LKH Algorithm: Implementation in C Programming Language

The Lin-Kernighan Heuristic (LKH) Algorithm is a popular combinatorial optimization algorithm that aims to find efficient solutions for the Traveling Salesman Problem (TSP). TSP, a classic optimization problem, involves finding the shortest possible route for a salesman to visit a defined set of cities and return to the original city.

To implement the LKH algorithm in C programming language, we need to break down the steps involved in solving the TSP using this heuristic. The algorithm takes an input of a distance matrix that represents the distances between all pairs of cities. Let's explore the C language implementation of this algorithm.

Step 1: Data Structures

To store the input data, we need to define appropriate structures. We can define a structure to represent a city, containing its index and coordinates.

typedef struct
  int index;
  double x;
  double y;
City;

We can also define a structure to represent a path, containing the number of cities and an array to store the order of visited cities.

typedef struct {
  int numOfCities;
  int* cities;
} Path;

Step 2: Initialization

Next, we need to initialize the necessary variables and data structures for the algorithm. We can start by reading the distance matrix and creating a dynamically allocated array to store the distances.

double** distances = (double**)malloc(numOfCities * sizeof(double*));
for (int i = 0; i < numOfCities; i++) {
  distances[i] = (double*)malloc(numOfCities * sizeof(double));
}
// Read distances and populate the distances array

We also need to initialize the path with an initial solution. This can be done randomly or by using a simple heuristic approach.

Step 3: Main Algorithm

The main algorithm of LKH consists of a series of iterations. Each iteration involves applying the Lin-Kernighan move to improve the current solution. The Lin-Kernighan move is a local search operator that exchanges two edges in the tour to create a shorter tour.

int hasImproved = 1;
while (hasImproved) {
  hasImproved = 0;
  for (int i = 1; i < numOfCities - 2; i++) {
    for (int j = i + 1; j < numOfCities - 1; j++) {
      // Apply Lin-Kernighan move and evaluate the improvement
      if (improvement > 0)
        // Update the path and mark improvement flag
        hasImproved = 1;
      
    }
  }
}

Step 4: Output

Finally, we need to output the best solution found by the algorithm. This can be done by printing the order of visited cities and the total distance of the tour.

printf("Best tour found:\n");
for (int i = 0; i < numOfCities; i++) {
  printf("%d ", path.cities[i]);
}
printf("\nTotal distance: %f\n", totalDistance);

Step 5: Cleanup

After obtaining the solution, we should free any dynamically allocated memory to avoid memory leaks.

for (int i = 0; i < numOfCities; i++) {
  free(distances[i]);
}
free(distances);

In conclusion, the LKH Algorithm is a powerful approach to solving the Traveling Salesman Problem. By implementing this algorithm in the C programming language, we can efficiently find near-optimal solutions for TSP instances. With proper initialization, main algorithm implementation, and output generation, we can harness the power of the LKH Algorithm to solve real-world optimization problems efficiently.

相似文章

友情链接
• 网站定制开发
• 帮你发
• 小蓄群站获客
• 雅圣洁家政