Parallel Space Decomposition of the Mesh Adaptive Direct Search Algorithm

This paper describes a Parallel Space Decomposition (PSD) technique for the Mesh Adaptive Direct Search (MADS) algorithm. MADS extends Generalized Pattern Search for constrained nonsmooth optimization problems. The objective here is to solve larger problems more efficiently. The new method (PSD-MADS) is an asynchronous parallel algorithm in which the processes solve problems over subsets of variables. The convergence analysis based on the Clarke calculus is essentially the same as for the MADS algorithm. A practical implementation is described and some numerical results on problems with up to 500 variables illustrate advantages and limitations of PSD-MADS

Real-Time Motion Planning of Legged Robots: A Model Predictive Control Approach

We introduce a real-time, constrained, nonlinear Model Predictive Control for the motion planning of legged robots. The proposed approach uses a constrained optimal control algorithm known as SLQ. We improve the efficiency of this algorithm by introducing a multi-processing scheme for estimating value function in its backward pass. This pass has been often calculated as a single process. This parallel SLQ algorithm can optimize longer time horizons without proportional increase in its computation time. Thus, our MPC algorithm can generate optimized trajectories for the next few phases of the motion within only a few milliseconds. This outperforms the state of the art by at least one order of magnitude. The performance of the approach is validated on a quadruped robot for generating dynamic gaits such as trotting.Comment: 8 page

Globally convergent evolution strategies for constrained optimization

International audienceIn this paper we propose, analyze, and test algorithms for constrained optimization when no use of derivatives of the objective function is made. The proposed methodology is built upon the globally convergent evolution strategies previously introduced by the authors for unconstrained optimization. Two approaches are encompassed to handle the constraints. In a first approach, feasibility is first enforced by a barrier function and the objective function is then evaluated directly at the feasible generated points. A second approach projects first all the generated points onto the feasible domain before evaluating the objective function.The resulting algorithms enjoy favorable global convergence properties (convergence to stationarity from arbitrary starting points), regardless of the linearity of the constraints.The algorithmic implementation (i) includes a step where previously evaluated points are used to accelerate the search (by minimizing quadratic models) and (ii) addresses the particular cases of bounds on the variables and linear constraints. Our solver is compared to others, and the numerical results confirm its competitiveness in terms of efficiency and robustness

Automated optimization of reconfigurable designs

Currently, the optimization of reconfigurable design parameters is typically done manually and often involves substantial amount effort. The main focus of this thesis is to reduce this effort. The designer can focus on the implementation and design correctness, leaving the tools to carry out optimization. To address this, this thesis makes three main contributions. First, we present initial investigation of reconfigurable design optimization with the Machine Learning Optimizer (MLO) algorithm. The algorithm is based on surrogate model technology and particle swarm optimization. By using surrogate models the long hardware generation time is mitigated and automatic optimization is possible. For the first time, to the best of our knowledge, we show how those models can both predict when hardware generation will fail and how well will the design perform. Second, we introduce a new algorithm called Automatic Reconfigurable Design Efficient Global Optimization (ARDEGO), which is based on the Efficient Global Optimization (EGO) algorithm. Compared to MLO, it supports parallelism and uses a simpler optimization loop. As the ARDEGO algorithm uses multiple optimization compute nodes, its optimization speed is greatly improved relative to MLO. Hardware generation time is random in nature, two similar configurations can take vastly different amount of time to generate making parallelization complicated. The novelty is efficient use of the optimization compute nodes achieved through extension of the asynchronous parallel EGO algorithm to constrained problems. Third, we show how results of design synthesis and benchmarking can be reused when a design is ported to a different platform or when its code is revised. This is achieved through the new Auto-Transfer algorithm. A methodology to make the best use of available synthesis and benchmarking results is a novel contribution to design automation of reconfigurable systems.Open Acces

Recurrent backpropagation and the dynamical approach to adaptive neural computation

Error backpropagation in feedforward neural network models is a popular learning algorithm that has its roots in nonlinear estimation and optimization. It is being used routinely to calculate error gradients in nonlinear systems with hundreds of thousands of parameters. However, the classical architecture for backpropagation has severe restrictions. The extension of backpropagation to networks with recurrent connections will be reviewed. It is now possible to efficiently compute the error gradients for networks that have temporal dynamics, which opens applications to a host of problems in systems identification and control