An effective algorithm for constrained optimization based on optics inspired optimization (OIO)

Abstract

Due to the law of reflection, the converging and diverging behavior of concave and convex mirrors causes that curved mirrors show different image types. The optics inspired optimization (OIO) is a recently proposed algorithm for unconstrained optimization which treats the surface of the function to be optimized as a wavy mirror in which each peak is assumed to reflect as a convex mirror and each valley to reflect as a concave one. Each individual is treated as an artificial light point that its glittered ray is reflected back by the function surface, given that the surface is convex or concave, and the artificial image (a new solution) is formed based on mirror equations adopted from Optics. There are several constraint handling techniques which have been proposed for handling infeasible solutions. However, these techniques may suffer from problem dependency, no unique way for designing their operators, no unique way for updating their internal parameters, increasing the computational complexity, etc. To equip OIO with a mechanism to handle constraints and to avoid the drawbacks of typical techniques, a feasibility measure is used beside the objective function value to bias the search toward feasible regions. Such a consideration requires to modify several modules in the basic OIO algorithm. To increase the probability to generate better solutions, a number of alternative solutions are produced from each individual and one is selected based on the sequential use of modified Deb’s tournament selection. Besides, Deb’s tournament selection rule is used in place of the greedy selection in basic OIO, along with allowing the survival of individuals with a good value of the objective function, regardless of their feasibility. Performance of the proposed algorithm is compared with a number of noticeable algorithms such as COPSO, ECHT-EP2, αSimplex etc, on CEC 2006 and CEC 2010 set of benchmark problems and on a set of mechanical design optimization problems. Results demonstrate that the proposed algorithm performs the global optimization task very well and competitive. Such an outcome encourages that further developments and applications of OIO would be worth to realize its full potency in the future studies.