Based on the concepts of homotopy, a novel cat swarm algorithm, called a homotopy-inspired cat swarm algorithm (HCSA),is proposed to deal with the problem of global optimization. Proceeding from dependent variables of optimized function,it traces a path from the solution of an easy problem to the solution of the given one by use of a homotopy--|a continuous transformation from the easy problem to the given one.This novel strategy enables the cat swarm algorithm (CSA) to improve the search efficiency. Theoretical analysis proves that HCSA converges to the global optimum. Experimenting with a wide range of benchmark functions, we show that the proposed new version of CSA, with the continuous transformation, performs better, or at least comparably, to classic CSA.

A novel Chaotic Improved Cat Swarm Algorithm (CCSA) is presented for global optimization. The CSA is a new meta-heuristic optimization developed based on imitating the natural behavior of cats and composed of two sub-models: tracing mode and seeking mode, which model upon the behaviors of cats. Here different chaotic maps are utilized to improve the seeking mode step of the algorithm. Seven different chaotic maps are investigated and the Logistic and Sinusoidal maps are found as the best choices. Comparing the new algorithm with the CSA method demonstrates the superiority of the CCSA for the benchmark functions.

A novel Chaotic Grenade Explosion Algorithm (CGEA) is presented for global optimization. The GEA is a new meta-heuristic optimization developed based on the observation of a grenade explosion, in which the thrown pieces of shrapnel destruct the objects near the explosion location. Here different chaotic maps are utilized to improve solution search equation of the algorithm. Seven different chaotic maps are investigated. Comparing the new algorithm with the GEA demonstrates the superiority of the CGEA for the benchmark functions.

Based on the concepts of homotopy, a novel Grenade Explosion Algorithm, called a homotopy-inspired Grenade Explosion Algorithm (HGEA),is proposed to deal with the problem of global optimization. Proceeding from dependent variables of optimized function,it traces a path from the solution of an easy problem to the solution of the given problem by use of a homotopy--|a continuous transformation from the easy problem to the given one.This novel strategy enables the Grenade Explosion Algorithm (GEA) to improve the search efficiency. Theoretical analysis proves that HGEA converges to the global optimum. Experimenting with a wide range of benchmark functions, we show that the proposed new version of GEA, with the continuous transformation, performs better, or at least comparably, to classic GEA.