Prepend Points are not being inlcuded in ranking of "global search"

[jmcastro2109]

Hi,

I am using the prepend_points option to add a candidate for optimality of a previous run.

println("Model: Baseline")

BEST_POINT= [2.0023715563522275, 0.47616619564356855, 4.0064103584405935, 9.991268276769539, 2.0070308283954614, 0.7000687884505741]
P = MinimizationProblem(x -> gmm_expanded(x,[]), [0.0,-0.98,0,0.0,0.1,0.0], [10,0.98,30,30,10.0,1.0])
local_method = NLoptLocalMethod(NLopt.LN_NELDERMEAD)
multistart_method = TikTak(2500)
p_expanded = multistart_minimization(multistart_method, local_method, P; use_threads = false, prepend_points = [BEST_POINT])
p_expanded.location, p_expanded.value

println("Estimation Results:", p_expanded.location)
println("Estimation Results:", p_expanded.value) 

However, after evaluating the 2500 Sobol points and the prepend_point, the "local phase" is not starting from the correct point, i.e

it is evaluating the prepend point here:

Parameters:[2.0023715563522275, 0.47616619564356855, 4.0064103584405935, 9.991268276769539, 2.0070308283954614, 0.7000687884505741]
Criterion Function:2.4557462126908754e-5

but when the local phase starts, it is starting from other visited minimum.

Parameters:[1.7097586400102227, 0.17207853362685677, 8.172369551469059, 7.004253780801954, 4.9741088445582955, 0.8102656679075574]
Criterion Function:16.682058405554365

[tpapp]

I looked at the code and it looks OK, can you please give me an MWE?

[jmcastro2109]

This code seems to generate the error:

using MultistartOptimization, NLopt

Point = [0.0,0.1]

function f(x,grad)
    if grad == []
    val = x[1]^2 + x[2]^2
    println("Param:",x)
    println("val:",val)
    end
    return val
end    


P = MinimizationProblem(x -> f(x,[]), [0.0,0.0], [100.0,100.0])
local_method = NLoptLocalMethod(NLopt.LN_NELDERMEAD)
multistart_method = TikTak(25)
p_expanded = multistart_minimization(multistart_method, local_method, P; use_threads = false, prepend_points = [Point])
p_expanded.location, p_expanded.value

It prints:

Param:[9.375, 46.875]
val:2285.15625
Param:[59.375, 96.875]
val:12910.15625
Param:[84.375, 21.875]
val:7597.65625
Param:[34.375, 71.875]
val:6347.65625
Param:[46.875, 9.375]
val:2285.15625
Param:[96.875, 59.375]
val:12910.15625
Param:[71.875, 34.375]
val:6347.65625
Param:[21.875, 84.375]
val:7597.65625
Param:[15.625, 15.625]
val:488.28125
Param:[65.625, 65.625]
val:8613.28125
Param:[90.625, 40.625]
val:9863.28125
Param:[40.625, 90.625]
val:9863.28125
Param:[28.125, 28.125]
val:1582.03125
Param:[78.125, 78.125]
val:12207.03125
Param:[53.125, 3.125]
val:2832.03125
Param:[3.125, 53.125]
val:2832.03125
Param:[4.6875, 26.5625]
val:727.5390625
Param:[54.6875, 76.5625]
val:8852.5390625
Param:[79.6875, 1.5625]
val:6352.5390625
Param:[29.6875, 51.5625]
val:3540.0390625
Param:[42.1875, 14.0625]
val:1977.5390625
Param:[92.1875, 64.0625]
val:12602.5390625
Param:[67.1875, 39.0625]
val:6040.0390625
Param:[17.1875, 89.0625]
val:8227.5390625
Param:[23.4375, 7.8125]
val:610.3515625
Param:[0.0, 0.1]
val:0.010000000000000002
Param:[6.603902043912098, 6.66163707083106]
val:87.988930669057
Param:[11.556828576846172, 6.66163707083106]
val:177.93769521807894
Param:[6.603902043912098, 11.657864873954356]
val:179.5173356249652
Param:[11.556828576846172, 1.6654092677077639]
val:136.33387478357523
Param:[6.603902043912097, 1.6654092677077648]
val:46.38511023455328
Param:[4.127438777445059, 0.0]
val:17.035750861557165
Param:[0.0, 4.996227803123296]
val:24.962292260702238
Param:[0.0, 0.0]
val:0.0
Param:[0.0, 0.0]
val:0.0
Param:[4.127438777445059, 0.0]
val:17.035750861557165
Param:[3.0955790830837944, 0.0]
val:9.582609859625904
Param:[0.0, 0.0]
val:0.0
Param:[4.300861384506421, 1.4336204615021404]
val:20.552676276376097
Param:[7.526507422886237, 1.4336204615021404]
val:58.70358161439923
Param:[4.300861384506421, 2.5088358076287456]
val:24.791665758378667
Param:[1.0752153461266047, 2.5088358076287456]
val:7.450345150186335
Param:[0.0, 3.046443480692048]
val:9.28081788105108
Param:[1.0752153461266047, 1.4336204615021404]
val:3.2113556681837645
Param:[0.0, 0.8960127884388378]
val:0.8028389170459415
Param:[0.0, 1.9712281345654428]
val:3.8857403585023556
Param:[0.0, 0.3584051153755352]
val:0.1284542267273507
Param:[0.0, 0.0]
val:0.0
Param:[0.0, 0.0]
val:0.0
Param:[0.02343750000000002, 0.1328125000000001]
val:0.01818847656250003
Param:[0.041015625000000035, 0.1328125000000001]
val:0.01932144165039066
Param:[0.02343750000000002, 0.2324218750000002]
val:0.054569244384765715
Param:[0.041015625000000035, 0.03320312500000003]
val:0.0027847290039062548
Param:[0.04980468750000004, 0.0]
val:0.0024805068969726606
Param:[0.03222656250000002, 0.0]
val:0.0010385513305664076
Param:[0.027832031250000014, 0.0]
val:0.0007746219635009773
Param:[0.054199218750000035, 0.0]
val:0.0029375553131103555
Param:[0.04650878906250003, 0.0]
val:0.0021630674600601222
Param:[0.0245361328125, 0.0]
val:0.0006020218133926392
Param:[0.01190185546874998, 0.0]
val:0.0001416541635990138
Param:[0.0, 0.0]
val:0.0
Param:[0.0, 0.0]
val:0.0
Param:[0.0, 0.0]
val:0.0
([0.0, 0.0], 0.0)

As you can see, the "local phase", does not start from [0.0,0.1], it starts from some other point.

[tpapp]

But note the line

Param:[0.0, 0.1]
val:0.010000000000000002

in your output. The point is visited, right after the starting points are generated.

[jmcastro2109]

Yes, I figured that out. However, I expected to apply the local optimizer to the prepended_point rather than starting from a linear combination of the prepended_point and the best starting point.