We present a hierarchical optimization architecture for large-scale power networks that overcomes limitations of fully centralized and fully decentralized architectures. The architecture leverages principles of multigrid computing schemes, which are widely used in the solution of partial differential equations on massively parallel computers. The top layer of the architecture uses a coarse representation of the entire network while the bottom layer is composed of a family of decentralized optimization agents each operating on a network subdomain at full resolution. We use an alternating direction method of multipliers (ADMM) framework to drive coordination of the decentralized agents. We show that state and dual information obtained from the top layer can be used to accelerate the coordination of the decentralized optimization agents and to recover optimality for the entire system. We demonstrate that the hierarchical architecture can be used to manage large collections of microgrids.
The breakthrough ideas in the modern proximal splitting methodologies allow us to express the set of all minimizers of a superposition of multiple nonsmooth convex functions as the fixed point set of computable nonexpansive operators. In this paper, we present practical algorithmic strategies for the hierarchical convex optimization problems which require further strategic selection of a most desirable vector from the solution set of the standard convex optimization. The proposed algorithms are established by applying the hybrid steepest descent method to special nonexpansive operators designe…
In this paper, we formulate newly a hierarchical convex optimization for multiclass SVM achieving maximum pairwise margins with least empirical hinge-loss. This optimization problem is a most faithful as well as robust multiclass extension of an NP-hard hierarchical optimization appeared for the first time in the seminal paper by C.~Cortes and V.~Vapnik almost 25 years ago. By extending the very recent fixed point theoretic idea [Yamada-Yamagishi 2019] with the generalized hinge loss function [Crammer-Singer 2001], we show that the hybrid steepest descent method [Yamada 2001] in the computatio…
Clinical pathways are standardized processes that outline the steps required for managing a specific disease. However, patient pathways often deviate from clinical pathways. Measuring the concordance of patient pathways to clinical pathways is important for health system monitoring and informing quality improvement initiatives. In this paper, we develop an inverse optimization-based approach to measuring pathway concordance in breast cancer, a complex disease. We capture this complexity in a hierarchical network that models the patient's journey through the health system. A novel inverse short…
Modeling Hierarchical Spaces: A Review and Unified Framework for Surrogate-Based Architecture Design
IRIT（图卢兹计算机研究所）；UT Capitole, Université de Toulouse（图卢兹大学图卢兹 Capitole 大学）；CNRS（法国国家科学研究中心）；Toulouse INP（图卢兹国立理工学院）；UT3（图卢兹第三大学）；UT2J（图卢兹第二大学让·饶勒斯）；GERAD（决策分析研究集团）；Polytechnique Montréal（蒙特利尔高等理工学院）；Institute of System Architectures in Aeronautics, German Aerospace Center (DLR)（德国航空航天中心（DLR）航空系统架构研究所）；ONERA（法国航空航天实验室）；Fédération ENAC ISAE-SUPAERO ONERA, Université de Toulouse（图卢兹大学 ENAC ISAE-SUPAERO ONERA 联合会）
We develop a normative framework for hierarchical model-based policy optimization based on applying second-order methods in the space of all possible state-action paths. The resulting natural path gradient performs policy updates in a manner which is sensitive to the long-range correlational structure of the induced stationary state-action densities. We demonstrate that the natural path gradient can be computed exactly given an environment dynamics model and depends on expressions akin to higher-order successor representations. In simulation, we show that the priorization of local policy updat…
Hierarchical Bayesian optimization of an aircraft-based multi-agent system-of-systems
IRIT, UMR 5505 CNRS, Université Toulouse Capitole, Université de Toulouse（图卢兹计算机科学研究所，法国国家科学研究中心联合研究单位5505，图卢兹第一大学，图卢兹大学）；ONERA, DTIS, Université de Toulouse（法国国家航空航天研究院，信息处理与系统部，图卢兹大学）；Fédération ENAC ISAE-SUPAERO ONERA, Université de Toulouse（法国国立民航大学-法国国立高等航空航天学院-法国国家航空航天研究院联合会，图卢兹大学）；German Aerospace Center (DLR), Institute of System Architectures in Aeronautics（德国航空航天中心，航空系统架构研究所）
In this paper we propose a hierarchical controller for autonomous racing where the same vehicle model is used in a two level optimization framework for motion planning. The high-level controller computes a trajectory that minimizes the lap time, and the low-level nonlinear model predictive path following controller tracks the computed trajectory online. Following a computed optimal trajectory avoids online planning and enables fast computational times. The efficiency is further enhanced by the coupling of the two levels through a terminal constraint, computed in the high-level controller. Incl…
This paper presents an adaptive discretization strategy for level set topology optimization of structures based on hierarchical B-splines. This work focuses on the influence of the discretization approach and the adaptation strategy on the optimization results and computational cost. The geometry of the design is represented implicitly by the iso-contour of a level set function. An immersed boundary technique, here the extended finite element method, is used to predict the structural response. Both the level set function and the state variable fields are discretized by hierarchical B-splines. …
