Scatter search and local NLP solvers: a multistart framework for global optimization. (English) Zbl 1241.90093

Summary: 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 any gradient-based local solver for nonlinear programming (NLP) problems. 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 155 smooth NLP and mixed integer nonlinear program (MINLP) problems due to C. A. Floudas et al. [Handbook of test problems for local and global optimization (Kluwer Academic Publishers, Boston, MA) (1999)], 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 100 constraints. Global solutions to almost all problems are found in a small number of local solver calls, often one or two.


90C11 Mixed integer programming
90C59 Approximation methods and heuristics in mathematical programming
90C25 Convex programming
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