Several algorithms have been proposed in recent decades to solve optimization problems, some of which have been inspired by nature. The collective behavior of ants is an example of intelligence in the nature which has been a source of inspiration for optimization algorithms. Based on the concept of path integration, ants are able to continuously calculate their current location from their previous trajectory when exploring to find food. In the return journey, they go by calculating the outcome of the route, without returning exactly from their path, choosing a direct path to return to their original point. In this paper, the behavior of desert ants in finding their return path to the nest is the source of inspiration. By modeling the swarm intelligence of these ants based on the results of empirical scientific research, a new optimization algorithm is presented, termed Ant Path Integration. In this paper, the mathematical relationships governing the concept of path integration are presented. Simulation results on a variety of benchmark functions, including some of the CEC2019 benchmarks, show the superiority of this algorithm in finding the optimal solution in comparison to some well-known optimization algorithms.