GlobalSearch
求全局最小值
说明
GlobalSearch 对象包含影响 run 如何重复运行局部求解器以生成 GlobalOptimSolution 对象的属性（选项）。运行时，求解器尝试找到具有最低目标函数值的解。
创建对象
语法
属性
对象函数
run | 运行多启动求解器 |
示例
创建一个具有多个局部极小值的优化问题，并尝试使用 GlobalSearch 找到全局最小值。目标是六峰驼峰问题（请参阅运行求解器）。
rng default % For reproducibility gs = GlobalSearch; 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]); x = run(gs,problem)
GlobalSearch stopped because it analyzed all the trial points. All 8 local solver runs converged with a positive local solver exit flag.
x = 1×2
-0.0898 0.7127
您可以使用以下语法在调用 x 时请求 run 处的目标函数值：
[x,fval] = run(gs,problem)
但是，如果您忽略了请求 fval，您仍然可以计算 x 处的目标函数值。
fval = sixmin(x)
fval = -1.0316
考虑一个具有多个局部极小值的函数。
fun = @(x) x.^2 + 4*sin(5*x); fplot(fun,[-5,5])
为了搜索全局最小值，请使用 GlobalSearch fmincon 算法运行 'sqp'。
rng default % For reproducibility opts = optimoptions(@fmincon,'Algorithm','sqp'); problem = createOptimProblem('fmincon','objective',... fun,'x0',3,'lb',-5,'ub',5,'options',opts); gs = GlobalSearch; [x,f] = run(gs,problem)
GlobalSearch stopped because it analyzed all the trial points. All 23 local solver runs converged with a positive local solver exit flag.
x = -0.3080
f = -3.9032
创建一个非默认的 MultiStart 对象。
ms = MultiStart('FunctionTolerance',2e-4,'UseParallel',true)
ms =
MultiStart with properties:
UseParallel: 1
Display: 'final'
FunctionTolerance: 2.0000e-04
MaxTime: Inf
OutputFcn: []
PlotFcn: []
StartPointsToRun: 'all'
XTolerance: 1.0000e-06
创建一个使用 GlobalSearch 中可用属性的 ms 对象。
gs = GlobalSearch(ms)
gs =
GlobalSearch with properties:
NumTrialPoints: 1000
BasinRadiusFactor: 0.2000
DistanceThresholdFactor: 0.7500
MaxWaitCycle: 20
NumStageOnePoints: 200
PenaltyThresholdFactor: 0.2000
Display: 'final'
FunctionTolerance: 2.0000e-04
MaxTime: Inf
OutputFcn: []
PlotFcn: []
StartPointsToRun: 'all'
XTolerance: 1.0000e-06
gs 具有与 FunctionTolerance 相同的非默认值 ms。但是 gs 不使用 UseParallel 属性。
创建一个 GlobalSearch 对象，其 FunctionTolerance 为 1e-4。
gs = GlobalSearch('FunctionTolerance',1e-4)gs =
GlobalSearch with properties:
NumTrialPoints: 1000
BasinRadiusFactor: 0.2000
DistanceThresholdFactor: 0.7500
MaxWaitCycle: 20
NumStageOnePoints: 200
PenaltyThresholdFactor: 0.2000
Display: 'final'
FunctionTolerance: 1.0000e-04
MaxTime: Inf
OutputFcn: []
PlotFcn: []
StartPointsToRun: 'all'
XTolerance: 1.0000e-06
将 XTolerance 属性更新为 1e-3，将 StartPointsToRun 属性更新为 'bounds'。
gs = GlobalSearch(gs,'XTolerance',1e-3,'StartPointsToRun','bounds')
gs =
GlobalSearch with properties:
NumTrialPoints: 1000
BasinRadiusFactor: 0.2000
DistanceThresholdFactor: 0.7500
MaxWaitCycle: 20
NumStageOnePoints: 200
PenaltyThresholdFactor: 0.2000
Display: 'final'
FunctionTolerance: 1.0000e-04
MaxTime: Inf
OutputFcn: []
PlotFcn: []
StartPointsToRun: 'bounds'
XTolerance: 1.0000e-03
您还可以使用圆点表示法一次更新一个属性。
gs.MaxTime = 1800
gs =
GlobalSearch with properties:
NumTrialPoints: 1000
BasinRadiusFactor: 0.2000
DistanceThresholdFactor: 0.7500
MaxWaitCycle: 20
NumStageOnePoints: 200
PenaltyThresholdFactor: 0.2000
Display: 'final'
FunctionTolerance: 1.0000e-04
MaxTime: 1800
OutputFcn: []
PlotFcn: []
StartPointsToRun: 'bounds'
XTolerance: 1.0000e-03
算法
有关该算法的详细描述，请参阅GlobalSearch 算法。Ugray 等人 [1] 描述了该算法以及生成试验点的散射搜索方法。
参考
[1] Ugray, Zsolt, Leon Lasdon, John Plummer, Fred Glover, James Kelly, and Rafael Martí. Scatter Search and Local NLP Solvers: A Multistart Framework for Global Optimization. INFORMS Journal on Computing, Vol. 19, No. 3, 2007, pp. 328–340.
