Concave cost transhipment problems are difficult to optimally solve for large-scale problems within a limited period of time. Recently, some modern meta-heuristics have been employed for the development of advanced local search based or population-based stochastic search algorithms that can improve the conventional heuristics. Besides these meta-heuristics, the ant colony system algorithm is a population-based stochastic search algorithm which has been used to obtain good results in many applications. This study employs the ant colony system algorithm, coupled with some genetic algorithm and threshold accepting algorithm techniques, to develop a population based stochastic search algorithm for efficiently solving square root concave cost transhipment problems. The developed algorithms are evaluated with a number of problem instances. The results indicate that the proposed algorithm is more effective for solving square root concave cost transhipment problems than other recently designed local search based algorithms and genetic algorithm.