Solver Technology - Global Optimization

Global Optimization

Frontline Systems' optimizers solve hard, non-convex global optimization problems using these methods:

• Multistart Methods
• Interval Methods
• Continuous Branch and Bound
• Genetic and Evolutionary Algorithms
• Tabu Search and Scatter Search

For an explanation of these types of problems, please see Optimization Problem Types: Global Optimization.

Multistart Methods

The Premium Solver Platform uses Multistart methods in conjunction with the nonlinear GRG Solver to solve global optimization problems, specifically multi-level single linkage (MSL) and an extension called topographic MSL.

The Large-Scale GRG Solver makes use of the Multistart methods in the Premium Solver Platform to solve larger global optimization problems.  The Large-Scale SQP Solver and the KNITRO Solver also make use of the Multistart methods to solve still larger-scale global optimization problems.

Interval Methods

The Premium Solver Platform includes an Interval Global Solver that uses the Moore-Skelboe Interval Branch and Bound method to solve global optimization problems.  It employs a variety of methods to tighten bounds on regions or reduce the size of "boxes," including the mean value form and the Interval Newton method with the Krawczyk operator, the linear enclosure form and the Simplex method for linear enclosures of constraints, and interval constraint propagation using both hull consistency and box consistency methods.

Continuous Branch and Bound

The Interval Global Solver uses Continuous Branch and Bound to solve global optimization problems, in conjunction with a repertoire of other methods.

Genetic and Evolutionary Algorithms

The Premium Solver Platform and the Large-Scale SQP Solver use an Evolutionary Solver, based on genetic algorithms, to solve smooth and nonsmooth global optimization problems.  The Evolutionary Solver's capabilities are described in Solver Technology: Nonsmooth Optimization.

Tabu Search and Scatter Search

The Evolutionary Solver and the OptQuest Solver Engine uses Tabu Search and Scatter Search to solve smooth and nonsmooth global optimization problems.  The OptQuest Solver's capabilities are described in Solver Technology: Nonsmooth Optimization.