Add Pareto optimization algorithm (#331)

Co-authored-by: Maksym Sitaylo <m.sitailo@sana-commerce.com>

Author: maxsIT

Algorithms.Tests/Other/ParetoOptimizationTests.cs

@@ -0,0 +1,46 @@
+using Algorithms.Other;
+using NUnit.Framework;
+using System;
+using System.Collections.Generic;
+using System.Linq;
+using System.Text;
+using System.Threading.Tasks;
+
+namespace Algorithms.Tests.Other
+{
+    public static class ParetoOptimizationTests
+    {
+        [Test]
+        public static void Verify_Pareto_Optimization()
+        {
+            // Arrange
+            var paretoOptimization = new ParetoOptimization();
+
+            var matrix = new List<List<decimal>>
+            {
+                new List<decimal> { 7, 6, 5, 8, 5, 6 },
+                new List<decimal> { 4, 8, 4, 4, 5, 3 },
+                new List<decimal> { 3, 8, 1, 4, 5, 2 },
+                new List<decimal> { 5, 6, 3, 6, 4, 5 },
+                new List<decimal> { 1, 4, 8, 6, 3, 6 },
+                new List<decimal> { 5, 1, 8, 6, 5, 1 },
+                new List<decimal> { 6, 8, 3, 6, 3, 5 }
+            };
+
+            var expectedMatrix = new List<List<decimal>>
+            {
+                new List<decimal> { 7, 6, 5, 8, 5, 6 },
+                new List<decimal> { 4, 8, 4, 4, 5, 3 },
+                new List<decimal> { 1, 4, 8, 6, 3, 6 },
+                new List<decimal> { 5, 1, 8, 6, 5, 1 },
+                new List<decimal> { 6, 8, 3, 6, 3, 5 }
+            };
+
+            // Act
+            var optimizedMatrix = paretoOptimization.Optimize(matrix);
+
+            // Assert
+            Assert.AreEqual(optimizedMatrix, expectedMatrix);
+        }
+    }
+}

Algorithms/Other/ParetoOptimization.cs

@@ -0,0 +1,75 @@
+using System;
+using System.Collections.Generic;
+using System.Linq;
+using System.Text;
+using System.Threading.Tasks;
+
+namespace Algorithms.Other
+{
+    /// <summary>
+    /// Almost all real complex decision-making task is described by more than one criterion.
+    /// Therefore, the methods of multicriteria optimization are important. For a wide range
+    /// of tasks multicriteria optimization, described by some axioms of "reasonable"
+    /// behavior in the process of choosing from a set of possible solutions X, each set of
+    /// selected solutions Sel X should be contained in a set optimal for Pareto.
+    /// </summary>
+    public class ParetoOptimization
+    {
+        /// <summary>
+        /// Performs decision optimizations by using Paretor's optimization algorithm.
+        /// </summary>
+        /// <param name="matrix">Contains a collection of the criterias sets.</param>
+        /// <returns>An optimized collection of the criterias sets.</returns>
+        public List<List<decimal>> Optimize(List<List<decimal>> matrix)
+        {
+            var optimizedMatrix = new List<List<decimal>>(matrix.Select(i => i));
+            int i = 0;
+            while (i < optimizedMatrix.Count)
+            {
+                for (int j = i + 1; j < optimizedMatrix.Count; j++)
+                {
+                    decimal directParwiseDifference = GetMinimalPairwiseDifference(optimizedMatrix[i], optimizedMatrix[j]);
+                    decimal indirectParwiseDifference = GetMinimalPairwiseDifference(optimizedMatrix[j], optimizedMatrix[i]);
+                    /*
+                     * in case all criteria of one set are larger that the criteria of another, this
+                     * decision is not optimal and it has to be removed
+                    */
+                    if (directParwiseDifference >= 0 || indirectParwiseDifference >= 0)
+                    {
+                        optimizedMatrix.RemoveAt(directParwiseDifference >= 0 ? j : i);
+                        i--;
+                        break;
+                    }
+                }
+
+                i++;
+            }
+
+            return optimizedMatrix;
+        }
+
+        /// <summary>
+        /// Calculates the smallest difference between criteria of input decisions.
+        /// </summary>
+        /// <param name="arr1">Criterias of the first decision.</param>
+        /// <param name="arr2">Criterias of the second decision.</param>
+        /// <returns>Values that represent the smallest difference between criteria of input decisions.</returns>
+        private decimal GetMinimalPairwiseDifference(List<decimal> arr1, List<decimal> arr2)
+        {
+            decimal min = decimal.MaxValue;
+            if (arr1.Count == arr2.Count)
+            {
+                for (int i = 0; i < arr1.Count; i++)
+                {
+                    decimal difference = arr1[i] - arr2[i];
+                    if (min > difference)
+                    {
+                        min = difference;
+                    }
+                }
+            }
+
+            return min;
+        }
+    }
+}

README.md

@@ -168,6 +168,7 @@ find more than one implementation for the same objective but using different alg
     * [Koch Snowflake](./Algorithms/Other/KochSnowflake.cs)
     * [RGB-HSV Conversion](./Algorithms/Other/RGBHSVConversion.cs)
     * [Flood Fill](./Algorithms/Other/FloodFill.cs)
+    * [Pareto Optimization](./Algorithms/Other/ParetoOptimization.cs)
   * [Problems](./Algorithms/Problems)
     * [Stable Marriage](./Algorithms/Problems/StableMarriage)
       * [Gale-Shapley](./Algorithms/Problems/StableMarriage/GaleShapley.cs)