GlobalOptimSolution

Optimization solution

Description

A GlobalOptimSolution object contains information on a local minimum, including location, objective function value, and start point or points that lead to the minimum.

GlobalSearch and MultiStart generate a vector of GlobalOptimSolution objects. The vector is ordered by objective function value, from lowest (best) to highest (worst). GlobalSearch and MultiStart combine solutions that coincide with previously found solutions to within tolerances. For GlobalSearch details, see Update Solution Set in When fmincon Runs. For MultiStart details, see Create GlobalOptimSolution Object.

Creation

When you execute run and request the solutions output, GlobalSearch and MultiStart create GlobalOptimSolution objects as output.

Properties

Exitflag — Exit condition of local solver

integer

Exit condition of the local solver, returned as an integer. Generally, a positive Exitflag corresponds to a local optimum, and a zero or negative Exitflag corresponds to an unsuccessful search for a local minimum.

For the exact meaning of each Exitflag, see the exitflag description in the appropriate local solver function reference page:

• fmincon exitflag

• fminunc exitflag

• lsqcurvefit exitflag

• lsqnonlin exitflag

Data Types: double

Fval — Objective function value

real scalar

Objective function value, returned as a real scalar. For the lsqnonlin and lsqcurvefit solvers, Fval is the sum of squares of the residual.

Data Types: double

Output — Output structure returned by the local solver

structure

Output structure returned by the local solver. For details, see the output description in the appropriate local solver function reference page:

• fmincon output

• fminunc output

• lsqcurvefit output

• lsqnonlin output

Data Types: struct

X — Local solution

array

Local solution, returned as an array with the same dimensions as problem.x0.

Data Types: double

X0 — Start points that lead to current solution

cell array

Start points that lead to current solution, returned as a cell array. Control the distance between points considered as distinct by setting the FunctionTolerance and XTolerance properties of the global solver.

Data Types: cell

Examples

Obtain Multiple Local Solutions

Use MultiStart to create a vector of GlobalOptimSolution objects for a problem with multiple local minima.

rng default % For reproducibility
ms = MultiStart;
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]);
[xmin,fmin,flag,outpt,allmins] = run(ms,problem,30);

MultiStart completed the runs from all start points. 

All 30 local solver runs converged with a positive local solver exitflag.

allmins is a vector of GlobalOptimSolution objects.

disp(allmins)

  1×6 GlobalOptimSolution array with properties:

    X
    Fval
    Exitflag
    Output
    X0

Plot the objective function values at the returned solutions.

plot(arrayfun(@(x)x.Fval,allmins),'k*')
xlabel('Solution number')
ylabel('Function value')
title('Solution Function Values')

To examine the initial points that lead to the various solutions, see Visualize the Basins of Attraction.

Version History

Introduced in R2010a