the plan derivation by applying the concept of Shapley values.

Abstract: Although automated planning and scheduling systems based on optimization models are increasingly being adopted into socially responsible tasks, the derived plan is often counterintuitive under complicated considerations. Users will claim the right to know the reason for “Why did the optimal plan include something or not include something else (that I would have chosen)?” Explanations of constraints and parameters that cause the unexpected plan derivation can play an important role in building trust between users and the scheduling system. However, existing approaches require an assumption of a specific problem setting, and have not addressed quantitative analysis for multiple types of factors. In this paper, we propose a general explanation framework to quantitatively evaluate the effect of constraints and parameters on the plan derivation by applying the concept of Shapley values, which satisfy the desirable axioms for explanations. The coalitional game based on optimization models is formulated to calculate the contributions of these factors to the fulfillment of values or conditions in which users are interested. Through numerical experiments of the typical personnel assignment problem, we show that our framework can identify the major causes efficiently under various parameter settings and provide directly understandable explanations compared to the basic contrastive explanations.