Create the Model-class

Prerequisites

• The Instantiation of Business Objects

Create the Model-class

In this example three different Set Problems are created. They all have the goal of minimizing the cost for choosing sets. Set Covering restricts the Selection of Sets to contain at least one of each element from the original Set. Set Packing restricts the same Selection to at most one element and Set Partitioning to exactly one element.

Model Generator Class

SetProblemModel.cs

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;


namespace SetProblems
{
    using OPTANO.Modeling.Optimization;
    using OPTANO.Modeling.Optimization.Operators;
    using OPTANO.Modeling.Optimization.Enums;

    /// <summary>
    /// A Set Problem Model
    /// </summary>
    public class SetProblemModel
    {

        /// <summary>
        /// Initializes a new instance of the 
        /// <see cref="SetProblemModel"/> class and initializes all fields. 
        /// </summary>
        /// <param name="nodes">
        /// The network nodes of the model
        /// </param>
        /// <param name="edges">
        /// The edges of the model
        /// </param>
        public SetProblemModel(List<ISet_E> sets, ISet_E fullSet)
        {
            this.Sets = sets;
            this.Model = new Model();
            this.FullSet = fullSet;

            // Set Variables
            this.y = new VariableCollection<ISet_E>(
               this.Model, 
               this.Sets, 
               "y", 
               item => $"Status of set {item.Name}",
               item => 0, 
               item => 1,
               item => VariableType.Binary); // it is a binary! only bounds of {0;1} are valid.

            // Create Constraints

            // Set Covering constraint (1) - constraint (2) and (3) need to be disabled
            // for each element of the original set at least one new set 
            // which contains the element has to be chosen

            foreach (IElement element in this.FullSet.Elements)
            {
                this.Model.AddConstraint(
                    Expression.Sum(this.Sets.Where(set => set.ContainsElement(element)).Select(set => y[set]))
                    >= 1,
                    $"Element {element} is contained");
            }

            // Set Packing constraint (2) - constraint (1) and (3) need to be disabled
            // for each element of the original set at most one new set
            // which contains the element has to be chosen

            //foreach (IElement element in this.FullSet.Elements)
            //{
            //    this.Model.AddConstraint(
            //        Expression.Sum(this.Sets.Where(set => set.ContainsElement(element)).Select(set => y[set])) 
            //        <= 1,
            //        $"Element {element} is contained");
            //}

            // Set Partitioning constraint (3) - constraint (1) and (2) need to be disabled
            // for each element of the original set exactly one new set
            // which contains the element has to be chosen

            //foreach (IElement element in this.FullSet.Elements)
            //{
            //    this.Model.AddConstraint(
            //        Expression.Sum(this.Sets.Where(set => set.ContainsElement(element)).Select(set => y[set])) 
            //        == 1,
            //        $"Element {element} is contained");
            //}

            // Add the objective
            // Sum of the lowest cost while set- covering(1), packing(2), partitioning(3)
            // \sum_{set \in sets} \{ y_{set} * cost_{set}\}
            this.Model.AddObjective(
                new Objective(Expression.Sum(this.Sets.Select(set => y[set] * set.Cost)),
                "Sum of all set costs",
                ObjectiveSense.Minimize)
                );
        }

        /// <summary>
        /// Gets the Model instance
        /// </summary>
        public Model Model { get; private set; }

        /// <summary>
        /// Gets the List of all Sets with Elements
        /// </summary>
        public List<ISet_E> Sets { get; }

        /// <summary>
        /// Gets the original full Set
        /// </summary>
        public ISet_E FullSet { get; }

        /// <summary>
        /// Gets the Collection of all design variables
        /// </summary>
        public VariableCollection<ISet_E> y { get; }
    }
}

Next Step

• Retrieve the Solution