This paper presents a meta-heuristic approach for the NP-hard multi-pickup and delivery problem with time windows based on Ant Colony Optimization (ACO) algorithm. ACO is an algorithm that mimics the behaviour of ant colonies in efficiently finding the shortest path from the nest to a food source. The Smooth Max-Min Ant System algorithm is used as a rule to update pheromone in the ACO algorithm. Visual Studio 2019 is used as the program software. The test instances of 24 types are used in computational experiments. The experiments have been tested with 100, 200, 500, 1000, 2000, and 3000 iterations. The results are then compared with those generated by the CPLEX optimizer. Among three window types, the instances belonging to Normal Time Windows produced the best results. For the same node cases, the instances with long requests were solved faster than those with short requests due to having fewer requests that needed to work with than the latter. The results were assessed via a comparison with the Adaptive Large Neighborhood Search, CPLEX, in which the ACO algorithm performed well in most instances. Since mathematical programming could not handle instances with 400 nodes, it could be said that the problem is complicated and complex. This demonstrated the NP-hard characteristics of the multi-pickup and delivery problem with the time windows problem.