A low-cost evolutionary algorithm for the unit commitment problem considering probabilistic unit outages

This article presents a solution method to the unit commitment problem with probabilistic unit failures and repairs, which is based on evolutionary algorithms and Monte Carlo simulations. Regarding the latter, thousands of availability–unavailability trial time patterns along the scheduling horizon are generated. The objective function to be minimised is the expected total operating cost, computed after adapting any candidate solution, i.e. any series of generating/non-generating (ON/OFF) unit states, to the availability–unavailability patterns and performing evaluations by considering fuel, start-up and shutdown costs as well as the cost for buying electricity from external resources, if necessary. The proposed method introduces a new efficient chromosome representation: the decision variables are integer IDs corresponding to the binary-to-decimal converted ON/OFF (1/0) scenarios that cover the demand in each hour. In contrast to previous methods using binary strings as chromosomes, the new chromosome must be penalised only if any of the constraints regarding start-up, shutdown and ramp times cannot be met, chromosome repair is avoided and, consequently, the dispatch problems are solved once in the preparatory phase instead of during the evolution. For all these reasons, with or without probabilistic outages, the proposed algorithm has much lower CPU cost. In addition, if probabilistic outages are taken into account, a hierarchical evaluation scheme offers extra noticeable gain in CPU cost: the population members are approximately pre-evaluated using a small ‘representative’ set of the Monte Carlo simulations and only a few top population members undergo evaluations through the full Monte Carlo simulations. The hierarchical scheme makes the proposed method about one order of magnitude faster than its conventional counterpart.