Hierarchical Genetic Algorithms with evolving objective functions
This is an incremental improvement for optimization in domains like routing and regression where objective functions are complex or unknown.
The authors tackled optimization problems by developing a hierarchical genetic algorithm framework that searches over simpler objective functions, demonstrating it on soft-TSP and polynomial regression. They showed the algorithm adapts to changed constraints and speeds up learning to find globally optimal solutions.
We propose a framework of genetic algorithms which use multi-level hierarchies to solve an optimization problem by searching over the space of simpler objective functions. We solve a variant of Travelling Salesman Problem called \texttt{soft-TSP} and show that when the constraints on the overall objective function are changed the algorithm adapts to churn out solutions for the changed objective. We use this idea to speed up learning by systematically altering the constraints to find a more globally optimal solution. We also use this framework to solve polynomial regression where the actual objective function is unknown but searching over space of available objective functions yields a good approximate solution.