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Most swarm intelligence algorithms were devised for continuous optimization problems. However, they have been adapted for discrete optimization as well with applications in different domains. This survey aims at providing an updated review of research of swarm intelligence algorithms for discrete optimization problems, comprising combinatorial or binary. The biological inspiration that motivated the creation of each swarm algorithm is introduced, and later, the discretization and encoding methods are used to adapt each algorithm for discrete problems. Methods are compared for different classes of problems and a critical analysis is provided, pointing to future trends.