An Evolutionary Algorithm for the Travelling Sales Man problem

This study explores the use of Genetic Algorithms (GA) to solve the NP-hard combinatorial optimization problem known as the Travelling Salesman Problem (TSP). The suggested GA, called GA-P, performs better than conventional techniques because it uses a new randomized crossover threshold. According to experimental assessments, GA-P outperforms a normal Genetic Algorithm with fixed crossover (GA-N, 628.6) and approaches the best Branch and Bound solutions (B&B, 560.6) with an average cost of 617.4 for 16-node graphs. With average execution times of 0.1347 seconds for 16 nodes, GA-P also demonstrates constant computational efficiency, outperforming B&B's exponentially growing temporal complexity (169.37 seconds for 16 nodes). In order to balance solution quality and computational cost, hyperparameter tweaking revealed the ideal values of population percentage (pp = 1.1), crossover proportion (cp = 0.8), mutation threshold (mt = 0.3), and exploration probability (ep = 0.2). The results show that GA-P is a scalable and efficient substitute for TSP, with room for improvement via parallelization and exploratory techniques.