General Optimization Framework Research Articles

Optimal allocation of quantized human eye depth perception for multi-focal 3D display design.

Creating immersive 3D stereoscopic, autostereoscopic, and lightfield experiences are becoming the center point of optical design of future head mounted displays and lightfield displays. However, despite the advancement in 3D and light field displays, there is no consensus on what are the necessary quantized depth levels for such emerging displays at stereoscopic or monocular modalities. Here we start from psychophysical theories and work toward defining and prioritizing quantized levels of depth that would saturate the human depth perception. We propose a general optimization framework, which locates the depth levels in a globally optimal way for band limited displays. While the original problem is computationally intractable, we manage to find a tractable reformulation as maximally covering a region of interest with a selection of hypographs corresponding to the monocular depth of field profiles. The results indicate that on average 1731 stereoscopic and 7 monocular depth levels (distributed optimally from 25 cm to infinity) would saturate the visual depth perception. Such that adding further depth levels adds negligible improvement. Also the first 3 depth levels should be allocated at (148), then (83, 170), then (53, 90, 170) distances respectively from the face plane to minimize the monocular error in the entire population. The study further discusses the 3D spatial profile of the quantized stereoscopic and monocular depth levels. The study provides fundamental guidelines for designing optimal near eye displays, light-field monitors, and 3D screens.

Realization of a Framework for Simulation-Based Large-Scale Shape Optimization Using Vertex Morphing

There is a significant tendency in the industry for automation of the engineering design process. This requires the capability of analyzing an existing design and proposing or ideally generating an optimal design using numerical optimization. In this context, efficient and robust realization of such a framework for numerical shape optimization is of prime importance. Another requirement of such a framework is modularity, such that the shape optimization can involve different physics. This requires that different physics solvers should be handled in black-box nature. The current contribution discusses the conceptualization and applications of a general framework for numerical shape optimization using the vertex morphing parametrization technique. We deal with both 2D and 3D shape optimization problems, of which 3D problems usually tend to be expensive and are candidates for special attention in terms of efficient and high-performance computing. The paper demonstrates the different aspects of the framework, together with the challenges in realizing them. Several numerical examples involving different physics and constraints are presented to show the flexibility and extendability of the framework.

Optimization with Partial Differential Equation Constraints for Bio-imaging Applications

Molecular transport and interaction are of funda- mental importance in biology and medicine. The spatiotemporal diffusion map can reflect the regulation of molecular interactions and their intracellular functions. To construct subcellular diffusion maps based on bio-imaging data, we explore a general optimization framework with diffusion equation constraints (OPT-PDE). For the solution of the spatially piecewise constant and anisotropic diffusion.

Topology optimization of hyperelastic structures with anisotropic fiber reinforcement under large deformations

Fiber-reinforced soft materials have emerged as promising candidates in various applications such as soft robotics and soft fibrous tissues. To enable a systematic approach to design fiber-reinforced materials and structures, we propose a general topology optimization framework for the computational optimized design of hyperelastic structures with nonlinear and anisotropic fiber reinforcements under large deformations. This framework simultaneously optimizes both the material distribution in the matrix phase and the orientations of the underlying fiber reinforcements, by parameterizing matrix and fiber phases individually using two sets of design variables. The optimized distribution of fiber orientations is chosen from a set of discrete orientations defined a priori, and several fiber orientation interpolation schemes are studied. In addition, this work proposes a novel anisotropic material interpolation scheme, which integrates both matrix and fiber design variables (both with material nonlinearity) into the stored-energy function. To improve the computational efficiency of both optimization and nonlinear structural analysis, we derive a fully decoupled fiber-matrix update scheme that performs parallel updates of the matrix and fiber design variables and employ the virtual element method (VEM) together with a tailored mesh adaptivity scheme to solve the finite elasticity boundary value problem. Design examples involving three objective functions are presented, demonstrating the efficiency and effectiveness of the proposed framework in designing anisotropic hyperelastic structures under large deformations.

A Model-Based Optimization Framework for Iterative Digital Breast Tomosynthesis Image Reconstruction.

Digital Breast Tomosynthesis is an X-ray imaging technique that allows a volumetric reconstruction of the breast, from a small number of low-dose two-dimensional projections. Although it is already used in the clinical setting, enhancing the quality of the recovered images is still a subject of research. The aim of this paper was to propose and compare, in a general optimization framework, three slightly different models and corresponding accurate iterative algorithms for Digital Breast Tomosynthesis image reconstruction, characterized by a convergent behavior. The suggested model-based implementations are specifically aligned to Digital Breast Tomosynthesis clinical requirements and take advantage of a Total Variation regularizer. We also tune a fully-automatic strategy to set a proper regularization parameter. We assess our proposals on real data, acquired from a breast accreditation phantom and a clinical case. The results confirm the effectiveness of the presented framework in reconstructing breast volumes, with particular focus on the masses and microcalcifications, in few iterations and in enhancing the image quality in a prolonged execution.

Demonstration actor critic

We study the problem of Reinforcement Learning from Demonstrations (RLfD), where the agent has access to not only reward signals from the environment, but also some available expert demonstrations. Recent works absorb ingredients from imitation learning and utilize demonstration data as reward reshaping. Despite their success, these methods update policy over these states seen in the demonstration data, in the same way as other states in the state space, overlooking the validity of direct supervision signals on these states. To address this issue, we propose a novel RLfD objective function with a new shaping reward, by optimizing which can directly leverage the supervision signal on these demonstrated states. We propose a general framework for policy optimization of the proposed objective, with convergence guarantees under the classic tabular setting. Based on that, we further make some approximations based on deep neural networks, and then introduce a new practical algorithm, called Demonstration Actor Critic (DAC) in large continuous domains. Extensive experiments on a range of popular benchmark sparse-reward tasks show that our method can lead to significant performance gains over several strong and off-the-shelf baselines.

