A hybrid method combining genetic algorithm and Hooke-Jeeves method for constrained global optimization

Abstract

A new global optimization method combining geneticalgorithm and Hooke-Jeeves method to solve a class of constrainedoptimization problems is studied in this paper. We first introducethe quadratic penalty function method and the exact penalty functionmethod to transform the original constrained optimization problemwith general equality and inequality constraints into a sequenceof optimization problems only with box constraints. Then, thecombination of genetic algorithm and Hooke-Jeeves method isapplied to solve the transformed optimization problems. SinceHooke-Jeeves method is good at local search, our proposed methoddramatically improves the accuracy and convergence rate of geneticalgorithm. In view of the derivative-free of Hooke-Jeeves method,our method only requires information of objective function valuewhich not only can overcome the computational difficulties causedby the ill-condition of the square penalty function, but also canhandle the non-differentiability by the exact penalty function.Some well-known test problems are investigated. The numericalresults show that our proposed method is efficient and robust.