A Survey of Swarm Algorithms Applied to Discrete Optimization Problems

Swarm-based algorithms are inspired by the behavior of some social living beings, such as ants, termites, birds, and fishes. Self-organization and decentralized control are remarkable features of swarm-based systems that, such as in nature, lead to an emergent behavior. Emergent behavior is a property that emerges through local interactions among system components and it is not possible to be achieved by any of the components of the system acting alone (Garnier et al., 2007). In the beginning, the two mainstreams of the Swarm Intelligence area were ant colony optimization (Dorigo and Stützle, 2004) and particle swarm optimization (PSO) (Kennedy and Eberhart, 2001). In recent years, new swarm intelligence algorithms have appeared, inspired by fish schools (Cai, 2010), gravity and mass interactions (Rashedi et al., 2009), as well as different aspects of the behavior of bees (Abbass, 2001b; Karaboga, 2005; Lucic and Teodorovic, 2002; Pham et al., 2005), bacteria (Passino, 2002), glowworms (Krishnanand and Ghose, 2005), fireflies (Yang, 2008), cockroaches (Havens et al., 2008), bats (Yang, 2009), and cuckoo birds (Yang and Deb, 2009). For a thorough review of recent approaches, see Parpinelli and Lopes (2011). Despite the swarm inspiration common to these approaches, they have their own particular way to exploit and explore the search space of the problem. Although almost all the above cited algorithms were designed to be applied to continuous optimization, several of them were later adapted to handle discrete domain problems. Unlike the continuous domain, in which the elements have the