What is gradient-free optimization

Global Optimization Toolbox


Solving non-smooth optimization problems and optimization problems with several maxima and minima

The Global Optimization Toolbox offers functions for the global solution of problems that comprise several maxima or minima. Solvers in the toolbox are surrogate, pattern search, genetic algorithm, particle swarm, simulated annealing, MultiStart and GlobalSearch. You can use these solvers to solve optimization problems where the objective function or the conditional function is continuous, discontinuous, stochastic, has no derivatives, or contains simulations or black box functions. For problems with multiple targets, you can use the genetic algorithm or the pattern search solver to identify a Pareto front.

You can improve solver effectiveness by customizing options and, for some solvers, customizing the build, update, and search functions. You can use custom data types with the genetic algorithm and simulated cooling solvers to solve problems that cannot be easily expressed using standard data types. Hybrid functionality allows you to improve a solution by applying a second solver after the first.

Pattern Search

Solve optimization problems by using one of three different direct search algorithms: Generalized Pattern Search (GPS), Generating Set Search (GSS), and Mesh Adaptive Search (MADS). In each step, a network pattern of points is generated and evaluated.

Genetic algorithm

Look for global minima by mimicking the principles of biological evolution. It does this by repeatedly changing a population of individual points using rules built on the basis of combinations of genes found in biological reproduction.

Swarm of particles

Use an algorithm to look for global minima that mimick the behavior of swarms of insects. Each particle moves at a speed and direction influenced by the best location it has found so far and the best location the swarm has found.

Show a five-movement path for each particle.

Selecting options

Optimize the speed calculation by setting the inertia and weights for individual and social adjustment. Set the size of the neighborhood. Accelerate the solution with parallel computing.

Integrated display functions.

To adjust

Provide your own function for creating the initial swarm. Apply a second optimization to refine solutions.

Particle swarm for a stochastic function.

Simulated annealing

Use a probabilistic search algorithm to find global minima. The algorithm emulates the physical process of annealing, in which a material is heated and then its temperature is slowly reduced to reduce defects so that the system energy is minimized.

Selecting options

Under Options for Algorithms, select Adaptive Simulated Annealing, Boltzmann Annealing, or Fast Annealing.

Visualization of simulated annealing.

Multi-objective optimization

Identify the Pareto front - the set of non-majorized solutions - for problems with multiple goals and with boundary conditions or with linear or nonlinear conditions. Use either pattern search or the genetic algorithm as a solver.

Selecting options for pattern search

Provide a set of starting points. Enter the desired size of the Pareto set, the minimum polling rate and the perimeter change tolerance. Automatically display Pareto fronts in 2D and 3D. Accelerate the solution with parallel computing.

Pareto interface of the three goals.

Set options for the genetic algorithm

Enter the proportion of individuals who should remain in the Pareto front with the highest rank. Automatically display Pareto fronts in 2D. Accelerate the solution with parallel computing.