Advancing Engineering Solutions with Protozoa-Based Differential Evolution: A Hybrid Optimization Approach

This paper presents a novel Hybrid Artificial Protozoa Optimizer with Differential Evolution (HPDE), combining the biologically inspired principles of the Artificial Protozoa Optimizer (APO) with the powerful optimization strategies of Differential Evolution (DE) to address complex and engineering design challenges. The HPDE algorithm is designed to balance exploration and exploitation features, utilizing innovative features such as autotrophic and heterotrophic foraging behaviors, dormancy, and reproduction processes alongside the DE strategy. The performance of HPDE was evaluated on the CEC2014 benchmark functions, and it was compared against two sets of state-of-the-art optimizers comprising 23 different algorithms. The results demonstrate HPDE’s good performance, outperforming competitors in 24 functions out of 30 from the first set and 23 functions from the second set. Additionally, HPDE has been successfully applied to a range of complex engineering design problems, including robot gripper optimization, welded beam design optimization, pressure vessel design optimization, spring design optimization, speed reducer design optimization, cantilever beam design optimization, and three-bar truss design optimization. The results consistently showcase HPDE’s good performance in solving these engineering problems when compared with the competing algorithms.