Surrogate Model Guided Optimization of Expensive Black-Box Multi-Objective Problems: A Posteriori Methods

Many engineering applications require the simultaneous optimization of multiple conflicting objective functions. Often, these objective functions are evaluated using highly accurate computer simulations that are computationally too expensive to be evaluated hundreds or thousands of times during optimization. Thus, the goal is to find good approximations of the Pareto front using as few of these expensive simulations as possible. Here, we describe an optimization approach based on surrogate models and diverse sampling strategies to accelerate the search for the Pareto solutions. We use a separate surrogate model for approximating each objective function and then we use the surrogate models to inform where additional expensive simulations should be run. The surrogate models are updated in an active learning framework whenever new information from the expensive simulations becomes available. The sampling strategies aim at balancing local improvements of the approximate Pareto front and global exploration to identify the extrema and fill in large gaps of the approximate Pareto front. We demonstrate on a large set of benchmark problems the effectiveness of the method for finding good approximations of the Pareto front.