The rank-based ant system (RAS) is a probabilistic technique that simulates the feeding behavior of ants and uses it to solve problems for which there is no efficient algorithm yet. This paper presents a combined method based on this algorithm along with two local search algorithms to solve the vehicle routing problem with simultaneous pickup and delivery of goods (VRPSPD), as one of the most important combined optimization problems. In this problem, vehicles not only deliver goods to customers as in the vehicle routing problem, but also receive goods from customers at the same time. The proposed method is different from the usual RAS method in the decision rule and evaporation update. This action prevents premature convergence, escapes from local optimal points and finds better solutions for the algorithm. The proposed algorithm has been implemented on 28 standard examples from the subject literature. The computational results show that the algorithm has been able to compete closely with other meta-heuristic algorithms for solving the VRPSPD problem. Also, this paper shows the effectiveness of the proposed algorithm for this problem.
