A Multistart Scatter Search Heuristic for Smooth NLP and MINLP Problems

The algorithm described here, called OptQuest/NLP or OQNLP, is a heuristic designed to find global optima for pure and mixed integer nonlinear problems with many constraints and variables, where all problem functions are differentiable with respect to the continuous variables. It uses OptQuest, a commercial implementation of scatter search developed by OptTek Systems, Inc., to provide starting points for a gradient-based local NLP solver. This solver seeks a local solution from a subset of these points, holding discrete variables fixed. The procedure is motivated by our desire to combine the superior accuracy and feasibility-seeking behavior of gradient-based local NLP solvers with the global optimization abilities of OptQuest. Computational results include 144 smooth NLP and MINLP problems due to Floudas et al, most with both linear and nonlinear constraints, coded in the GAMS modeling language. Some are quite large for global optimization, with over 100 variables and many constraints. Global solutions to almost all problems are found in a small number of NLP solver calls, often one or two.