An efficient global optimization approach for solving mixed-integer nonlinear programming problems

Mixed-integer nonlinear programming (MINLP) problems involving general constraints and objective functions with continuous and integer variables occur frequently in engineering design, chemical process industry and management. Although many optimization approaches have been developed for MINLP problems, these methods can only find a local or approximate solution or use too many extra binary variables and constraints to reformulate the problem. Therefore, this study proposes a novel method for solving an MINLP problem to obtain a global optimal solution. The MINLP problem is transformed into a convex mixed-integer program by the convexification strategies and piecewise linearization techniques. A global optimum of the MINLP problem can then be found within the tolerable error. Numerical examples are also presented to demonstrate the effectiveness of the proposed method.