Solving Traveling Salesman Problem Using Genetic Algorithm

Traveling Salesman Problem:

The Traveling Salesman Problem (TSP) aims to find the shortest possible route that visits each city exactly once from a given set of cities and returns to the origin city. As an NP-hard problem, TSP computations become extremely time-consuming unless approximate solutions are accepted [3]. Currently, the only guaranteed method for optimal solutions at any scale is enumerating all possible tours and selecting the minimum-cost route. Each possible tour represents a permutation of cities {1,2,3,...,n}, where n is the number of cities, resulting in n! possible tours. As n increases, polynomial-time cost calculation for each tour becomes impossible. While such exhaustive methods guarantee optimality, their time complexity makes them impractical even for small cases.

This project implements a genetic algorithm solution for TSP using MATLAB code. Genetic algorithms simulate natural selection and genetic mechanisms by evolving solutions through crossover and mutation operations, with fitness-based selection. Key implementation components include: 1) Population initialization with random city permutations 2) Fitness evaluation using tour distance calculation 3) Selection operators favoring shorter routes 4) Crossover operations combining parent routes 5) Mutation introducing route variations. The algorithm efficiently explores solution spaces without guaranteeing optimality but produces high-quality approximations within feasible timeframes.

The accompanying MATLAB code provides a complete genetic algorithm implementation for TSP, including helper functions for solution evaluation and improvement. The main script orchestrates evolutionary iterations while modular functions handle specific operations like route encoding, distance computation, and genetic operators. Users can modify parameters like population size, mutation rate, and termination conditions to optimize performance for different problem instances. This code serves as an educational foundation for understanding and customizing evolutionary approaches to combinatorial optimization problems.