[wpimath] Add simulated annealing

Co-authored-by: Ashray._.g <ashray.gupta@gmail.com>

wpimath/src/main/java/edu/wpi/first/math/optimization/SimulatedAnnealing.java

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+// Copyright (c) FIRST and other WPILib contributors.
+// Open Source Software; you can modify and/or share it under the terms of
+// the WPILib BSD license file in the root directory of this project.
+
+package edu.wpi.first.math.optimization;
+
+import java.util.function.Function;
+import java.util.function.ToDoubleFunction;
+
+/**
+ * An implementation of the Simulated Annealing stochastic nonlinear optimization method.
+ *
+ * @see <a
+ *     href="https://en.wikipedia.org/wiki/Simulated_annealing">https://en.wikipedia.org/wiki/Simulated_annealing</a>
+ */
+public final class SimulatedAnnealing<T> {
+  private final double m_initialTemperature;
+  private final Function<T, T> m_neighbor;
+  private final ToDoubleFunction<T> m_cost;
+
+  /**
+   * Constructor for Simulated Annealing that can be used for the same functions but with different
+   * initial states.
+   *
+   * @param initialTemperature The initial temperature. Higher temperatures make it more likely a
+   *     worse state will be accepted during iteration, helping to avoid local minima. The
+   *     temperature is decreased over time.
+   * @param neighbor Function that generates a random neighbor of the current state vector.
+   * @param cost Function that returns the scalar cost of a state vector.
+   */
+  public SimulatedAnnealing(
+      double initialTemperature, Function<T, T> neighbor, ToDoubleFunction<T> cost) {
+    m_initialTemperature = initialTemperature;
+    m_neighbor = neighbor;
+    m_cost = cost;
+  }
+
+  /**
+   * Runs the Simulated Annealing algorithm.
+   *
+   * @param initialGuess The initial state.
+   * @param iterations Number of iterations to run the solver.
+   * @return The optimized state vector.
+   */
+  public T solve(T initialGuess, int iterations) {
+    T minState = initialGuess;
+    double minCost = Double.MAX_VALUE;
+
+    T state = initialGuess;
+    double cost = m_cost.applyAsDouble(state);
+
+    for (int i = 0; i < iterations; ++i) {
+      double temperature = m_initialTemperature / i;
+
+      T proposedState = m_neighbor.apply(state);
+      double proposedCost = m_cost.applyAsDouble(proposedState);
+      double deltaCost = proposedCost - cost;
+
+      double acceptanceProbability = Math.exp(-deltaCost / temperature);
+
+      // If cost went down or random number exceeded acceptance probability,
+      // accept the proposed state
+      if (deltaCost < 0 || acceptanceProbability >= Math.random()) {
+        state = proposedState;
+        cost = proposedCost;
+      }
+
+      // If proposed cost is less than minimum, the proposed state becomes the
+      // new minimum
+      if (proposedCost < minCost) {
+        minState = proposedState;
+        minCost = proposedCost;
+      }
+    }
+
+    return minState;
+  }
+}

