Global Optimization Toolbox

Introduction

Global Optimization Toolbox provides methods that search for global solutions to problems that contain multiple maxima or minima. It includes global search, multistart, pattern search, genetic algorithm, and simulated annealing solvers. You can use these solvers to solve optimization problems where the objective or constraint function is continuous, discontinuous, stochastic, does not possess derivatives, or includes simulations or black-box functions with undefined values for some parameter settings.

Genetic algorithm and pattern search solvers support algorithmic customization. You can create a custom genetic algorithm variant by modifying initial population and fitness scaling options or by defining parent selection, crossover, and mutation functions. You can customize pattern search by defining polling, searching, and other functions.

Plot of different types of problems Global Optimization Toolbox can solve: nonsmooth (top), single global minimum nested inside multiple local minima (left), multiple local minima with no global minimum (right).

Key Features

• Interactive tools for defining and solving optimization problems and monitoring solution progress
• Global search and multistart solvers for finding single or multiple global optima
• Genetic algorithm solver that supports linear, nonlinear, and bound constraints
• Multiobjective genetic algorithm with Pareto-front identification, including linear and bound constraints
• Pattern search solver that supports linear, nonlinear, and bound constraints
• Simulated annealing tools that implement a random search method, with options for defining annealing process, temperature schedule, and acceptance criteria
• Parallel computing support in multistart, genetic algorithm, and pattern search solvers
• Custom data type support in genetic algorithm, multiobjective genetic algorithm, and simulated annealing solvers

Plot of a nonsmooth objective function (bottom) that is not easily solved using traditional gradient-based optimization techniques. The Optimization Tool (middle) shows the solution found using pattern search in Global Optimization Toolbox. Iterative results for function value and mesh size are shown in the top figure.