Competitive traveling salesman problem is one type of traveling salesman problem in which multiple agents compete in visiting several cities. A reward will be given to the agent who visits a city before his rival agent. Each agent’s goal was to use as little time as possible while collecting as many rewards as feasible across the shortest possible journey distance. It is still impossible to find an efficient algorithm to handle this challenging decision-making situation. To increase the quality of the answers with less computing complexity, we examine a simulated annealing strategy for the competitive traveling salesman problem. This approach utilizes a simulated annealing-based method that depends upon the cooling rate and temperature to identify the nearest city.