Binary particle swarm optimization: a forma analysis approach

PSO was originally designed as a numerical optimization technique based on swarm intelligence [1]. This paper aims to generalize PSO in a rigorous manner with forma analysis [2]. Thus, binary PSO operators can be formally derived in a principled manner. Forma analysis is a formal but practical method that allows the problem representation and its operators to be structured in a formal manner by using equivalence relations. Since equivalence relations/classes have the ability to capture the properties of solutions, concrete operators can thus be mathematically derived by manipulating these equivalence relations in a formal way. Our approach (as illustrated in Figure 1) can be explained as, given an operator template, any suitable description of the considered problem domain gives rise to a concrete operator, whose behaviors and performance are related to the assumption we make to describe the search space.