The set cover problem is a classical question in combinatorics, computer science and complexity theory. It is one of Karp’s 21 NP-complete problems shown to be NP-complete in 1972. Several algorithms have been proposed to solve this problem, based on genetic algorithms (GA), Particle Swarm Optimizer (PSO) and in recent years algorithms based in behavior algorithms based groups or herds of animals, such as frogs, bats, bees and domestic cats. This work presents the basic features of the algorithm based on the behavior of domestic cats and results to solve the SCP bi-objective, experimental results and opportunities to improve results using adaptive techniques applied to Cat Swarm Optimization. For this purpose we will use instances of SCP OR-Library of Beasley by adding an extra function fitness to transform the Beasly instance to Bi-Objective problem.