A supervised learning approach involving active subspaces for an efficient genetic algorithm in high-dimensional optimization problems

In this work, we present an extension of the genetic algorithm (GA) which exploits the supervised learning technique called active subspaces (AS) to evolve the individuals on a lower dimensional space. In many cases, GA requires in fact more function evaluations than others optimization method to converge to the global optimum. Thus, complex and high-dimensional functions may result extremely demanding (from computational viewpoint) to optimize with the standard algorithm. To address this issue, we propose to linearly map the input parameter space of the original function onto its AS before the evolution, performing the mutation and mate processes in a lower dimensional space. In this contribution, we describe the novel method called ASGA, presenting differences and similarities with the standard GA method. We test the proposed method over n-dimensional benchmark functions -- Rosenbrock, Ackley, Bohachevsky, Rastrigin, Schaffer N. 7, and Zakharov -- and finally we apply it to an aeronautical shape optimization problem.