Constrained Optimization based on Quadratic Approximations in Genetic Algorithms

An aspect that often causes difficulties when using Genetic Algorithms for optimization is that these algorithms operate as unconstrained search procedures and most of the real-world problems have constraints of different types. There is a lack of efficient constraint handling technique to bias the search in constrained search spaces toward the feasible regions. We propose a novel methodology to be coupled with a Genetic Algorithm to solve optimization problems with inequality constraints. This methodology can be seen as a local search operator that uses quadratic and linear approximations for both objective function and constraints. In the local search phase, these approximations define an associated problem with a quadratic objective function and quadratic and/or linear constraints that is solved using an LMI (linear matrix inequality) formulation. The solution of this associated problems is then re-introduced in the GA population.We test the proposed methodology with a set of analytical function and the results show that the hybrid algorithm has a better performancewhen compared to the same Genetic Algorithmwithout the proposed local search operator. The tests also suggest that the proposed methodology is at least equivalent, and sometimes better than other methods that have been reported recently in literature.