Global Optimization Toolbox
Solve multiple maxima, multiple minima, and nonsmooth optimization problems
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Global Optimization Toolbox provides functions that search for global solutions to problems that contain multiple maxima or minima. Toolbox solvers include surrogate, pattern search, genetic algorithm, particle swarm, simulated annealing, multistart, and global search. You can use these solvers for optimization problems where the objective or constraint function is continuous, discontinuous, stochastic, does not possess derivatives, or includes simulations or black-box functions. For problems with multiple objectives, you can identify a Pareto front using genetic algorithm or pattern search solvers.
You can improve solver effectiveness by adjusting options and, for applicable solvers, customizing creation, update, and search functions. You can use custom data types with the genetic algorithm and simulated annealing solvers to represent problems not easily expressed with standard data types. The hybrid function option lets you improve a solution by applying a second solver after the first.
Define and Solve Optimization Problems
Define your optimization problem, apply a solver, and set options for algorithm behavior, tolerances, stopping criteria, visualizations, and customizations.
GlobalSearch and MultiStart
Apply gradient-based solvers to find local minima from multiple starting points in search of global minima. Other local or global minima are returned. Solve unconstrained and constrained problems that are smooth.
Surrogate Optimization
Search for global minima on problems with time-consuming objective functions, which can be nonsmooth. The solver builds an approximation to the function that can be quickly evaluated and minimized.
Pattern Search
Start from the current point and add a set of vectors to get new trial points. Evaluate the objective function on the trial points and use that information to update the current point. Repeat until the current point is an optimum.
Genetic Algorithm
Search for global minima by mimicking the principles of biological evolution, repeatedly modifying a population of individual points using rules modeled on gene combinations in biological reproduction.
Particle Swarm
Search for global minima using an algorithm inspired by the behavior of insects swarming. Each particle moves with a velocity and direction influenced by the best location it has found so far and the best location the swarm has found.
Simulated Annealing
Search for global minima with a probabilistic search algorithm that mimics the physical process of annealing, in which a material is heated and then the temperature is slowly lowered to decrease defects, thus minimizing the system energy.
Multiobjective Optimization
Identify the Pareto front—the set of nondominated solutions—for problems with multiple objectives and bound, linear, or nonlinear constraints. Use either the pattern search or genetic algorithm solvers.
Product Resources:
"I...applied a pattern search algorithm in Global Optimization Toolbox to optimize for factors such as throughput, required production equipment, manpower, and waste. It would take thousands of experiments to assess all possible model variants. I could achieve the same results with a fraction of this number using the pattern search algorithm."
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