Mixed discrete synthetic approach for nonlinear design optimization

Engineering optimization problems often encounter mixed discrete design variables. Very few of the existing methods can obtain a globally optimal solution if the objective functions are non-convex and nondifferentiable. In this research, a mixed discrete synthetic approach (MDSA), taking the advantages of random search methods and deterministic search methods, is proposed. Specifically, the modified complex algorithm is combined with the hybrid negative sub-gradient search, coupled with an implicit enumeration checking-point technique, for the solution of mixed-discrete optimization problems. The MDSA is used for the optimal designs of a pressure vessel and a welded beam. The numerical results demonstrate the high reliability and effectiveness of the MDSA as an advanced global method in solving mixed-discrete engineering optimization problems.