In this chapter, we describe the ant colony optimization (ACO) algorithm and other advanced algorithms that are derived from the basic approach. ACO is applied to solve NP‐hard problems with combinatorial nature, and this algorithm is classified in soft computing branch. In the first section, we articulate the history of ACO and characteristics of ACO are described, and then the inspiration of the ant's nature along with double bridge experiment is explained. In the second section, we introduce ACO as a meta‐heuristic, and the mechanism and steps of the algorithm are then described. In the third section, the newest versions of ACO are introduced and described. We categorize all versions into two classes comprising approaches with different pheromone trail updating strategy, and hybrid approaches. In the fourth section, we introduce some multi‐objective ACO in literature, and lastly, the new application of bi‐objective ACO for surgical case scheduling (SCS) problem is described. In the last section, we suggest the meta‐heuristic ant system (AS) to tackle the combinatorial nature of bi‐objective SCS problem. Therefore, we give a terse description of basic ACO and equations of some advanced ACO in literature.