Models and Algorithms for Reserve Deliverability in Cross-Zonal Balancing Capacity Markets

What the math gives to ML

The paper develops a constructive way to replace exponentially many activation scenarios by a conservative polyhedral inner approximation built from reusable exchange patterns. Its key asset is a one-sided decomposition inequality: if a feasible activation is represented as a nonnegative combination of patterns, then bounding the positive contribution of every pattern separately certifies all combined activations without enumerating every joint scenario. This structure can transfer to constrained mixture-of-experts routing, where expert and device traffic patterns must remain feasible under arbitrary token activation. The practical adaptation is a pattern-based router with a small active column pool and periodic separation that adds only useful patterns violating capacity or communication constraints.