A multi-parent genetic algorithm for solving longitude–latitude-based 4D traveling salesman problems under uncertainty

In this study, we propose a mathematical model of a 4D clustered traveling salesman problem (CTSP) to address the cost-effective security and risk-related difficulties associated with the TSP. We used a multiparent-based memetic genetic algorithm to optimize paths between all clusters and proposed unique heuristic approaches to create clusters and reconnect them. We constructed a 4D CTSP considering multiple routes between two locations and multiple available vehicles on each route. Travel expenses and risks impact every itinerary; however, the behaviors of these costs and risks are always uncertain. We inspected various standard benchmark problems from (TSPLIB) using the proposed calculations. Real-life problems in the tourism industry motivate a longitude–latitude-based CTSP with risk constraints. Thus, we determined the risk of each path based on longitude and latitude. The contributions of this study are twofold: developing a genetic algorithm and heuristics based on mathematical modeling of a real problem.