Apply ordinal optimization to solve the quadratic programming problems

Abstract

In this work, a two-stage approach is proposed for solving a class of Quadratic programming Problems containing Continuous and Discrete control variables (QPCD). In the firststage, a heuristic search technique was used to choose N excellent solutions from entire solution space. In the second-stage, the sensitivity theory was utilized to evaluate the N excellent solutions and pick the top S solutions to build the candidate subset. These S candidate solutions in the candidate subset were evaluated using the exact model. The Ordinal Optimization theory showed that the optimal solution chosen from candidate subset belongs to the good enough solution with high probability. The proposed approach was compared with the traditional Lagrange relaxing method for solving the IEEE 30-bus power systems. The performances were evaluated by two compared indexes, Time Reducing Index and Objective value Reducing Index. Test results demonstrate that the proposed approach outperforms the traditional Lagrange relaxing method.