Merge pull request #92 from jmejia8/develop

Add BRKGA optimizer

Author: jmejia8

docs/references.bib

@@ -257,3 +257,17 @@ @INPROCEEDINGS{Takahama2006Constrained
   number={},
   pages={1-8},
   doi={10.1109/CEC.2006.1688283}}
+
+@article{Gonalves2010,
+  doi = {10.1007/s10732-010-9143-1},
+  url = {https://doi.org/10.1007/s10732-010-9143-1},
+  year = {2010},
+  month = aug,
+  publisher = {Springer Science and Business Media {LLC}},
+  volume = {17},
+  number = {5},
+  pages = {487--525},
+  author = {Jos{\'{e}} Fernando Gon{\c{c}}alves and Mauricio G. C. Resende},
+  title = {Biased random-key genetic algorithms for~combinatorial optimization},
+  journal = {Journal of Heuristics}
+}

docs/src/algorithms.md

@@ -22,6 +22,7 @@ contributor's understanding of the algorithms detailed in the published paper.
 | GA        |  Single    |      ✅     |   ➖        |   ✅        | [`GA`](@ref)           |
 | CCMO      |  Multi     |      ✅     |   ➖        |   ✅        | [`CCMO`](@ref)         |
 | $\varepsilon$DE |  Single   | ✅     |   ➖        |   ✅        | [`εDE`](@ref)          |
+| BRKGA     |  Single    |      ✅     |   ➖        |   ✅        | [`BRKGA`](@ref)           |
 
 
 ✅ = supported,
@@ -174,3 +175,11 @@ CCMO
 ```@docs
 εDE
 ```
+
+## BRKGA
+
+Biased Random Key Genetic Algorithm by [Gonalves2010](@cite).
+
+```@docs
+BRKGA
+```

src/Metaheuristics.jl

@@ -14,6 +14,7 @@ export hval, gval, hvals, gvals
 export NSGA3, gen_ref_dirs
 
 export SMS_EMOA, SPEA2, MCCGA, CCMO
+export BRKGA
 
 export PerformanceIndicators, pareto_front, nadir, ideal
 export termination_status_message
@@ -120,7 +121,7 @@ include("algorithms/Restart/Restart.jl")
 
 # genetic algorithm
 include("algorithms/MCCGA/MCCGA.jl")
-
+include("algorithms/BRKGA/BRKGA.jl")
 
 include("algorithms/stop_criteria.jl")
 

src/algorithms/BRKGA/BRKGA.jl

@@ -0,0 +1,73 @@
+"""
+    BRKGA(num_elites = 20, num_mutants = 10, num_offsprings = 70, bias = 0.7)
+
+Biased Random Key Genetic Algorithm (BRKGA).
+
+### Example
+
+```julia-repl
+julia> target_perm = collect(reverse(1:10))
+10-element Vector{Int64}:
+ 10
+  9
+  8
+  7
+  6
+  5
+  4
+  3
+  2
+  1
+
+julia> decode(rk) = sortperm(rk);
+
+julia> f(rk) = sum(abs.(decode(rk) - target_perm));
+
+julia> res = optimize(f, [zeros(10) ones(10)], BRKGA(num_elites=70))
+Optimization Result
+===================
+  Iteration:       22
+  Minimum:         0
+  Minimizer:       [0.938595, 0.851247, 0.823736, …, 0.375321]
+  Function calls:  2200
+  Total time:      0.0238 s
+  Stop reason:     Due to Convergence Termination criterion.
+
+julia> decode(minimizer(res))
+10-element Vector{Int64}:
+ 10
+  9
+  8
+  7
+  6
+  5
+  4
+  3
+  2
+  1
+```
+"""
+function BRKGA(;
+        num_elites = 20,
+        num_mutants = 10,
+        num_offsprings = 70,
+        N = num_elites + num_mutants + num_offsprings,
+        bias = 0.7,
+        kargs...
+    )
+
+    initializer = RandomInBounds(;N)
+    selection   = BiasedSelection(num_elites, num_offsprings)
+    crossover   = BinomialCrossover(p = bias, n_offsprings = 1)
+    mutation    = InsertRandomMutation(num_mutants)
+    environmental_selection = ElitistReplacement()
+
+    GA(;initializer,
+       selection,
+       crossover,
+       mutation,
+       environmental_selection,
+       kargs...
+      )
+end
+

src/operators/crossover/binomial.jl

@@ -0,0 +1,28 @@
+mutable struct BinomialCrossover
+    p::Float64
+    n_offsprings::Int
+    rng
+end
+
+function BinomialCrossover(;p = 0.5, n_offsprings = 2, rng=default_rng_mh())
+    BinomialCrossover(p, n_offsprings, rng)
+end
+
+function crossover(population, c::BinomialCrossover)
+    Q = positions(population)
+
+    Q1 = Q[1:2:end-1, :]
+    Q2 = Q[2:2:end,   :]
+
+    mask = rand(c.rng, size(Q,1)÷2, size(Q, 2)) .<= c.p
+    Q1[mask] = Q2[mask]
+
+    if c.n_offsprings > 2
+        return Q1
+    end
+
+    Q1 = Q[1:2:end-1, :]
+    Q2[mask] = Q1[mask]
+    return vcat(Q1, Q2)
+end
+

src/operators/mutation/insert_random.jl

@@ -0,0 +1,9 @@
+mutable struct InsertRandomMutation
+    num_mutants::Int
+end
+
+function mutation!(Q, m::InsertRandomMutation)
+    # TODO: add rng
+    R = rand(m.num_mutants, size(Q, 2))
+    vcat(Q, R)
+end

src/operators/mutation/mutation.jl

@@ -1,3 +1,6 @@
+include("insert_random.jl")
+
+
 """
     DE_mutation(population, F = 1.0, strategy = :rand1)
 

src/operators/operators.jl

@@ -12,6 +12,7 @@ include("selection/selection.jl")
 include("crossover/order.jl")
 include("crossover/sbx.jl")
 include("crossover/uniform.jl")
+include("crossover/binomial.jl")
 
 include("mutation/bitflip.jl")
 include("mutation/polynomial.jl")

src/operators/selection/selection.jl

@@ -58,3 +58,20 @@ function binary_tournament(population, fitness::Vector{T})  where T <: Real
 
     return fitness[a] < fitness[b] ? population[a] : population[b]
 end
+
+mutable struct BiasedSelection
+    num_elites::Int
+    num_offsprings::Int
+end
+
+
+function selection(population, parameters::BiasedSelection)
+    elites = 1:parameters.num_elites
+    no_elites = parameters.num_elites+1:length(population)
+    n = parameters.num_offsprings ÷ 2
+
+    parent = ones(Int, 2n)
+    parent[1:2:end] = rand(elites, n)
+    parent[2:2:end] = rand(no_elites, n)
+    parent
+end

test/combinatorial.jl

@@ -52,10 +52,23 @@
         @test minimum(result) ≈ f(1:n)
         test_results(result)
     end
- 
+
+    function rkga()
+        n = 5
+        target_perm = collect(reverse(1:n))
+        # decoder
+        decode(rk) = sortperm(rk);
+        # objective function
+        f(rk) = sum(abs.(decode(rk) - target_perm));
+        res = optimize(f, [zeros(n) ones(n)], BRKGA(num_elites=50))
+        @test decode(minimizer(res)) == target_perm
+    end
+
+
+    rkga()
     #### Permutation
     TSP_problem()
- 
+
     #### Binary
     options = Options(seed = 1, f_tol = 1e-16, iterations=1000)
     information = Information(f_optimum = 0.0)