Solution Approaches for Balanced Task Allocation in Multiple Traveling Salesman Problems

In multiple traveling salesman problems (mTSP), balanced task allocation serves as a common objective function. However, practical applications often face constraints such as limited number of salesmen and time window restrictions. Our research demonstrates that genetic algorithms (GA) and simulated annealing (SA) provide effective solutions for balanced mTSP. Key implementation aspects include introducing crossover and mutation operations to enhance population diversity, enabling better exploration of the solution space. The crossover operation typically combines route segments from parent solutions, while mutation introduces random perturbations to escape local optima. Additionally, adaptive parameter tuning dynamically adjusts mutation rates and selection pressures based on population fitness. Local search mechanisms like 2-opt or 3-opt optimization can be integrated to refine routes by eliminating path crossings. The algorithm workflow generally involves: 1) Initializing population with feasible routes, 2) Evaluating fitness based on balanced workload distribution, 3) Applying selection, crossover, and mutation operations, 4) Incorporating SA's temperature-controlled acceptance criteria for solution diversification. Convergence is accelerated through elitism strategies that preserve best-performing solutions across generations. This combined approach demonstrates significant value in real-world applications where equitable workload distribution among salesmen is critical, particularly in logistics planning and service route optimization scenarios. The methodology effectively balances computational efficiency with solution quality through hybrid metaheuristic techniques.