4. Applications of Modified Optimization Algorithms to the Unconstrained and Constrained Problems

This chapter presents the applications of the modified PSO, HEA and ABC algorithms. Thirteen unconstrained and twenty-four constrained benchmark problems available in the literature are considered to check the performance of the modified algorithms. In addition, different mechanical element design optimization problems such as design of a simple gear train, radial ball bearing, Belleville spring, multi-plate disc clutch brake, robot gripper, hydrostatic thrust bearing, a four-stage gear train, pressure vessel, welded beam, tension/compression spring, speed reducer, stiffened cylindrical shell, step cone pulley, screw jack, C-clamp, hydrodynamic bearing, cone clutch, cantilever support, hydraulic cylinder and a planetary gear train are presented and the effectiveness of the applications of the modified algorithms is checked. It is observed that the modifications in PSO and HEA are effective than their basic versions. Modifications in ABC are not so effective for the constrained benchmark functions but are found effective for the unconstrained benchmark functions and mechanical design problems.