A solution framework for linear PDE-constrained mixed-integer problems

Abstract We present a general numerical solution method for control problems with state variables defined by linear PDE over finite set of binary or continuous variables. show empirically that naive approach applies discretization scheme to the PDEs derive constraints mixed-integer program (MILP) leads systems are too large be solved state-of-the-art solvers MILPs, especially if we desire an accurate approximation Our framework comprises two techniques mitigate rise computation times increasing level: First, system is basis space in preprocessing step. Second, certain just imposed on demand via IBM ILOG CPLEX feature lazy constraint callback. These compared where relations obtained directly included MILP. demonstrate our examples: modeling spread wildfire and mitigation water contamination. In both examples computational results time significantly reduced methods. particular, dependence size spatial reduced.