Good day.
I’m new to Julia and using different sources implemented optimization procedure of PredatorPrey ODE system (2 possible models):
using ProgressBars, Distributions, DelimitedFiles, DifferentialEquations, DiffEqParamEstim, Optimization, NLopt
data = transpose(readdlm(“LV2_30_Julia.csv”, ‘,’))
function myoptimization(p, opt)
g_minf = Inf
g_minx = Array{Float64}(undef, 0)
loops = 10
for j in 1:loops
(minf,minx,ret) = NLopt.optimize(opt,rand(Uniform(0, 1), length(p)))
if minf < g_minf
g_minf = minf
g_minx = minx
end
end
next_opt = false
add_loops = 0
while next_opt && add_loops < 50
init_p = Array([rand(Normal(g_minx[i], sqrt(g_minx[i])/3)) for i in 1:length(g_minx)])
init_p[init_p.<= 0] .= 0.000001
(minf,minx,ret) = NLopt.optimize(opt, init_p)
if minf < g_minf
if g_minf  minf < 1e10
next_opt = false
println("Exit on tolerance")
end
g_minf = minf
g_minx = minx
end
add_loops += 1
end
return g_minf, g_minx
end
u0 = [1.0;2.0]
tspan = (0.0,30.0)
t = collect(range(0,stop=30,length=31))
function f1(du,u,p,t)
du[1] = p[1] * u[1]  p[2] * u[1] * u[2]
du[2] = p[3] * u[2] + p[4] * u[1] * u[2]
end
p1 = [0.5,0.5,0.5,0.5]
lb1 = [0,0,0,0]
ub1 = [1000,1000,1000,1000]
prob1 = ODEProblem(f1,u0,tspan,p1)
obj1 = build_loss_objective(prob1, AutoVern9(Rodas5()),L2Loss(t,data),Optimization.AutoFiniteDiff())
opt1 = Opt(:LN_BOBYQA, 4)
min_objective!(opt1, obj1)
maxeval!(opt1, 100000)
lower_bounds!(opt1,lb1)
upper_bounds!(opt1,ub1)
function f2(du,u,p,t)
du[1] = p[1] * u[1] *(1  u[1]/p[5])  p[2] * u[2] * u[1]
du[2] = p[3] * u[2] + p[4] * u[1] * u[2]
end
p2 = [0.5,0.5,0.5,0.5,0.5]
lb2 = [0,0,0,0,0]
ub2 = [1000,1000,1000,1000,1000]
prob2 = ODEProblem(f2,u0,tspan,p2)
obj2 = build_loss_objective(prob2, AutoVern9(Rodas5()),L2Loss(t,data),Optimization.AutoFiniteDiff())
opt2 = Opt(:LN_BOBYQA, 5)
min_objective!(opt2, obj2)
maxeval!(opt2, 100000)
lower_bounds!(opt2,lb2)
upper_bounds!(opt2,ub2)
cur_exp = 10
all_best_w_m1 = Array{Float64}(undef, cur_exp,4)
all_best_w_m2 = Array{Float64}(undef, cur_exp,5)
all_best_res_m1 = Array{Float64}(undef, cur_exp,1)
all_best_res_m2 = Array{Float64}(undef, cur_exp,1)
for i in ProgressBar(1:cur_exp)
g_minf, g_minx = myoptimization(p1, opt1)
all_best_w_m1[i,:] = g_minx
all_best_res_m1[i] = g_minf
g_minf, g_minx = myoptimization(p2, opt2)
all_best_w_m2[i,:] = g_minx
all_best_res_m2[i] = g_minf
end
The questions are the following:

Using LN_BOBYQA above code returns reasonable estimations but it is too slow (compared to the similar implementation in Python with scipy library run on the same data: 15 min against 4 min.)  is there way to optimize here something to run it much faster? (time is stated using the ProgressBar)

With LD_SLSQP as optimization algorithm (which is used in Python implementation) this code runs almost immediately but no optimization is done (it seems that it returns the initial random parameters), and no error from Julia is returned. Is there something I should add to run LD_SLSQP?