TSP - Travelling Salesman Problem

The Nearest Insertion Heuristic is a popular approximation algorithm for solving the Traveling Salesman Problem (TSP). This heuristic aims to find a near-optimal solution by iteratively adding nodes in a way that minimizes the increase in cost. Below, I'll explain how this works and provide a brief overview of its implementation.

Nearest Insertion Heuristic

The nearest insertion algorithm starts with an arbitrary node and then repeatedly adds the closest unvisited node to the current tour until all nodes are included. The key steps are:

1. Initialization: Start with any single vertex.
2. Insertion Step:
   • Find the unvisited vertex that is closest to some edge in the current path (or cycle).
   • Insert this vertex into the position where it minimizes the increase in total tour length.

Steps of Nearest Insertion Heuristic

1. Start with a single node: Choose an arbitrary starting node and initialize the tour.
2. Find nearest unvisited node: For each edge in the current path, find the closest unvisited node to that edge.
3. Insert the node: Insert the found node into the position where it minimizes the increase in total tour length.

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