Create the Model-class

Prerequisites

Create the Model-class

In this example a simple Knapsack Model is created. The Knapsack Model consists of Knapsack Items. The objective function of the Knapsack Model is to maximize the value of all items under the constraint, that the total weight of the items does not exceed a defined maximum.

Model Generator Class

KnapsackModel.cs

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


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

    /// <summary>
    /// A Knapsack Model
    /// </summary>
    public class KnapsackModel
    {

        /// <summary>
        /// Initializes a new instance of the <see cref="KnapsackModel"/> class and initializes all fields. 
        /// </summary>
        /// <param name="items">
        /// The items of the model
        /// </param>
        /// <param name="maxWeight">
        /// The maximum weight of all items taken
        /// </param>
        public KnapsackModel(IEnumerable<KnapsackItem> items, double maxWeight)
        {
            this.Items = items;
            this.MaxWeight = maxWeight;
            this.Model = new Model();

            // Choose Item Variable
            this.y = new VariableCollection<KnapsackItem>(
               this.Model,
               this.Items,
               "y", 
               item => $"Status of item {item.Name}",
               item => 0,
               item => 1,
               item => VariableType.Binary); // it is a binary! only bounds of {0;1} are valid.

            // Create Constraints

            // the sum of the weight of the items selected cannot exceed the maximum weight
            this.Model.AddConstraint(
                Expression.Sum(this.Items.Select(item => this.y[item] * item.Weight))
                <= MaxWeight,
                $"Sum of all weights"
                );


            // Add the objective
            // Sum of all item values.
            // \sum_{item \in Items} \{ y_{item} * value_{item}\}
            this.Model.AddObjective(
            new Objective(Expression.Sum(this.Items.Select(item => (y[item] * item.Value))),
            "Sum of all item-values",
            ObjectiveSense.Maximize)
            );
        }

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

        /// <summary>
        /// Gets the edges of this network
        /// </summary>
        public IEnumerable<KnapsackItem> Items { get; }

        /// <summary>
        /// Maximum weight the knapsack can take
        /// </summary>
        public double MaxWeight { get; }

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

Next Step