Conformal Variable Fixing for Mixed-Integer Optimization

We present a method for accelerating repeated solves of mixed-integer optimization problems with fixed structure and varying data. A learned predictor maps problem data to binary variable assignments. We use conformal prediction to decide which assignments we can be confident to fix, leaving the remaining binary variables and all continuous variables to an optimization solver. This yields a reduced problem with fewer binary variables. We also introduce a nonconformity score that measures how far the predicted assignments must be relaxed for the reduced problem to contain a near-optimal solution. Under exact optimization, our method returns a feasible solution for every feasible instance. For calibration and test instances drawn independently from the same distribution, the returned solution is near-optimal with probability at least a user-specified level. Experiments on four benchmark families in control, robotics, and transportation show that the method can reduce solve times while maintaining high solution quality.