SwarmOps works for real-valued and single-objective optimization problems, that is, optimization problems that map candidate solutions from -dimensional real-valued spaces to one-dimensional real-valued spaces. Mathematically speaking, we consider optimization problems to be functions  of the following form:

In SwarmOps, it is assumed that  is a minimization problem, meaning that we are searching for the candidate solution with the smallest value . Mathematically, this may be written as the following:

Find , such that .

Typically, however, it is not possible to locate the exact optimum; we must be satisfied with a candidate solution of sufficient quality that is perhaps not quite optimal. In this chapter, we refer to the optimization problem  as the fitness function, but it is can also be known as the cost function, objective function, error function, quality measure, and so on. We may also refer to candidate solutions as positions, agents, or particles, and to all possible candidate solutions as the search-space.