Global optimization of mixed-integer nonlinear programming for engineering design problems

Abstract

This study utilizes an efficient global optimization method to solve engineering design problems involving nonconvex functions and mixed variables such as integer, discrete and continuous variables. The problems are usually formulated as mixed-integer nonlinear programming problems. Although many optimization approaches have been developed to solve mixed-integer nonlinear programming problems, these methods can only find an approximate solution or use too many extra binary variables and constraints to reformulate the problem. Therefore, this study presents a deterministic optimization method for solving engineering optimization problems by superior linearization techniques and convexification strategies. The constructed problem can be transformed into a convex mixed-integer program solvable to obtain a global optimum. Numerical examples are also solved by the presented method and compare the solutions with previously studies. The comparison results reveal that the presented method is better than the heuristic algorithms in finding a high quality solution.