A global approach for nonlinear mixed discrete programming in design optimization

Most current nonlinear mixed discrete programs can only find locally optimal solutions. This paper proposes an optimization method to find the global solution of a nonlinear mixed discrete program. Based on the fact that: ‘For a discrete variable xi, iff xi∈∈k1,k2,...,km∈ then (xi-k1)(xi-k2)ëëë(xikm)=0ⁿ, the original mixed discrete program is transformed into a penalty optimization program with continuous variables. This penalty optimization program is then solved to find a local optimum. Utilizing the Multi-Level Single Linkage technique, enough starting points are systematically generated to search for most local optima within the feasible region. A global optimum is then found at a pre-specified sufficiently high confidence level such as 99.5%. Some examples of design optimization in literature are tested, which demonstrate that the proposed method is superior to current methods for finding the global optimum.