Mixed-integer non-linear programming approach to structural optimization

The paper presents the Mixed-Integer Non-Linear Programming (MINLP) approach to structural optimization. MINLP is a combined discrete/continuous optimization technique, where discrete binary 0-1 variables are defined for optimization of discrete alternatives and continuous variables for optimization of parameters. The MINLP optimization is performed through three steps: i.e. the generation of a mechanical superstructure, the modelling of an MINLP model formulation and the solution of the defined MINLP problem. As the discrete/continuous optimization problems are usually non-convex and highly non-linear, the Modified Outer-Approximation/Equality-Relaxation (OA/ER) algorithm is applied for the optimization. The accompanied Linked Multilevel Hierarchical Strategy (LMHS) is developed to accelerate the convergence of the mentioned algorithm. Two examples are presented at the end of the paper.