Lets gooooo

BusinessLogic/Algorithms/TwoPhaseSimplex.cs

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+using Common;
+using Models;
+using System;
+using System.Collections.Generic;
+using System.Linq;
+using System.Text;
+using System.Threading.Tasks;
+
+namespace BusinessLogic.Algorithms
+{
+    public class TwoPhaseSimplex : Algorithm
+    {
+        private int numberOfArtificialVars = 0;
+
+        public override void PutModelInCanonicalForm(Model model)
+        {
+
+            for (int i = 0; i < model.Constraints.Count; i++)
+            {
+                if (model.Constraints[i].RightHandSide < 0)
+                {
+                    for (int j = 0; j < model.Constraints[i].DecisionVariables.Count; j++)
+                    {
+                        model.Constraints[i].DecisionVariables[j].Coefficient *= -1;
+                    }
+
+                    model.Constraints[i].RightHandSide *= -1;
+
+                    if (model.Constraints[i].InequalitySign == InequalitySign.LessThanOrEqualTo)
+                    {
+                        model.Constraints[i].InequalitySign = InequalitySign.GreaterThanOrEqualTo;
+                    }
+                    else if (model.Constraints[i].InequalitySign == InequalitySign.GreaterThanOrEqualTo)
+                    {
+                        model.Constraints[i].InequalitySign = InequalitySign.LessThanOrEqualTo;
+                    }
+                }
+            }
+
+
+            List<List<double>> tableZero = new List<List<double>>();
+
+
+            tableZero.Add(new List<double>());
+
+            foreach (var decVar in model.ObjectiveFunction.DecisionVariables)
+            {
+                tableZero[0].Add(decVar.Coefficient * -1);
+            }
+
+            foreach (var constraint in model.Constraints)
+            {
+                if (constraint.InequalitySign == InequalitySign.LessThanOrEqualTo ||
+                    constraint.InequalitySign == InequalitySign.GreaterThanOrEqualTo)
+                {
+                    tableZero[0].Add(0);
+                }
+
+                if (constraint.InequalitySign == InequalitySign.EqualTo ||
+                    constraint.InequalitySign == InequalitySign.GreaterThanOrEqualTo)
+                {
+                    tableZero[0].Add(0);
+                }
+            }
+
+            tableZero[0].Add(0);
+
+            for (int i = 0; i < model.Constraints.Count; i++)
+            {
+                List<double> constraintValues = new List<double>();
+
+                foreach (var decVar in model.Constraints[i].DecisionVariables)
+                {
+                    constraintValues.Add(decVar.Coefficient);
+                }
+
+                for (int j = 0; j < model.Constraints.Count; j++)
+                {
+                    if (model.Constraints[j].InequalitySign == InequalitySign.LessThanOrEqualTo)
+                    {
+                        if (j == i)
+                        {
+                            constraintValues.Add(1);
+                        }
+                        else
+                        {
+                            constraintValues.Add(0);
+                        }
+                    }
+                    else if (model.Constraints[j].InequalitySign == InequalitySign.GreaterThanOrEqualTo)
+                    {
+                        if (j == i)
+                        {
+                            constraintValues.Add(-1);
+                        }
+                        else
+                        {
+                            constraintValues.Add(0);
+                        }
+                    }
+                }
+
+                constraintValues.Add(model.Constraints[i].RightHandSide);
+
+                for (int j = 0; j < model.Constraints.Count; j++)
+                {
+                    if (model.Constraints[j].InequalitySign == InequalitySign.EqualTo ||
+                        model.Constraints[j].InequalitySign == InequalitySign.GreaterThanOrEqualTo)
+                    {
+                        if (j == i)
+                        {
+                            constraintValues.Insert(constraintValues.Count - 1, 1);
+                        }
+                        else
+                        {
+                            constraintValues.Insert(constraintValues.Count - 1, 0);
+                        }
+                    }
+                }
+
+                tableZero.Add(constraintValues);
+            }
+
+            numberOfArtificialVars = model.Constraints.Where(c => c.InequalitySign ==
+            InequalitySign.EqualTo || c.InequalitySign == InequalitySign.GreaterThanOrEqualTo).Count();
+
+            List<double> wRow = new List<double>();
+            for (int i = 0; i < tableZero[0].Count; i++)
+            {
+                wRow.Add(0);
+            }
+
+            for (int i = 1; i < tableZero.Count; i++)
+            {
+                if (model.Constraints[i - 1].InequalitySign == InequalitySign.EqualTo ||
+                    model.Constraints[i - 1].InequalitySign == InequalitySign.GreaterThanOrEqualTo)
+                {
+                    for (int j = 0; j < (tableZero[i].Count - numberOfArtificialVars - 1); j++)
+                    {
+                        wRow[j] += tableZero[i][j];
+                    }
+
+                    wRow[wRow.Count - 1] += tableZero[i][tableZero[i].Count - 1];
+                }
+            }
+
+            tableZero.Insert(0, wRow);
+            model.Result.Add(tableZero);
+        }
+
+        public override void Solve(Model model)
+        {
+            Iterate(model);
+            var lastTable = model.Result[model.Result.Count - 1];
+
+            if (lastTable[0][lastTable[0].Count - 1] > 0)
+            {
