  A general condition determining the optimal performance of a complex system
has not yet been found and the possibility of its existence is unknown. To
contribute in this direction, an optimization algorithm as a complex system is
presented. The performance of the algorithm for any problem is controlled as a
convex function with a single optimum. To characterize the performance
optimums, certain quantities of the algorithm and the problem are suggested and
interpreted as their complexities. An optimality condition of the algorithm is
computationally found: if the algorithm shows its best performance for a
problem, then the complexity of the algorithm is in a linear relationship with
the complexity of the problem. The optimality condition provides a new
perspective to the subject by recognizing that the relationship between certain
quantities of the complex system and the problem may determine the optimal
performance.
