Сизов Дмитрий. Технология SEQ-MPI. Алгоритм глобального поиска (Стронгина) для одномерных задач оптимизации. Распараллеливание по характеристикам. Вариант 11. (#149)

## Description

- **Task**: Алгоритм глобального поиска (Стронгина) для одномерных задач
оптимизации. Распараллеливание по характеристикам / Global Search
Algorithm (Strongin) for One-Dimensional Optimization Problems.
Parallelization by Characteristics.
- **Variant**: 11
- **Technology**: SEQ+MPI
- **Description:**

- The solution is based on **Strongin’s global search algorithm**, a
deterministic
method for one-dimensional global optimization. The algorithm
iteratively refines
a closed interval by evaluating the objective function at selected
points and
choosing the most promising interval according to the Strongin
characteristic.
    
- In the sequential version, the algorithm maintains an ordered set of
sampled
points, computes an adaptive Lipschitz-like estimate, and selects the
interval
with the maximum characteristic for further refinement. The process
continues
until the required accuracy is reached or the iteration limit is
exceeded.
    
- The parallel MPI version applies **parallelization by interval
characteristics**.
At each iteration, the set of intervals is distributed among MPI
processes, which
compute characteristics locally. The globally best interval is selected
using
`MPI_Allreduce`, after which a new sampling point is generated and
broadcast to
all processes. This approach preserves the deterministic behavior of the
algorithm while reducing execution time for computationally intensive
cases.

---

## Checklist

- [x] **CI Status**: All CI jobs (build, tests, report generation) are
passing on my branch in my fork
- [x] **Task Directory & Naming**: I have created a directory named
`<lastName>_<firstInitial>_<short_task_name>`
- [x] **Full Task Definition**: I have provided the complete task
description in the pull request body.
- [x] **clang-format**: My changes pass `clang-format` locally in my
fork (no formatting errors)
- [x] **clang-tidy**: My changes pass `clang-tidy` locally in my fork
(no warnings/errors)
- [x] **Functional Tests**: All functional tests are passing locally on
my machine
- [x] **Performance Tests**: All performance tests are passing locally
on my machine
- [x] **Branch**: I am working on a branch named exactly as my task
directory (e.g., `nesterov_a_vector_sum`), not on `master`.
- [x] **Truthful Content**: I confirm that every detail provided in this
pull request is accurate and truthful to the best of my knowledge.

Author: SizovDmitry

tasks/sizov_d_global_search/common/include/common.hpp

@@ -0,0 +1,44 @@
+#pragma once
+
+#include <functional>
+#include <string>
+
+#include "task/include/task.hpp"
+
+namespace sizov_d_global_search {
+
+using Function = std::function<double(double)>;
+
+struct Problem {
+  Function func;
+  double left = 0.0;
+  double right = 0.0;
+  double accuracy = 1e-4;
+  double reliability = 3.0;
+  int max_iterations = 300;
+  bool enable_stable_heuristic = true;
+  bool enable_point_limit = true;
+};
+
+struct Solution {
+  double argmin = 0.0;
+  double value = 0.0;
+  int iterations = 0;
+  bool converged = false;
+};
+
+struct TestCase {
+  std::string name;
+  Problem problem;
+};
+
+static constexpr double kDefaultAccuracy = 1e-4;
+static constexpr double kDefaultReliability = 3.0;
+static constexpr int kDefaultMaxIterations = 300;
+
+using InType = Problem;
+using OutType = Solution;
+using TestType = TestCase;
+using BaseTask = ppc::task::Task<InType, OutType>;
+
+}  // namespace sizov_d_global_search

