This project was done for the Design of Algorithms curricular unit @ FEUP - Faculdade de Engenharia da Universidade do Porto. It implements different algorithms and heuristics for solving the Traveling Salesman Problem (TSP) using C++ and provides a menu-based interface to interact with the algorithms and compare their performance on various graphs.
TSP Backtracking - It gives the optimal solution, efficient for small graphs.
Kruskal and Prim - Algorithms designed to find the Minimum Spanning Tree (MST) of the graph that help in other algorithms such as Christofides and Greedy Heuristics.
TSP 2 Approximation Heuristic - Relies on the triangular inequality, guarantees a ratio of at most 2 times the optimal solution.
TSP Nearest Neighbor Heuristic - Greedy heuristic which always chooses the next cheapest node to visit, similar to Prim's algorithm.
TSP Greedy Heuristic - Another greedy heuristic which always chooses the cheapest edge, similar to Kruskal's algorithm. Implemented with a priority queue and used in complete graphs.
TSP 1 Tree Lower Bound - Algorithm that calculates the largest MST with Prim after removing each node. Finds the best lower bound for the optimal solution.
Christofides Algorithm - Maybe the best algorithm for finding an approximation for the optimal solution in an efficient way in complete graphs. Guarantees a ratio of at most 1.5 times the optimal solution.
TSP 2 Opt Improvement - Algorithm that takes a TSP path as input and, using local search, keeps swapping pairs of nodes until it doesn't find a better path. Improves many of the above algorithms' solutions.
Other Functions - Other functions implemented to parse the information given on the csv files, the Haversine function for finding the distance between two geographical locations, and other algorithms.
