Restriction techniques for the unit-commitment problem with total procurement costs

Many discrete optimization problems may be solved much easier, if the solution space can be restricted in a convenient way. For a given specific problem, the restriction techniques can be helpful if an available optimization solver, perceived as a black box, is capable of solving quickly only reduced subproblems of a limited size. For the family of hard unit-commitment problems we investigate a hierarchical search algorithm, which is based on decomposition of the problem into two subproblems. The upper-level subproblem is a relatively small decision "kernel" of the problem that can be solved approximately by a search algorithm. We define an appropriate restricted decision space for this subproblem. The lower-level subproblem is an appropriate restriction of the original problem that can be solved efficiently by a dedicated solver. Our approach was analyzed on a set of historical data from the Polish electrical balancing market and the best known solutions were improved by the average of about 2-5%.