Homotopy-Inspired Grenade Explosion Algorithm for Global Numerical Optimization

Abstract

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.