Development of an adaptive infill criterion for constrained multi-objective asynchronous surrogate-based optimization

The use of surrogate modeling techniques to efficiently solve a single objective optimization (SOO) problem has proven its worth in the optimization community. However, industrial problems are often characterized by multiple conflicting and constrained objectives. Recently, a number of infill criteria have been formulated to solve multi-objective optimization (MOO) problems using surrogates and to determine the Pareto front. Nonetheless, to accurately resolve the front, a multitude of optimal points must be determined, making MOO problems by nature far more expensive than their SOO counterparts. As of yet, even though access to of high performance computing is widely available, little importance has been attributed to batch optimization and asynchronous infill methodologies, which can further decrease the wall-clock time required to determine the Pareto front with a given resolution. In this paper a novel infill criterion is developed for generalized asynchronous multi-objective constrained optimization, which allows multiple points to be selected for evaluation in an asynchronous manner while the balance between design space exploration and objective exploitation is adapted during the optimization process in a simulated annealing like manner and the constraints are taken into account. The method relies on a formulation of the expected improvement for multi-objective optimization, where the improvement is formulated as the Euclidean distance from the Pareto front taken to a higher power. The infill criterion is tested on a series of test cases and proves the effectiveness of the novel scheme.