Reducing Combinatorial Redundancy in Mixed-Integer MPC via Ranking-Based Feasible-Set Restriction for Reconfigurable Batteries
When mixed-integer model predictive control must select which of several similar units to activate, many same-size selections can yield closely spaced predicted outcomes, and branch-and-bound may fail to certify optimality within one sampling period. We propose a ranking-based feasible-set restriction for this class of decisions: the units are ordered by a suitability score computed at each sampling instant, and a monotone constraint permits only the top-ranked units to be active. The optimizer then chooses only how many units to activate, so the admissible selections per prediction stage grow linearly instead of combinatorially, while the model, cost function, and remaining constraints are retained. We instantiate the method for reconfigurable battery packs in which each series-connected cell can be bypassed, scoring cells with fixed weights on normalized state of health, state of charge, and voltage headroom. In a 20-cell simulation over a dynamic drive cycle with a 1 s limit per online solve, all active online restricted solves terminate at the root node with certified optimality, compared with 77.83% certification for unrestricted subset selection, and the 95th-percentile solver time is lower by a factor of 13.4. The cycle-mean cell-to-cell standard deviation in state of charge falls 8.7-fold without power curtailment, at the expense of 3.45 times as much cell switching. Solving both problems from identical states along two trajectories shows that the restriction raises the optimal cost by 0.26% and 0.14% on average at states where both solves are certified and uncurtailed.