Hybrid gradient projection based Genetic Algorithms for constrained optimization

Abstract

Genetic Algorithms (GAs) are a highly successful population based approach to solve global optimization problems. They have carved out a niche for themselves in solving optimization problems of varying difficulty levels involving single and multiple objectives. Most real-world optimization problems involve equality and / or inequality constraints and hence posed as constrained optimization problems. The most common approach to solve such problems using GAs is the method of penalty functions, which however suffers from the drawback of appropriate selection of penalty parameters for their optimal functioning. Given the nature of the problems at hand, we have used an adaptive mutation based Real-Coded GA (RGA), which uses a popular penalty parameter-less approach to handle constraints and search the feasible region effectively for the global best solution, and at the same time use an adaptive mutation strategy to maintain diversity in the population to enable creation of new solutions. We have coupled our RGA with ideas from the gradient projection method to specifically handle equality constraints. We have found our simple procedure working quite well in most of the test problems provided as part of the competition on Single-objective Constrained Real Parameter Optimization in CEC 2010 and hence simplicity remains the hallmark of our study here.