A novel differential search algorithm and applications for structure design

Differential Search method is recently proposed to solve box constrained global optimization problems. In this paper, we will further extend this method to solve generalized constrained optimization problems, particularly for structure design optimization problems. To handle the constraints, we first propose a novel dynamic S-type soft-threshold penalty method. Then, the original constrained optimization problem is transformed into a sequence of unconstrained optimization problems. The proposed method is mainly comprised of two steps: parameter iteration and solution iteration. The parameter iteration is to update the dynamic penalty parameter through a soft-threshold scheme and the solution iteration is to implement Differential Search algorithm to solve an unconstrained optimization problem. Two benchmark sets, CEC2006 and CEC2010, and four engineering structure design optimization problems are solved by our proposed algorithm as well as many other swarm-based algorithms proposed in recent literatures. Numerical results show that our method can achieve better performance but with fewer function evaluations comparing with the existing algorithms.