The paper explains a paradigm for the integration of engineering knowledge with the search strategy of a Branch and Bound algorithm. The optimization is fairly generic and addresses industrial applications comprising power-generating units. The solution concerns the allocation of the units over time and considers expected variations in the heat load and power. The engineering knowledge exploits the Hardware Composites, a conceptual tool for the operation of utility systems. The knowledge is capitalized at three different levels: (i) to exclude redundant combinations of decision variables, (ii) to prioritize the branching of the algorithm, and (iii) to prune the binary tree. Using a non-commercial LP, an MILP solver is designed and compared with highly-valued, state-of-the-art commercial solvers. The comparisons are particularly impressive in that the customized development outperforms the sophisticated packages and accommodates accelerations of at least two orders of magnitude.