wpimath/src/main/java/edu/wpi/first/math/path/TravelingSalesman.java

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+// Copyright (c) FIRST and other WPILib contributors.
+// Open Source Software; you can modify and/or share it under the terms of
+// the WPILib BSD license file in the root directory of this project.
+
+package edu.wpi.first.math.path;
+
+import edu.wpi.first.math.Num;
+import edu.wpi.first.math.Vector;
+import edu.wpi.first.math.geometry.Pose2d;
+import edu.wpi.first.math.optimization.SimulatedAnnealing;
+import java.util.function.ToDoubleBiFunction;
+
+/**
+ * Given a list of poses, this class finds the shortest possible route that visits each pose exactly
+ * once and returns to the origin pose.
+ *
+ * @see <a
+ *     href="https://en.wikipedia.org/wiki/Travelling_salesman_problem">https://en.wikipedia.org/wiki/Travelling_salesman_problem</a>
+ */
+public class TravelingSalesman {
+  // Default cost is 2D distance between poses
+  private final ToDoubleBiFunction<Pose2d, Pose2d> m_cost;
+
+  /**
+   * Constructs a traveling salesman problem solver with a cost function defined as the 2D distance
+   * between poses.
+   */
+  public TravelingSalesman() {
+    this((Pose2d a, Pose2d b) -> Math.hypot(a.getX() - b.getX(), a.getY() - b.getY()));
+  }
+
+  /**
+   * Constructs a traveling salesman problem solver with a user-provided cost function.
+   *
+   * @param cost Function that returns the cost between two poses. The sum of the costs for every
+   *     pair of poses is minimized.
+   */
+  public TravelingSalesman(ToDoubleBiFunction<Pose2d, Pose2d> cost) {
+    m_cost = cost;
+  }
+
+  /**
+   * Finds the path through every pose that minimizes the cost.
+   *
+   * @param <Poses> A Num defining the length of the path and the number of poses.
+   * @param poses An array of Pose2ds the path must pass through.
+   * @param iterations The number of times the solver attempts to find a better random neighbor.
+   * @return The optimized path as a list of Pose2ds.
+   */
+  public <Poses extends Num> Pose2d[] solve(Pose2d[] poses, int iterations) {
+    var solver =
+        new SimulatedAnnealing<>(
+            1,
+            this::neighbor,
+            // Total cost is sum of all costs between adjacent pose pairs in path
+            (Vector<Poses> state) -> {
+              double sum = 0;
+              for (int i = 0; i < state.getNumRows(); ++i) {
+                sum +=
+                    m_cost.applyAsDouble(
+                        poses[(int) state.get(i, 0)],
+                        poses[(int) (state.get((i + 1) % poses.length, 0))]);
+              }
+              return sum;
+            });
+
+    var initial = new Vector<Poses>(() -> poses.length);
+    for (int i = 0; i < poses.length; ++i) {
+      initial.set(i, 0, i);
+    }
+
+    var indices = solver.solve(initial, iterations);
+
+    var solution = new Pose2d[poses.length];
+    int dest = 0;
+    for (int src = 0; src < indices.getNumRows(); ++src) {
+      solution[dest] = poses[(int) indices.get(src, 0)];
+      ++dest;
+    }
+
+    return solution;
+  }
+
+  /**
+   * A random neighbor is generated to try to replace the current one.
+   *
+   * @param state A vector that is a list of indices that defines the path through the path array.
+   * @return Generates a random neighbor of the current state by flipping a random range in the path
+   *     array.
+   */
+  private <Poses extends Num> Vector<Poses> neighbor(Vector<Poses> state) {
+    var proposedState = new Vector<Poses>(state);
+
+    int rangeStart = (int) (Math.random() * (state.getNumRows() - 1));
+    int rangeEnd = (int) (Math.random() * (state.getNumRows() - 1));
+    if (rangeEnd < rangeStart) {
+      int temp = rangeEnd;
+      rangeEnd = rangeStart;
+      rangeStart = temp;
+    }
+
+    for (int i = rangeStart; i <= (rangeStart + rangeEnd) / 2; ++i) {
+      double temp = proposedState.get(i, 0);
+      proposedState.set(i, 0, state.get(rangeEnd - (i - rangeStart), 0));
+      proposedState.set(rangeEnd - (i - rangeStart), 0, temp);
+    }
+
+    return proposedState;
+  }
+}

wpimath/src/main/native/include/frc/optimization/SimulatedAnnealing.h

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+// Copyright (c) FIRST and other WPILib contributors.
+// Open Source Software; you can modify and/or share it under the terms of
+// the WPILib BSD license file in the root directory of this project.
+
+#pragma once
+
+#include <cmath>
+#include <functional>
+#include <limits>
+#include <random>
+
+namespace frc {
+
+/**
+ * An implementation of the Simulated Annealing stochastic nonlinear
+ * optimization method.
+ *
+ * @see <a
+ * href="https://en.wikipedia.org/wiki/Simulated_annealing">https://en.wikipedia.org/wiki/Simulated_annealing</a>
+ */
+template <typename T>
+class SimulatedAnnealing {
+ public:
+  /**
+   * Constructor for Simulated Annealing that can be used for the same functions
+   * but with different initial states.
+   *
+   * @param initialTemperature The initial temperature. Higher temperatures make
+   *     it more likely a worse state will be accepted during iteration, helping
+   *     to avoid local minima. The temperature is decreased over time.
+   * @param neighbor Function that generates a random neighbor of the current
+   *     state vector.
+   * @param cost Function that returns the scalar cost of a state vector.
+   */
+  SimulatedAnnealing(double initialTemperature,
+                     std::function<T(const T&)> neighbor,
+                     std::function<double(const T&)> cost)
+      : m_initialTemperature{initialTemperature},
+        m_neighbor{neighbor},
+        m_cost{cost} {}
+
+  /**
+   * Runs the Simulated Annealing algorithm.
+   *
+   * @param initialGuess The initial state.
+   * @param iterations Number of iterations to run the solver.
+   * @return The optimized state vector.
+   */
+  T Solve(const T& initialGuess, int iterations) {
+    T minState = initialGuess;
+    double minCost = std::numeric_limits<double>::infinity();
+
+    std::random_device rd;
+    std::mt19937 gen{rd()};
+    std::uniform_real_distribution<> distr{0.0, 1.0};
+
+    T state = initialGuess;
+    double cost = m_cost(state);
+
+    for (int i = 0; i < iterations; ++i) {
+      double temperature = m_initialTemperature / i;
+
+      T proposedState = m_neighbor(state);
+      double proposedCost = m_cost(proposedState);
+      double deltaCost = proposedCost - cost;
+
+      double acceptanceProbability = std::exp(-deltaCost / temperature);
+
+      // If cost went down or random number exceeded acceptance probability,
+      // accept the proposed state
+      if (deltaCost < 0 || acceptanceProbability >= distr(gen)) {
+        state = proposedState;
+        cost = proposedCost;
+      }
+
+      // If proposed cost is less than minimum, the proposed state becomes the
+      // new minimum
+      if (proposedCost < minCost) {
+        minState = proposedState;
+        minCost = proposedCost;
+      }
+    }
+
+    return minState;
+  }
+
+ private:
+  double m_initialTemperature;
+  std::function<T(const T&)> m_neighbor;
+  std::function<double(const T&)> m_cost;
+};
+
+}  // namespace frc