Fast Yaw Optimization for Wind Plant Wake Steering Using Boolean Yaw Angles

In wind plants, turbines can be yawed into the wind to steer their wakes away from downstream turbines and achieve an overall increase in plant power. Mathematical optimization is typically used to determine the best yaw angles at which to operate the turbines in a plant. In this paper, we present a new method to rapidly determine the yaw angles in a wind plant. In this method, we define the turbine yaw angles as Boolean—either yawed at a predefined angle or nonyawed—as opposed to the typical methods of formulating yaw angles as continuous or with fine discretizations. We then optimize which turbines should be yawed with a greedy algorithm that sweeps through the turbines from the most upstream to the most downstream. We demonstrate that our new Boolean optimization method can find turbine yaw angles that perform well compared to a traditionally used gradient-based optimizer where the yaw angles are defined as continuous. There is less than 0.6 % difference in the optimized power between the two optimization methods for randomly placed turbine layouts. Additionally, we show that our new method is much more computationally efficient than the traditional method. For plants with nonzero optimal yaw angles, our new method is generally able to solve for the turbine yaw angles 50–150 times faster, and in some extreme cases up to 500 times faster, than the traditional method.

Positive semidefinite penalty method for quadratically constrained quadratic programming

Quadratically constrained quadratic programming (QCQP) appears widely in engineering applications such as wireless communications and networking and multiuser detection with examples like the MAXCUT problem and boolean optimization. A general QCQP problem is NP-hard. We propose a penalty formulation for the QCQP problem based on semidefinite relaxation. Under suitable assumptions we show that the optimal solutions of the penalty problem are the same as those of the original QCQP problem if the penalty parameter is sufficiently large. Then, to solve the penalty problem, we present a proximal point algorithm and an update rule for the penalty parameter. Numerically, we test our algorithm on two well-studied QCQP problems. The results show that our proposed algorithm is very effective in finding high-quality solutions.

MOVING OBJECTS AWARE SENSOR MESH FUSION FOR INDOOR RECONSTRUCTION FROM A COUPLE OF 2D LIDAR SCANS

Indoor mapping attracts more attention with the development of 2D and 3D camera and Lidar sensor. Lidar systems can provide a very high resolution and accurate point cloud. When aiming to reconstruct the static part of the scene, moving objects should be detected and removed which can prove challenging. This paper proposes a generic method to merge meshes produced from Lidar data that allows to tackle the issues of moving objects removal and static scene reconstruction at once. The method is adapted to a platform collecting point cloud from two Lidar sensors with different scan direction, which will result in different quality. Firstly, a mesh is efficiently produced from each sensor by exploiting its natural topology. Secondly, a visibility analysis is performed to handle occlusions (due to varying viewpoints) and remove moving objects. Then, a boolean optimization allows to select which triangles should be removed from each mesh. Finally, a stitching method is used to connect the selected mesh pieces. Our method is demonstrated on a Navvis M3 (2D laser ranger system) dataset and compared with Poisson and Delaunay based reconstruction methods.

Towards a Better Basis Search through a Surrogate Model-Based Epistasis Minimization for Pseudo-Boolean Optimization

Epistasis, which indicates the difficulty of a problem, can be used to evaluate the basis of the space in which the problem lies. However, calculating epistasis may be challenging as it requires all solutions to be searched. In this study, a method for constructing a surrogate model, based on deep neural networks, that estimates epistasis is proposed for basis evaluation. The proposed method is applied to the Variant-OneMax problem and the NK-landscape problem. The method is able to make successful estimations on a similar level to basis evaluation based on actual epistasis, while significantly reducing the computation time. In addition, when compared to the epistasis-based basis evaluation, the proposed method is found to be more efficient.

Finding Most Compatible Phylogenetic Trees over Multi-State Characters

The reconstruction of the evolutionary tree of a set of species based on qualitative attributes is a central problem in phylogenetics. In the NP-hard perfect phylogeny problem the input is a set of taxa (species) and characters (attributes) on them, and the task is to find an evolutionary tree that describes the evolution of the taxa so that each character state evolves only once. However, in practical situations a perfect phylogeny rarely exists, motivating the maximum compatibility problem of finding the largest subset of characters admitting a perfect phylogeny. Various declarative approaches, based on applying integer programming (IP), answer set programming (ASP) and pseudo-Boolean optimization (PBO) solvers, have been proposed for maximum compatibility. In this work we develop a new hybrid approach to solving maximum compatibility for multi-state characters, making use of both declarative optimization techniques (specifically maximum satisfiability, MaxSAT) and an adaptation of the Bouchitt'e-Todinca approach to triangulation-based graph optimization problems. Empirically our approach outperforms in scalability the earlier proposed approaches w.r.t. various parameters underlying the problem.

SAT-Based Generation of Optimum Circuits with Polymorphic Behavior Support

This paper presents a method for generating optimum multi-level implementations of Boolean functions based on Satisfiability (SAT) and Pseudo-Boolean Optimization (PBO) problems solving. The method is able to generate one or enumerate all optimum implementations, while the allowed target gate types and gates costs can be arbitrarily specified. Polymorphic circuits represent a newly emerging computation paradigm, where one hardware structure is capable of performing two or more different intended functions, depending on instantaneous conditions in the target operating environment. In this paper we propose the first method ever, generating provably size-optimal polymorphic circuits. Scalability and feasibility of the method are documented by providing experimental results for all NPN-equivalence classes of four-input functions implemented in AND–Inverter and AND–XOR–Inverter logics without polymorphic behavior support being used and for all pairs of NPN–equivalence classes of three-input functions for polymorphic circuits. Finally, several smaller benchmark circuits were synthesized optimally, both in standard and polymorphic logics.