Global Optimization Toolbox User's Guide - MathWorks

as the upper bound for each dimension for initial point generation. For
bounded problems, and problems with linear constraints, ga uses the
bounds and constraints to make the initial population.
Write Constraints
simulannealbnd and patternsearch do not require bounds, although they
can use bounds.
Ensure ga Options Maintain Feasibility
The ga solver generally maintains strict feasibility with respect to bounds
and linear constraints. This means that, at every iteration, all members of a
population satisfy the bounds and linear constraints.
However, you can set options that cause this feasibility to fail. For example
if you set MutationFcn to @mutationgaussian or @mutationuniform, the
mutation function does not respect constraints, and your population can
become infeasible. Similarly, some crossover functions can cause infeasible
populations, although the default gacreationlinearfeasible does respect
bounds and linear constraints. Also, ga can have infeasible points when using
custom mutation or crossover functions.
To ensure feasibility, use the default crossover and mutation functions for ga.
Be especially careful that any custom functions maintain feasibility with
respect to bounds and linear constraints.
Gradients and Hessians
If you use GlobalSearch or MultiStart with fmincon, yournonlinear
constraint functions can return derivatives (gradient or Hessian). For details,
see “Gradients and Hessians” on page 2-4.
Vectorized Constraints
The ga and patternsearch solvers optionally compute the nonlinear
constraint functions of a collection of vectors in one function call. This method
can take less time than computing the objective functions of the vectors
serially. This method is called a vectorized function call.
For the solver to compute in a vectorized manner, you must vectorize both
your objective (fitness) function and nonlinear constraint function. For details,
see “Vectorizing the Objective and Constraint Functions” on page 4-84.
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