The Informational Approach to Global Optimization in presence of very noisy evaluation results. Application to the optimization of renewable energy integration strategies

We consider the problem of global optimization of a function f from very noisy evaluations. We adopt a Bayesian sequential approach: evaluation points are chosen so as to reduce the uncertainty about the position of the global optimum of f, as measured by the entropy of the corresponding random variable (Informational Approach to Global Optimization, Villemonteix et al., 2009). When evaluations are very noisy, the error coming from the estimation of the entropy using conditional simulations becomes non negligible compared to its variations on the input domain. We propose a solution to this problem by choosing evaluation points as if several evaluations were going to be made at these points. The method is applied to the optimization of a strategy for the integration of renewable energies into an electrical distribution network

A novel non-intrusive method using design of experiments and smooth approximation to speed up multi-period load-flows in distribution network planning

International audienceAlternative solutions to network reinforcement are now being investigated in distribution network planning studies to reduce the costs and periods for integrating renewable energy sources. However, a thorough techno-economic analysis of these solutions requires a large number of multi-period load-flow calculations, which makes it hard to implement in planning tools. A non-intrusive approximation method is therefore proposed to obtain fast and accurate multi-period load-flows. This method builds a surrogate model of the load-flow solver using polynomial regression and kriging, combined with Latin hypercube sampling. Case studies based on real distribution networks show that the proposed method is more efficient for distribution network planning in presence of renewable energy sources than time subsampling and, in some cases, voltage linearization. In particular, accurate 10-minute profiles of voltages, currents, and network power losses are obtained in a satisfactory computation time

A Bayesian approach for the optimal integration of renewable energy sources in distribution networks over multi-year horizons

International audienceWe propose a method to optimise the planning strategy of an active distribution network. The problem is formulated as the search for the planning strategy parameters minimising antagonist objectives. These objectives are computed using a numerical simulator of the distribution networks and stochastic scenarios. Since simulations take a high amount of CPU time, we suggest using Bayesian optimisation algorithms, where the costs are modelled with Gaussian random processes. The main idea is to compute predictions of the costs and uncertainty intervals, which are then used to guide the optimisation algorithm. A case study illustrates the performance of the proposed method

Extension of the Pareto Active Learning Method to Multi-Objective Optimization for Stochastic Simulators

International audienceWe address the problem of optimizing an expensive-to-evaluate stochastic simulator with multiple outputs. The goal is to estimate Pareto-optimal solutions within a limited budget of evaluations. Pareto Active Learning (PAL), proposed by Zuluaga et al. (Proc. 30th Int. Conf. on Machine Learning, PMLR 28(1):462-470, 2013), is presented as an algorithm for this task. However, it appears that significant limitations arise with this algorithm when using stochastic simulators. For instance, the original algorithm assumes that the variance of the output at one point is zero once there is an observation at this point. In this talk, we propose an extension of the original algorithm to deal with stochastic simulators whose outputs may have high variance. The proposed approach is assessed on a set of test problems and compared to other techniques: a random exploration of the search space and a scalarization-based optimization algorithm adapted from ParEGO. Results show a good performance of the new algorithm in the majority of the test cases

Bayesian multi-objective optimization for stochastic simulators: an extension of the Pareto Active Learning method

This article focuses on the multi-objective optimization of stochastic simulators with high output variance, where the input space is finite and the objective functions are expensive to evaluate. We rely on Bayesian optimization algorithms, which use probabilistic models to make predictions about the functions to be optimized. The proposed approach is an extension of the Pareto Active Learning (PAL) algorithm for the estimation of Pareto-optimal solutions that makes it suitable for the stochastic setting. We named it Pareto Active Learning for Stochastic Simulators (PALS). The performance of PALS is assessed through numerical experiments over a set of bi-dimensional, bi-objective test problems. PALS exhibits superior performance when compared to other scalarization-based and random-search approaches

Bayesian multi-objective optimization for stochastic simulators: an extension of the Pareto Active Learning method

This article focuses on the multi-objective optimization of stochastic simulators with high output variance, where the input space is finite and the objective functions are expensive to evaluate. We rely on Bayesian optimization algorithms, which use probabilistic models to make predictions about the functions to be optimized. The proposed approach is an extension of the Pareto Active Learning (PAL) algorithm for the estimation of Pareto-optimal solutions that makes it suitable for the stochastic setting. We named it Pareto Active Learning for Stochastic Simulators (PALS). The performance of PALS is assessed through numerical experiments over a set of bi-dimensional, bi-objective test problems. PALS exhibits superior performance when compared to other scalarization-based and random-search approaches