MIXED DISCRETE AND CONTINUOUS VARIABLE OPTIMIZATION BASED ON CONSTRAINT AGGREGATION AND RELATIVE SENSITIVITY

This work presents a new approach for solving nonlinear mixed discrete-continuous variable problems with constraints. The proposed method falls under the category of direct search methods for discrete variables. Different from the traditional direct search methods that determine the search direction based on decreasing objective function within the feasible space, a relative sensitivity that jointly considers change in objective and constraint functions is introduced in this work to help determining the search direction. For feasible discrete points, the coordinate direction with the maximum relative sensitivity is taken as the search direction, so that the objective function value decreases the fastest with minimum increase in constraint values. For infeasible points, the search direction is determined by the minimum relative sensitivity, so that the points can be dragged into the feasible region with constraints decreasing the fastest and minimum increase of the objective. In addition, in order to reduce the number of constraints and calculate the relative sensitivity, a constraint aggregation technique with Kreisselmeier-Steinhauser function is applied to transform all constraints into an equivalent differentiable inequality constraint. The efficacy and accuracy of the proposed approach is demonstrated with different types of test problems and application to a design problem. The proposed method has advantages in solving nonlinear mixed discrete-continuous variable problems with constraints compared to other existing methods.