Nonsmooth Optimization

Frontline Systems' optimizers solve nonsmooth optimization problems using these methods:

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

The standard Microsoft Excel Solver and the Premium Solver do not offer built-in facilities for solving global optimization problems.

Genetic and Evolutionary Algorithms

The Premium Solver Platform uses a hybrid Evolutionary Solver to solve nonsmooth optimization problems.  This hybrid Solver uses a combination of methods from genetic and evolutionary algorithms and "classical" optimization methods.  It handles integer variables and alldifferent constraints (i.e. permutations of sets of variables) as native types.

The Large-Scale SQP Solver Engine integrates the same hybrid Evolutionary Solver as the Premium Solver Platform to solve nonsmooth optimization problems, using the SQP method for local searches.  This Solver is especially effective on problems with a mix of many linear or smooth nonlinear functions and some nonsmooth functions. Genetic algorithm methods in this Solver use four types of mutation operators, two of which are specific for permutations, and four types of crossover operators, two of which are specific for permutations. Tournament selection is used for crossover candidates, and an algorithm that assigns greater probability of elimination to the least fit members is used to update the population.

"Classical" methods in this Solver use a gradient-free direct search, a gradient-based quasi-Newton method, and a linearized local gradient method.  Several methods are used to satisfy constraints, including both stochastic "constraint repair" methods and deterministic linear and nonlinear constraint solving methods.

Tabu Search and Scatter Search

The OptQuest Solver Engine uses tabu search and scatter search to solve nonsmooth optimization problems.  It handles integer variables and the alldifferent constraint (i.e. permutations of sets of variables) as native types. Scatter search in the OptQuest Solver systematically generates linear combinations of certain reference points to create new points, each of which maps into an associated point that satisfies integer and alldifferent constraints.  Tabu search is then superimposed to control the composition of reference points at each stage.  Tabu search in the OptQuest Solver maintains a memory of past search results to guide direction, intensification and diversification of future searches.