Ordinal optimization approach for mixed variable nonlinear optimization problems of large network systems

Mixed integer-discrete-continuous variable nonlinear optimization problem of large network systems is a hard optimization problem due to involving integer and discrete variables and its large dimension. In this paper, we propose an approach of multiple ordinal optimization to solve this hard optimization problem for a good enough solution. Each ordinal optimization iteration is designed to choose better solutions from a candidate solution set using limited computation time based on a surrogate model of the considered problem. Our approach consists of five ordinal optimization iterations. The surrogate model of the considered problem is elaborated iteration by iteration, and the size and solution quality of the selected solution set is reduced and improved iteration by iteration. The solution obtained in the last iteration, which employs the exact model, is the good enough solution we obtain for the considered problem. To demonstrate the computational efficiency of the proposed approach and the quality of the obtained good enough solution, we have applied our method to the capacitor placement problem of large electric power systems and compare the results with those obtained by Genetic Algorithm (GA) and Tabu Search (TS) method. The comparisons show that the proposed approach outperforms GA and TS method in the aspects of both computational efficiency and solution quality.