Global Optimization of Mixed-Integer Nonlinear Problems

Two novel deterministic global optimization algorithms for nonconvex mixed-integer problems (MINLPs) are proposed, using the advances of the BB algorithm for noncon-vex NLPs Adjiman et al. (1998a). The Special Structure Mixed-Integer BB algorithm (SMIN-BB addresses problems with nonconvexities in the continuous variables and linear and mixed-bilinear participation of the binary variables. The General Structure Mixed-Integer BB algorithm (GMIN-BB), is applicable to a very general class of problems for which the continuous relaxation is twice continuously diierentiable. Both algorithms are developed using the concepts of branch-and-bound, but they diier in their approach to each of the required steps. The SMIN-BB algorithm is based on the convex underestimation of the continuous functions while the GMIN-BB algorithm is centered around the convex relaxation of the entire problem. Both algorithms rely on optimization or interval based variable bound updates to enhance eeciency. A series of medium-size engineering applications demonstrates the performance of the algorithms. Finally, a comparison of the two algorithms on the same problems highlights the value of algorithms which can handle binary or integer variables without reformulation.