tasks/sizov_d_global_search/data/tests.json

@@ -0,0 +1,44 @@
+[
+  {
+    "name": "case_001_linear_inc",
+    "function": { "expression": "x" },
+    "problem": { "left": -5.0, "right": 5.0 },
+    "expected": { "argmins": [-5.0], "value": -5.0 }
+  },
+
+  {
+    "name": "case_002_linear_dec",
+    "function": { "expression": "-2*x + 3" },
+    "problem": { "left": -5.0, "right": 5.0 },
+    "expected": { "argmins": [5.0], "value": -7.0 }
+  },
+
+  {
+    "name": "case_003_quadratic",
+    "function": { "expression": "(x - 2)^2 + 1" },
+    "problem": { "left": 0.0, "right": 4.0 },
+    "expected": { "argmins": [2.0], "value": 1.0 }
+  },
+
+  {
+    "name": "case_004_abs_shift",
+    "function": { "expression": "abs(x - 1)" },
+    "problem": { "left": -4.0, "right": 4.0 },
+    "expected": { "argmins": [1.0], "value": 0.0 }
+  },
+  
+  {
+    "name": "case_005_exp",
+    "function": { "expression": "exp(x)" },
+    "problem": { "left": 0.0, "right": 2.0 },
+    "expected": { "argmins": [0.0], "value": 1.0 }
+  },
+
+  {
+    "name": "case_006_log_abs_shift",
+    "function": { "expression": "log(abs(x - 1) + 2)" },
+    "problem": { "left": -2.0, "right": 4.0 },
+    "expected": { "argmins": [1.0], "value": 0.6931471805599453 }
+  }
+
+]

tasks/sizov_d_global_search/info.json

@@ -0,0 +1,9 @@
+{
+  "student": {
+    "first_name": "Дмитрий",
+    "last_name": "Сизов",
+    "middle_name": "Игоревич",
+    "group_number": "3823Б1ФИ2",
+    "task_number": "3"
+  }
+}

tasks/sizov_d_global_search/mpi/include/ops_mpi.hpp

@@ -0,0 +1,62 @@
+#pragma once
+
+#include <cstddef>
+#include <vector>
+
+#include "sizov_d_global_search/common/include/common.hpp"
+#include "task/include/task.hpp"
+
+namespace sizov_d_global_search {
+
+class SizovDGlobalSearchMPI : public BaseTask {
+ public:
+  static constexpr ppc::task::TypeOfTask GetStaticTypeOfTask() {
+    return ppc::task::TypeOfTask::kMPI;
+  }
+
+  explicit SizovDGlobalSearchMPI(const InType &in);
+
+ private:
+  bool ValidationImpl() override;
+  bool PreProcessingImpl() override;
+  bool RunImpl() override;
+  bool PostProcessingImpl() override;
+
+  struct IntervalChar {
+    double characteristic = 0.0;
+    int index = -1;
+  };
+
+  struct InsertMsg {
+    double x_new = 0.0;
+    double y_new = 0.0;
+    int idx = -1;
+  };
+
+  static void GetChunk(std::size_t intervals, int rank, int size, std::size_t &begin, std::size_t &end);
+
+  [[nodiscard]] double EstimateM(double reliability, int rank, int size) const;
+  [[nodiscard]] double Characteristic(std::size_t i, double m) const;
+  [[nodiscard]] double NewPoint(std::size_t i, double m) const;
+
+  [[nodiscard]] IntervalChar ComputeLocalBestInterval(double m, int rank, int size) const;
+  static int ReduceBestIntervalIndex(const IntervalChar &local, int n, int size);
+
+  [[nodiscard]] bool CheckStopByAccuracy(const Problem &p, int best_idx, int rank) const;
+
+  void BroadcastState(int rank);
+  void BroadcastNewPoint(int best_idx, double m, const Problem &p, int rank);
+  void BroadcastResult(int rank);
+
+  static void BroadcastInsertMsg(InsertMsg &msg, int rank);
+
+  std::vector<double> x_;
+  std::vector<double> y_;
+
+  double best_x_ = 0.0;
+  double best_y_ = 0.0;
+  int iterations_ = 0;
+  bool converged_ = false;
+};
+
+}  // namespace sizov_d_global_search