+                throw new InfeasibleException("The problem is infeasible");
+            }
+
+            bool allArtificialsNonBasic = true;
+            for (int i = lastTable[0].Count - (numberOfArtificialVars + 1); i < lastTable[0].Count - 1; i++)
+            {
+                if (IsVariableBasic(i, lastTable))
+                {
+                    allArtificialsNonBasic = false;
+                    break;
+                }
+            }
+
+            if (allArtificialsNonBasic)
+            {
+                lastTable.RemoveAt(0);
+
+                for (int i = 0; i < lastTable.Count; i++)
+                {
+                    for (int j = 0; j < numberOfArtificialVars; j++)
+                    {
+                        lastTable[i].RemoveAt(lastTable[i].Count - 2);
+                    }
+                }
+            }
+            else
+            {
+                for (int i = 0; i < model.ObjectiveFunction.DecisionVariables.Count; i++)
+                {
+                    if (lastTable[0][i] < 0)
+                    {
+                        for (int j = 0; j < lastTable.Count; j++)
+                        {
+                            lastTable[j].RemoveAt(i);
+                        }
+                    }
+                }
+
+                for (int i = lastTable[0].Count - (numberOfArtificialVars + 1); i < lastTable[0].Count - 1; i++)
+                {
+                    if (!IsVariableBasic(i, lastTable))
+                    {
+                        for (int j = 0; j < lastTable.Count; j++)
+                        {
+                            lastTable[j].RemoveAt(i);
+                        }
+                    }
+                }
+
+                lastTable.RemoveAt(0);
+            }
+
+            var primalSimplex = new PrimalSimplex();
+            primalSimplex.Solve(model);
+        }
+
+        private bool IsOptimal(Model model)
+        {
+            bool isOptimal = true;
+            var table = model.Result[model.Result.Count - 1];
+
+            for (int i = 0; i < table[0].Count - 1; i++)
+            {
+                if (table[0][i] > 0)
+                {
+                    isOptimal = false;
+                    break;
+                }
+            }
+
+            return isOptimal;
+        }
+
+        private void Iterate(Model model)
+        {
+            if (IsOptimal(model))
+                return;
+
+            int pivotColumn = GetPivotColumn(model);
+            int pivotRow = GetPivotRow(model, pivotColumn);
+
+            if (pivotRow == -1)
+                throw new InfeasibleException("There is no suitable row to pivot on - the problem is infeasible");
+
+            Pivot(model, pivotRow, pivotColumn);
+
+            Iterate(model);
+        }
+
+        private void Pivot(Model model, int pivotRow, int pivotColumn)
+        {
+            var previousTable = model.Result[model.Result.Count - 1];
+            var newTable = new List<List<double>>();
+
+            for (int i = 0; i < previousTable.Count; i++)
+            {
+                newTable.Add(new List<double>());
+
+                for (int j = 0; j < previousTable[i].Count; j++)
+                {
+                    newTable[i].Add(previousTable[i][j]);
+                }
+            }
+
+            double factor = 1 / newTable[pivotRow][pivotColumn];
+            for (int i = 0; i < newTable[pivotRow].Count; i++)
+            {
+                newTable[pivotRow][i] *= factor;
+            }
+
+            double pivotColumnValue;
+            for (int i = 0; i < newTable.Count; i++)
+            {
+                pivotColumnValue = newTable[i][pivotColumn];
+
+                if (i != pivotRow && pivotColumnValue != 0)
+                {
+                    for (int j = 0; j < newTable[i].Count; j++)
+                    {
+                        newTable[i][j] += (-1 * pivotColumnValue * newTable[pivotRow][j]);
+                    }
+                }
+            }
+
+            model.Result.Add(newTable);
+        }
+
+        private int GetPivotColumn(Model model)
+        {
+            int colIndex = -1;
+            var table = model.Result[model.Result.Count - 1];
+            double mostPositive = 0;
+
+            for (int i = 0; i < table[0].Count - 1; i++)
+            {
+                if (table[0][i] > 0 && table[0][i] > mostPositive)
+                {
+                    mostPositive = table[0][i];
+                    colIndex = i;
+                }
+            }
+
+            return colIndex;
+        }
+
+        private int GetPivotRow(Model model, int pivotColumn)
+        {
+            int rowIndex = -1;
+            var table = model.Result[model.Result.Count - 1];
+
+            double lowestRatio = double.MaxValue;
+            for (int i = 1; i < table.Count; i++)
+            {
+                if (table[i][pivotColumn] > 0)
+                {
+                    double ratio = table[i][table[i].Count - 1] / table[i][pivotColumn];
+                    if (ratio < lowestRatio && ratio >= 0)
+                    {
+                        lowestRatio = ratio;
+                        rowIndex = i;
+                    }
+                }
+            }
+
+            return rowIndex;
+        }
+
+        private bool IsVariableBasic(int index, List<List<double>> table)
+        {
+            bool isBasic = true;
+
+            for (int i = 0; i < table.Count; i++)
+            {
+                int numberOfOnes = 0;
+
+                if (table[i][index] == 1)
+                    numberOfOnes++;
+
+                if ((table[i][index] != 0 && table[i][index] != 1) || numberOfOnes > 1)
+                {
+                    isBasic = false;
+                    break;
+                }
+            }
+
+            return isBasic;
+        }
+    }
+}