About Multiple Solutions
You obtain multiple solutions in an object by calling
[x,fval,exitflag,output,manymins] = run(...);
manymins is a vector of solution objects; see
manymins vector is in
order of objective function value, from lowest (best) to highest (worst). Each
solution object contains the following properties (fields):
X— a local minimum
Fval— the value of the objective function at
X0— a cell array of start points that led to the solution point
There are several ways to examine the vector of solution objects:
In the MATLAB® Workspace Browser. Double-click the solution object, and then double-click the resulting display in the Variables editor.
Using dot notation.
GlobalOptimSolutionproperties are capitalized. Use proper capitalization to access the properties.
For example, to find the vector of function values, enter:
fcnvals = [manymins.Fval] fcnvals = -1.0316 -0.2155 0
To get a cell array of all the start points that led to the lowest function value (the first element of
smallX0 = manymins(1).X0
Plot some field values. For example, to see the range of resulting
This results in a histogram of the computed function values. (The figure shows a histogram from a different example than the previous few figures.)
Change the Definition of Distinct Solutions
You might find out, after obtaining multiple local solutions,
that your tolerances were not appropriate. You can have many more
local solutions than you want, spaced too closely together. Or you
can have fewer solutions than you want, with
together too many solutions.
To deal with this situation, run the solver again with different
determine how the solvers group their outputs into the
These tolerances are properties of the
For example, suppose you want to use the
fmincon to solve the problem in Example of Run with MultiStart. Further
suppose that you want to have tolerances of
run method groups local solutions whose objective
function values are within
each other, and which are also less than
from each other. To obtain the solution:
% % Set the random stream to get exactly the same output % rng(14,'twister') ms = MultiStart('FunctionTolerance',0.01,'XTolerance',0.01); opts = optimoptions(@fmincon,'Algorithm','active-set'); sixmin = @(x)(4*x(1)^2 - 2.1*x(1)^4 + x(1)^6/3 ... + x(1)*x(2) - 4*x(2)^2 + 4*x(2)^4); problem = createOptimProblem('fmincon','x0',[-1,2],... 'objective',sixmin,'lb',[-3,-3],'ub',[3,3],... 'options',opts); [xminm,fminm,flagm,outptm,someminsm] = run(ms,problem,50); MultiStart completed the runs from all start points. All 50 local solver runs converged with a positive local solver exit flag. someminsm someminsm = 1x5 GlobalOptimSolution Properties: X Fval Exitflag Output X0
In this case,
MultiStart generated five distinct
solutions. Here “distinct” means that the solutions
are more than 0.01 apart in either objective function value or location.