Hard Test Problems

This package implements challenging test problems for testing metaheuristics (evolutionary algorithms) for single, multi-objective and bilevel optimization.

Installation

Open the Julia (Julia 1.1 or Later) REPL and press ] to open the Pkg prompt. To add this package, use the add command:

pkg> add HardTestProblems

Or, equivalently, via the Pkg API:

julia> import Pkg; Pkg.add("HardTestProblems")

Benchmarks

• RW-MOP-2021 Real world multi-objective Constrained Optimization Test Suite.
• CEC2020-BC-SO Bound-constrained test problems for single-objective optimization.
• PMM Pseudo-feasible solutions in evolutionary bilevel optimization: Test problems and performance assessment
• SMD Scalable test problems for single-objective bilevel optimization.
• CEC2017 Competition on Constrained Real-Parameter Optimization.

Usage

RW-MOP-2021

Use the get_RW_MOP_problem to obtain the objective function and the corresponding attributes:

julia> using HardTestProblems

julia> HardTestProblems.NAME_OF_PROBLEMS_RW_MOP_2021
50-element Vector{String}:
 "pressure_vessel"
 "vibrating_platform"
 "two_bar_Truss_design_problems"
 "weldan_beam_design"
 ⋮
 "minimization_of_active_power_loss_in_islanded_microgrids_3"
 "power_distribution_system_planning"

julia> f, conf =  get_RW_MOP_problem(1);

julia> conf
Dict{Symbol, Any} with 8 entries:
  :xmin     => [0.51, 0.51, 10.0, 10.0]
  :xmax     => [99.49, 99.49, 200.0, 200.0]
  :n        => 4
  :function => "pressure_vessel"
  :gn       => 2
  :hn       => 0
  :fn       => 2
  :nadir    => [3.59649e5, -7330.38]

julia> f(conf[:xmin])
([12.40080078125, -7330.382858376184], [0.0329, 0.1305], [0.0])

Note that f is in the form f(x) = Tuple([f1, f2,...], [g1, g2,...], [h1, h2,...]). A feasible solution is such that gi <= 0 and hi = 0.

CEC2020-BC-SO

You can do the following to obtain the problem information:

julia> using HardTestProblems

julia> HardTestProblems.NAME_OF_PROBLEMS_CEC2020
10-element Vector{String}:
 "cec2020_f1"
 "cec2020_f2"
  ⋮
  "cec2020_f10"

julia> f, conf = get_cec2020_problem(1, n=10);

julia> conf
Dict{Symbol, Any} with 8 entries:
  :xmin     => [-100.0, -100.0, -100.0, -100.0, -100.0, -100.0, -100.0, -100.0, -100.0, -100.0]
  :xmax     => [100.0, 100.0, 100.0, 100.0, 100.0, 100.0, 100.0, 100.0, 100.0, 100.0]
  :n        => 10
  :minimum  => 100
  :function => "cec2020_f1"
  :gn       => 0
  :hn       => 0
  :fn       => 1

julia> f(conf[:xmin])
2.0983079296144998e11

Each problems is defined for dimension n in [2,5,10,15,20,30,50,100].

PMM

julia> using HardTestProblems

julia> F, f, conf = PMM_get_problem(2,uldim=2,lldim=3);

julia> conf
Dict{Symbol, Any} with 15 entries:
  :follower_optimum      => 0.0
  :n_inequality_follower => 0
  :xbest                 => [0.0, 0.0]
  :problem               => "PMM2"
  :n_equality_follower   => 0
  :lldim                 => 3
  :uldim                 => 2
  :n_equality_leader     => 0
  :n_inequality_leader   => 0
  :xmin                  => [-10.0, -10.0]
  :leader_optimum        => 0.0
  :xmax                  => [10.0, 10.0]
  :ymax                  => [10.0, 10.0, 10.0]
  :ymin                  => [-10.0, -10.0, -10.0]
  :ybest                 => [0.0, 1.41421, 1.73205]

SMD

julia> using HardTestProblems

julia> F, f, conf = SMD_get_problem(12,uldim=2,lldim=3); # for SMD12

julia> conf
Dict{Symbol, Any} with 14 entries:
  :follower_optimum      => 4.0
  :n_inequality_follower => 3
  :xbest                 => [1.0, 1.0]
  :n_equality_follower   => 0
  :lldim                 => 3
  :uldim                 => 2
  :n_equality_leader     => 0
  :n_inequality_leader   => 3
  :xmin                  => [-5.0, -1.0]
  :leader_optimum        => 3.0
  :xmax                  => [10.0, 1.0]
  :ymax                  => [10.0, 10.0, 0.785388]
  :ymin                  => [-5.0, -5.0, -0.785388]
  :ybest                 => [1.0, 1.0, 0.0]

julia> F(conf[:xbest], conf[:ybest]) # upper level function
(3.0, [-0.0, -0.0, -1.0], [0.0])

julia> f(conf[:xbest], conf[:ybest]) # lower level function
(4.0, [-0.0, -0.0, -0.0], [0.0])