// (c) 2023-2024 Fair Isaac Corporation
using System;
using Optimizer;
using Optimizer.Objects;
using static Optimizer.Objects.Utils;
namespace XpressExamples
{
/// <summary>
/// Code example showing how to build nonlinear formulae
/// </summary>
/// <remarks>
/// Maximize the area of polygon of N vertices and diameter of 1
/// The position of vertices is indicated as (rho,theta) coordinates
/// where rho denotes the distance to the base point
/// (vertex with number N - 1) and theta the angle from the x-axis.
///
/// Demonstrating how to build nonlinear formulae from strings and token sequences
///
/// <code>
/// Variables:
///
/// r : 0..N-1 ! Distance of vertex from the base point
/// theta : 0..N-1 ! Angle from x-axis
///
/// Objective:
/// (sum (i in 1..N-2) (r(i)*r(i-1)*sin(theta(i)-theta(i-1)))) * 0.5
///
/// Constraints:
/// Vertices in increasing degree order:
/// theta(i) >= theta(i-1) +.0001 : i = 1..N-2
/// Boundary conditions:
/// theta(N-1) <= Pi
/// 0.1 <= r(i) <= 1 : i = 0..N-2
/// Third side of all triangles <= 1
/// r(i)^2 + r(j)^2 - r(i)*r(j)*2*cos(theta(j)-theta(i)) <= 1 : i in 0..N-3, j in i..N-2
/// </code>
/// </remarks>
public class PolygonObjects
{
/// the number of vertices/sides of the polygon
const int NSIDES = 5;
public static void Main(string[] args)
{
using (XpressProblem prob = new XpressProblem())
{
// Output all messages.
prob.callbacks.AddMessageCallback(DefaultMessageListener.Console);
/****VARIABLES****/
/// THETA corresponds to the angle relative to the x-axis of vertex i
Variable[] theta = prob.AddVariables(NSIDES - 1)
.WithType(ColumnType.Continuous)
.WithUB(Math.PI)
.WithName("theta_{0}")
.ToArray();
/// R corresponds to the distance from the base point to vertex i
Variable[] r = prob.AddVariables(NSIDES - 1)
.WithType(ColumnType.Continuous)
.WithLB(0.1)
.WithUB(1.0)
.WithName("r_{0}")
.ToArray();
/// Objective transfer column
Variable objective = prob.AddVariable(
XPRS.MINUSINFINITY,
XPRS.PLUSINFINITY,
ColumnType.Continuous,
"objective");
Expression[] area = new Expression[NSIDES - 2];
/// Objective transfer row
for (int i = 0; i < NSIDES - 2; i++)
{
area[i] = 0.5 * r[i] * r[i + 1] * Sin(theta[i + 1] - theta[i]);
}
prob.AddConstraint(Sum(area).Eq(objective));
/// Set the objective
prob.SetObjective(objective, ObjSense.Maximize);
/// The distance between any pair of points is at most 1
for (int i = 0; i < NSIDES - 1; i++)
{
for (int j = i + 1; j < NSIDES - 1; j++)
{
prob.AddConstraint(r[i] * r[i] + r[j] * r[j] - 2.0 * r[i] * r[j] * Cos(theta[j] - theta[i]) <= 1.0);
}
}
/// Ordering the vertices: theta_i+1 >= theta_i
prob.AddConstraints(NSIDES - 2,
(i) => Sum(theta[i + 1], theta[i].Mul(-1)).Geq(0.0));
/// Optimize
prob.Optimize("s");
if (prob.SolStatus != Optimizer.SolStatus.Optimal &&
prob.SolStatus != Optimizer.SolStatus.Feasible)
throw new Exception("optimization failed with status " + prob.SolStatus);
double[] sol = prob.GetSolution();
/* Print out the solution */
Console.WriteLine("Objective: {0:f4}", prob.ObjVal);
foreach (Variable v in r)
{
Console.Write("{0}: {1:f4}\n", v.GetName(), v.GetValue(sol));
}
Console.WriteLine();
foreach (Variable v in theta)
{
Console.Write("{0}: {1:f4}\n", v.GetName(), v.GetValue(sol));
}
Console.WriteLine();
}
}
}
}
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