Engineering Generative Adversarial Networks for Constrained and Multiobjective Problems

Abstract In a previous publication we have discussed a method for training a conditional Generative Adversarial Network (cGAN) on images of thermo-mechanical simulation results for an aero engine secondary air system seal, demonstrating the predictability of the Deep Learning models for key outputs of interest and assessing the ability of these models to generate designs in specific categories. The work was focused on the intricacies of training the ENGAN (Engineering cGAN) with data being categorised for a single output variable. A network trained for a single output is not aware of the other outputs and constraints and could generate solutions that are infeasible or not Pareto optimal. In this article we present the notion of Multi-objective (MO) ENGANs. We have been inspired by an idea from the Non-dominated Sorting Genetic Algorithm (NSGA2) where a Genetic algorithm is used to minimize an amalgamation of the Pareto rank and the crowding distance, driving the designs towards the Pareto front (Pareto front rank of 1). Following a similar principle, an ENGAN was trained using the same images as in the previous study but using a categorization based on Pareto front labels. This paper demonstrates that the network trained in this fashion is able to discriminate between feasible and non-feasible designs as well as discriminate between designs with low and high Pareto front ranking. The trained ENGAN is successfully able to generate 100% feasible designs which are also close to Pareto optimal. The network can be used to generate large quantities of feasible designs which can then be used for design space exploration purposes, saving a considerable amount of time from laborious design search and optimization practices. Furthermore, the network can be used to create an initial population of feasible and optimal designs, which can then be used in various applications such as building surrogate models in the region of optimality or initializing a Genetic algorithm or using the points for multi-start gradient methods to perform a more aggressive optimization study. This study shows that the images can be categorized for training using arbitrary rules that are mutually inclusive or exclusive. The multi-mode labelling ENGAN combines the targeting capability of the Single Objective ENGANs with the awareness of Pareto optimality and global feasibility. We were able to also target individually each of the objective functions at their optimal values, i.e., the corners of the Pareto front and separately its interior using a single network, as well as any other feasible design. This can eliminate the need of training of separate networks for each objective function, which can save considerable amount of time and GPU related costs, especially when training is performed on a subscription type of services such as the Microsoft Azure.