"Int64" error message during Optimisation

Specific Domains Optimization (Mathematical)
1

Hi, I am trying to find multiple parameters for the optimized system which is governed by a system of equations.

In my code, I need to be able to use 4 or 5 equations and determine the parameters for the optimized system. I have simplified the code to a system of 3 equations for simplicity, (but it is 5 equations), as below:

using Optimization, ForwardDiff, OptimizationOptimJL, OptimizationBBO

function f1(du, u, p, t)
    x, y = u
    α, β, δ, γ = p
    du[1] = dx = α * x - β * x * y
    du[2] = dy = -δ * y + γ *x * y
    du[3] = dz = α*x
end

u0 = [1.0; 1.0; 1.0]
tspan = (0.0, 10.0)
p = [1.5, 1.0, 3.0, 1.0]
prob = ODEProblem(f1, u0, tspan, p)

t = collect(range(0, stop = 10, length = 200))  # Creates the time vector
data = Array(solve(prob, Tsit5(), saveat = t, abstol = 1e-12, reltol = 1e-12))

bound = Tuple{Float64, Float64}[(0, 10), (0, 10), (0, 10), (0, 10),
                                (0, 10), (0, 10), (0, 10), (0, 10),
                                (0, 10), (0, 10), (0, 10), (0, 10),
                                (0, 10), (0, 10), (0, 10), (0, 10), (0, 10), (0, 10)]


obj = multiple_shooting_objective(prob, Tsit5(), L2Loss(t, data),Optimization.AutoForwardDiff(); discontinuity_weight = 1.0, abstol = 1e-12, reltol = 1e-12)

optprob = Optimization.OptimizationProblem(obj, zeros(18), lb = first.(bound), ub = last.(bound))
optsol = solve(optprob, BBO_adaptive_de_rand_1_bin_radiuslimited(), maxiters = 10000)

Optimised_parameters = optsol.u[(end - 1):end]
println("Optimised parameters: ")
println("p₁: ", Optimised_parameters[1])
println("p₂: ", Optimised_parameters[2])
println(" ")

However, I am getting the error message:

ERROR: InexactError: Int64(4.666666666666667)
Stacktrace:
  [1] Int64
    @ .\float.jl:994 [inlined]
  [2] (::DiffEqParamEstim.var"#43#48"{…})(p::Vector{…}, ::SciMLBase.NullParameters)
    @ DiffEqParamEstim C:\Users\Finn Mezzetti\.julia\packages\DiffEqParamEstim\6z5Ou\src\multiple_shooting_objective.jl:33
  [3] (::OptimizationFunction{…})(::Vector{…}, ::Vararg{…})
    @ SciMLBase C:\Users\Finn Mezzetti\.julia\packages\SciMLBase\VAClc\src\scimlfunctions.jl:3944
  [4] (::OptimizationBBO.var"#20#22"{OptimizationCache{…}})(θ::Vector{Float64})
    @ OptimizationBBO C:\Users\Finn Mezzetti\.julia\packages\OptimizationBBO\UYBCT\src\OptimizationBBO.jl:146
  [5] fitness(x::Vector{…}, p::BlackBoxOptim.FunctionBasedProblem{…})
    @ BlackBoxOptim C:\Users\Finn Mezzetti\.julia\packages\BlackBoxOptim\lZtsr\src\problem.jl:61
  [6] setup_problem(func::Function, parameters::BlackBoxOptim.ParamsDictChain)
    @ BlackBoxOptim C:\Users\Finn Mezzetti\.julia\packages\BlackBoxOptim\lZtsr\src\bboptimize.jl:37
  [7] bbsetup(functionOrProblem::Function, parameters::Dict{…}; kwargs::@Kwargs{…})
    @ BlackBoxOptim C:\Users\Finn Mezzetti\.julia\packages\BlackBoxOptim\lZtsr\src\bboptimize.jl:111
  [8] bbsetup
    @ C:\Users\Finn Mezzetti\.julia\packages\BlackBoxOptim\lZtsr\src\bboptimize.jl:109 [inlined]
  [9] __solve(cache::OptimizationCache{…})
    @ OptimizationBBO C:\Users\Finn Mezzetti\.julia\packages\OptimizationBBO\UYBCT\src\OptimizationBBO.jl:158
 [10] solve!(cache::OptimizationCache{…})
    @ SciMLBase C:\Users\Finn Mezzetti\.julia\packages\SciMLBase\VAClc\src\solve.jl:186
 [11] solve(::OptimizationProblem{…}, ::BBO_adaptive_de_rand_1_bin_radiuslimited; kwargs::@Kwargs{…})
    @ SciMLBase C:\Users\Finn Mezzetti\.julia\packages\SciMLBase\VAClc\src\solve.jl:94

