Theoretical proof of edge search strategy applied to power plant start-up scheduling

Power plant start-up scheduling is aimed at minimizing the start-up time while limiting maximum turbine rotor stresses. This scheduling problem is highly nonlinear and has a number of local optima. In our previous research, we proposed an efficient search model: genetic algorithms (GAs) with enforcement operation to focus the search along the edge of the feasible space where the optimal schedule is supposed to stay. Based on a nonlinear dynamic simulation and a linear inverse calculation with the iteration method, the enforcement operation is applied to move schedules generated by GA toward the edge. We prove that the optimal schedule lies on the edge, ensuring that searching along the edge instead of the entire space can improve the search efficiency significantly without missing the optimum. Furthermore, we provide a theoretical setting equation for the inverse enforcement gains of the linear inverse calculation, intended to move schedules closer to the edge at each iteration of the enforcement operation. The theoretical setting equation is verified and discussed with the test results. We propose the theoretical setting equation with the test results as a guideline for the use of our proposed search model: GA with enforcement operation.