Add problems chain and polygon

src/COPSBenchmark.jl

@@ -5,6 +5,7 @@ using JuMP
 
 
 include("bearing.jl")
+include("chain.jl")
 include("camshape.jl")
 include("catmix.jl")
 include("channel.jl")
@@ -14,6 +15,7 @@ include("glider.jl")
 include("marine.jl")
 include("methanol.jl")
 include("pinene.jl")
+include("polygon.jl")
 include("robot.jl")
 include("rocket.jl")
 include("steering.jl")

src/chain.jl

@@ -0,0 +1,59 @@
+# Hanging Chain
+
+# Find the chain (of uniform density) of length L suspended between two points with minimal
+# potential energy.
+
+#   This is problem 4 in the COPS (Version 3) collection of 
+#   E. Dolan and J. More'
+#   see "Benchmarking Optimization Software with COPS"
+#   Argonne National Labs Technical Report ANL/MCS-246 (2004)
+
+# This file has been adapted from https://github.com/JuliaSmoothOptimizers/OptimizationProblems.jl
+
+function chain_model(n::Int)
+  nh = max(2, div(n - 4, 4))
+
+  L = 4
+  a = 1
+  b = 3
+  tmin = b > a ? 1 / 4 : 3 / 4
+  tf = 1.0
+  h = tf / nh
+
+  nlp = Model()
+
+  @variable(nlp, u[k = 1:(nh + 1)], start = 4 * abs(b - a) * (k / nh - tmin))
+  @variable(nlp, x1[k = 1:(nh + 1)], start = 4 * abs(b - a) * k / nh * (1 / 2 * k / nh - tmin) + a)
+  @variable(
+    nlp,
+    x2[k = 1:(nh + 1)],
+    start =
+      (4 * abs(b - a) * k / nh * (1 / 2 * k / nh - tmin) + a) * (4 * abs(b - a) * (k / nh - tmin))
+  )
+  @variable(nlp, x3[k = 1:(nh + 1)], start = 4 * abs(b - a) * (k / nh - tmin))
+
+  @objective(nlp, Min, x2[nh + 1])
+
+  for j = 1:nh
+    @constraint(nlp, x1[j + 1] - x1[j] - 1 / 2 * h * (u[j] + u[j + 1]) == 0)
+  end
+  @constraint(nlp, x1[1] == a)
+  @constraint(nlp, x1[nh + 1] == b)
+  @constraint(nlp, x2[1] == 0)
+  @constraint(nlp, x3[1] == 0)
+  @constraint(nlp, x3[nh + 1] == L)
+
+  @constraint(
+    nlp,
+    [j = 1:nh],
+    x2[j + 1] - x2[j] - 1 / 2 * h * (x1[j] * sqrt(1 + u[j]^2) + x1[j + 1] * sqrt(1 + u[j + 1]^2)) ==
+    0
+  )
+  @constraint(
+    nlp,
+    [j = 1:nh],
+    x3[j + 1] - x3[j] - 1 / 2 * h * (sqrt(1 + u[j]^2) + sqrt(1 + u[j + 1]^2)) == 0
+  )
+
+  return nlp
+end

src/polygon.jl

@@ -0,0 +1,31 @@
+# Find the polygon of maximal area, among polygons with nv sides and    
+#   diameter d <= 1
+
+#   This is problem 1 in the COPS (Version 3) collection of 
+#   E. Dolan and J. More'
+#   see "Benchmarking Optimization Software with COPS"
+#   Argonne National Labs Technical Report ANL/MCS-246 (2004)
+
+# This file has been adapted from https://github.com/JuliaSmoothOptimizers/OptimizationProblems.jl
+
+function polygon_model(n::Int)
+  nlp = Model()
+  N = div(n, 2)
+  @variable(nlp, 0 <= r[1:N] <= 1, start = 1)
+  @variable(nlp, 0 <= θ[i = 1:N] <= π, start = i * π / (N - 1) - π / (N - 1))
+
+  # impose an order to the angles
+  @constraint(nlp, θ[N] == π)
+  @constraint(nlp, r[N] == 0)
+  for i = 1:(N - 1)
+    @constraint(nlp, θ[i + 1] - θ[i] >= 0.0)
+  end
+  for i = 1:(N - 1)
+    for j = (i + 1):N
+      @constraint(nlp, r[i]^2 + r[j]^2 - 2 * r[i] * r[j] * cos(θ[i] - θ[j]) - 1 <= 0)
+    end
+  end
+
+  @objective(nlp, Min, -0.5 * sum(r[i] * r[i + 1] * sin(θ[i + 1] - θ[i]) for i = 1:(N - 1)))
+  return nlp
+end

test/runtests.jl

@@ -6,6 +6,7 @@ using COPSBenchmark
 
 COPS_INSTANCES = [
     (COPSBenchmark.bearing_model, (50, 50), -1.5482e-1),
+    (COPSBenchmark.chain_model, (800,), 5.06891),
     (COPSBenchmark.camshape_model, (1000,), 4.2791), # TODO: result is slightly different
     (COPSBenchmark.catmix_model, (100,), -4.80556e-2),
     (COPSBenchmark.channel_model, (200,), 1.0),
@@ -15,6 +16,7 @@ COPS_INSTANCES = [
     (COPSBenchmark.marine_model, (100,), 1.97462e7),
     (COPSBenchmark.methanol_model, (100,), 9.02229e-3),
     (COPSBenchmark.pinene_model, (100,), 1.98721e1),
+    (COPSBenchmark.polygon_model, (100,), -0.674981), # N.B: objective depends on the optimizer used.
     (COPSBenchmark.robot_model, (200,), 9.14138),
     (COPSBenchmark.rocket_model, (400,), 1.01283),
     (COPSBenchmark.steering_model, (200,), 5.54577e-1),