Which indicates that somewhere it is receiving an integer but expecting a Float. I am not sure how to fix this so I can extend the system to include more equations.
Any help would be much appreciated!

2

At first glance it seems due to the fact that your time scale and/or your variable bounds have integer type. Can you try using floats for those?

3

Both t and bound are float values, if those are what you refer to.

4

My bad, I saw only the integer definitions but I missed the conversions. Ignore my previous message.

5

When I run your code I get:

julia> data = Array(solve(prob, Tsit5(), saveat = t, abstol = 1e-12, reltol = 1e-12))
ERROR: UndefVarError: `Tsit5` not defined in `Main`
Suggestion: check for spelling errors or missing imports.

Please make sure you provide minimal working examples that others can run, it appears you are missing package imports here.

6

Good idea. Here is a working example with all the necessary imports:

# Install and import all necessary packages:
using Pkg
function install_package(pkg_name::String)
    if !(pkg_name in keys(Pkg.installed()))
        Pkg.add(pkg_name)
    end
end

packages = [
    "DifferentialEquations",
    "RecursiveArrayTools",
    "Plots",
    "DiffEqParamEstim",
    "Optimization",
    "ForwardDiff",
    "OptimizationOptimJL",
    "OptimizationBBO"
]

for pkg in packages
    install_package(pkg)
end

using DifferentialEquations
using RecursiveArrayTools
using Plots
using DiffEqParamEstim
using Optimization
using ForwardDiff
using OptimizationOptimJL
using OptimizationBBO

function f1(du, u, p, t)
    x, y = u
    α, β, δ, γ = p
    du[1] = dx = α * x - β * x * y
    du[2] = dy = -δ * y + γ *x * y
end

u0 = [1.0; 1.0]
tspan = (0.0, 10.0)
p = [1.5, 1.0, 3.0, 1.0]
prob = ODEProblem(f1, u0, tspan, p)

t = collect(range(0, stop = 10, length = 200))  # Creates the time vector
data = Array(solve(prob, Tsit5(), saveat = t, abstol = 1e-12, reltol = 1e-12))

bound = Tuple{Float64, Float64}[(0, 10), (0, 10), (0, 10), (0, 10),
                                (0, 10), (0, 10), (0, 10), (0, 10),
                                (0, 10), (0, 10), (0, 10), (0, 10),
                                (0, 10), (0, 10), (0, 10), (0, 10), (0, 10), (0, 10)]


obj = multiple_shooting_objective(prob, Tsit5(), L2Loss(t, data),Optimization.AutoForwardDiff(); discontinuity_weight = 1.0, abstol = 1e-12, reltol = 1e-12)

optprob = Optimization.OptimizationProblem(obj, zeros(18), lb = first.(bound), ub = last.(bound))
optsol = solve(optprob, BBO_adaptive_de_rand_1_bin_radiuslimited(), maxiters = 10000)

Optimised_parameters = optsol.u[(end - 1):end]
println("Optimised parameters: ")
println("p₁: ", Optimised_parameters[1])
println("p₂: ", Optimised_parameters[2])
println(" ")

This example has one less “du” term. I am trying to have a system that can have up to 5 du equations. I added the third term and received the error from up above. Any ideas on how to fix this?