Gaussian Process Regression Based Multi-Objective Bayesian Optimization for Power System Design

Abstract

Within a disruptively changing environment, design of power systems becomes a complex task. Meeting multi-criteria requirements with increasing degrees of freedom in design and simultaneously decreasing technical expertise strengthens the need for multi-objective optimization (MOO) making use of algorithms and virtual prototyping. In this context, we present Gaussian Process Regression based Multi-Objective Bayesian Optimization (GPR-MOBO) with special emphasis on its profound theoretical background. A detailed mathematical framework is provided to derive a GPR-MOBO computer implementable algorithm. We quantify GPR-MOBO effectiveness and efficiency by hypervolume and the number of required computationally expensive simulations to identify Pareto-optimal design solutions, respectively. For validation purposes, we benchmark our GPR-MOBO implementation based on a mathematical test function with analytically known Pareto front and compare results to those of well-known algorithms NSGA-II and pure Latin Hyper Cube Sampling. To rule out effects of randomness, we include statistical evaluations. GPR-MOBO turnes out as an effective and efficient approach with superior character versus state-of-the art approaches and increasing value-add when simulations are computationally expensive and the number of design degrees of freedom is high. Finally, we provide an example of GPR-MOBO based power system design and optimization that demonstrates both the methodology itself and its performance benefits.

Multiobjective Hyperparameter Optimization of Artificial Neural Networks for Optimal Feedforward Torque Control of Synchronous Machines

“…, n m of neurons per hidden layer, training methods and training parameters) and the objectives according to which we want to optimize (e.g., MSE e y , number N flop of FLOPs and number N param of parameters). The core of the workflow lies in the execution of a multi-objective hyperparameter optimization (MO-HPO) that identifies the Pareto front efficiently and effectively by, e.g., model-based direct search algorithms [85], genetic algorithms [86], or hybrid algorithms [87,88]. MO-HPO, along with the training of several ANNs, yields a set of Pareto optimal ANN designs that represent solutions balancing multiple objectives.…”

MOBCA: Multi-Objective Besiege and Conquer Algorithm

“…Hypervolume is a widely employed performance metric in the domain of multiobjective optimization [45][46][47]. It quantifies the hypervolume enclosed by a set of solutions within the objective space, representing the volume of the space dominated by these solutions.…”

A Comparative Study on the Performance of Covariance Functions in Gaussian Process Regression model: Application to Global Wheat Price

“…Next, GPR has had a significant impact on energy sustainability, with research being performed specifically for power system design optimization utilizing GPR based on Multi-Objective Bayesian Optimization (GPR-MOBO) [22]. Meanwhile, work on increasing the performance of GPR and Gradient Descent (GD) utilizing the inversion approach has been done to reduce computing time by implementing predictions on hydrocarbon depth in Seabed logging (SBL) [23].…”