Gabriel Ha, MathWorks
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.
Use Global Optimization Toolbox to search for the best, or global, solution to an optimization problem. The toolbox provides a wide variety of solvers for applications which can involve challenging nonlinear or noisy problems, such as computational finance and engineering.
Traditional nonlinear solvers may converge to a local minimum instead of the global minimum. In contrast, MultiStart and GlobalSearch solvers use randomized search methods in combination with gradient-based solvers to search efficiently for the global minimum or maximum of continuous problems which might have multiple local solutions.
All Global Optimization Toolbox solvers apply to smooth problems such as this one modeling optical interference. The surrogate optimization solver finds this global maximum, even with many local solutions present. Some of the solvers also apply to nonsmooth or stochastic problems where gradient-based solvers are inadequate. PatternSearch solver quickly searches this nonsmooth problem for the global maximum without using gradient information. You can use any of these solvers for nonsmooth problems, including surrogate, genetic algorithm, particle swarm, and simulated annealing.
Discrete-valued nonlinear problems can be solved with the genetic algorithm and surrogate solvers. This circuit example is an integer-constrained problem, as values for components need to come from a list of available sizes.
For problems with multiple objectives, you can explore trade-offs between those objectives by generating pareto fronts with paretoSearch and genetic algorithm multiobjective solvers.
Many global optimization algorithms can run even faster using Parallel Computing Toolbox. In this cell tower placement example, we get the same results faster using 4 parallel workers.
Find more information at the links below or return to the Global Optimization Toolbox page.
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