Metamodel-assisted evolutionary algorithms for the unit commitment problem with probabilistic outages

An efficient method for solving power generating unit commitment (UC) problems with probabilistic unit outages is proposed. It is based on a two-level evolutionary algorithm (EA) minimizing the expected total operating cost (TOC) of a system of power generating units over a scheduling period, with known failure and repair rates of each unit. To compute the cost function value of each EA population member, namely a candidate UC schedule, a Monte Carlo simulation must be carried out. Some thousands of replicates are generated according to the units’ outage and repair rates and the corresponding probabilities. Each replicate is represented by a series of randomly generated availability and unavailability periods of time for each unit and the UC schedule under consideration accordingly. The expected TOC is the average of the TOCs of all Monte Carlo replicates. Therefore, the CPU cost per Monte Carlo evaluation increases noticeably and so does the CPU cost of running the EA. To reduce it, the use of a metamodel-assisted EA (MAEA) with on-line trained surrogate evaluation models or metamodels (namely, radial-basis function networks) is proposed. A novelty of this method is that the metamodels are trained on a few “representative” unit outage scenarios selected among the Monte Carlo replicates generated once during the optimization and, then, used to predict the expected TOC. Based on this low cost, approximate pre-evaluation, only a few top individuals within each generation undergo Monte Carlo simulations. The proposed MAEA is demonstrated on test problems and shown to drastically reduce the CPU cost, compared to EAs which are exclusively based on Monte Carlo simulations.