Promoting the performance of district heating from waste heat recovery in China: A general solving framework based on the two-stage branch evaluation method

Recycling heat from local industrial processes is one of the suitable and strategic opportunities for district heating all over the world. However, in northern China, the majority of low-grade energy has been wasted, the main difficulties are of an institutional and commercial character. The rapid development of renewables and constant promotion of time-of-use tariff policy has provided new chances for power-to-heat implementation and thermal energy storage. In this study, a general configuration optimization framework of additional waste heat recovery and storage (WHRS) devices is proposed, which is based on the cost-benefit analysis. Due to the implicit nature of such an optimization problem, conventional economic dispatch, two-stage branch evaluation, linear programming solver, and two kinds of advanced optimization algorithms (i.e., Genetic Algorithm and Pattern Search) have been integrated systematically. Moreover, case studies and sensitivity analyses are conducted to verify the feasibility of the proposed optimization model and to reveal the effects of uncertain economic parameters, respectively. The results show that the average time-consuming of Pattern Search is only 4.9% of the GA optimizations. When introducing additional WHRS devices with optimal configurations, the total operating costs decreased by 6.9% and the cost proportion of gas boiler declines remarkably from 8.6% to 2.0%.

Universal machine learning for topology optimization

We put forward a general machine learning-based topology optimization framework, which greatly accelerates the design process of large-scale problems, without sacrifice in accuracy. The proposed framework has three distinguishing features. First, a novel online training concept is established using data from earlier iterations of the topology optimization process. Thus, the training is done during, rather than before, the topology optimization. Second, a tailored two-scale topology optimization formulation is adopted, which introduces a localized online training strategy. This training strategy can improve both the scalability and accuracy of the proposed framework. Third, an online updating scheme is synergistically incorporated, which continuously improves the prediction accuracy of the machine learning models by providing new data generated from actual physical simulations. Through numerical investigations and design examples, we demonstrate that the aforementioned framework is highly scalable and can efficiently handle design problems with a wide range of discretization levels, different load and boundary conditions, and various design considerations (e.g., the presence of non-designable regions).

A review of cooperative path planning of an unmanned aerial vehicle group

As a cutting-edge branch of unmanned aerial vehicle (UAV) technology, the cooperation of a group of UAVs has attracted increasing attention from both civil and military sectors, due to its remarkable merits in functionality and flexibility for accomplishing complex extensive tasks, e.g., search and rescue, fire-fighting, reconnaissance, and surveillance. Cooperative path planning (CPP) is a key problem for a UAV group in executing tasks collectively. In this paper, an attempt is made to perform a comprehensive review of the research on CPP for UAV groups. First, a generalized optimization framework of CPP problems is proposed from the viewpoint of three key elements, i.e., task, UAV group, and environment, as a basis for a comprehensive classification of different types of CPP problems. By following the proposed framework, a taxonomy for the classification of existing CPP problems is proposed to describe different kinds of CPPs in a unified way. Then, a review and a statistical analysis are presented based on the taxonomy, emphasizing the coordinative elements in the existing CPP research. In addition, a collection of challenging CPP problems are provided to highlight future research directions.

Ultrametric fitting by gradient descent * *This article is an updated version of: Chierchia G and Perret B 2019 Ultrametric fitting by gradient descent 33rd Conf. Neural Information Processing Systems (NeurIPS 2019), Vancouver, Canada vol 32 eds H Wallach, H Larochelle, A Beygelzimer, F d’Alché-Buc, E Fox and R Garnett pp 3181–92

We study the problem of fitting an ultrametric distance to a dissimilarity graph in the context of hierarchical cluster analysis. Standard hierarchical clustering methods are specified procedurally, rather than in terms of the cost function to be optimized. We aim to overcome this limitation by presenting a general optimization framework for ultrametric fitting. Our approach consists of modeling the latter as a constrained optimization problem over the continuous space of ultrametrics. So doing, we can leverage the simple, yet effective, idea of replacing the ultrametric constraint with a min–max operation injected directly into the cost function. The proposed reformulation leads to an unconstrained optimization problem that can be efficiently solved by gradient descent methods. The flexibility of our framework allows us to investigate several cost functions, following the classic paradigm of combining a data fidelity term with a regularization. While we provide no theoretical guarantee to find the global optimum, the numerical results obtained over a number of synthetic and real datasets demonstrate the good performance of our approach with respect to state-of-the-art agglomerative algorithms. This makes us believe that the proposed framework sheds new light on the way to design a new generation of hierarchical clustering methods. Our code is made publicly available at https://github.com/PerretB/ultrametric-fitting.

Irrigation water resources management under uncertainty: An interval nonlinear double-sided fuzzy chance-constrained programming approach

An interval nonlinear double-sided fuzzy chance-constrained programming (INDFCCP) approach is formulated to effectively allocate irrigation water among competing water users. The INDFCCP approach is formulated by combining inexact quadratic programming (IQP) and double-sided fuzzy chance-constrained programming (DFCCP) within a general optimization framework. This approach has the following features. (1) It’s able to handle interval and fuzzy uncertainties, and nonlinearity existing in the objective functions. (2) It’s capable of addressing these fuzzy constraints and fuzzy variables where different confidence levels and satisfaction degree levels should be satisfied. (3) Each fuzzy chance-constraint can be further analyzed with the maximum and minimum reliability scenarios, which makes it possible to reflect variations of system conditions. (4) Interval quadratic crop water production functions (IQCWPFs) are employed in place of deterministic ones to quantitatively describe the mathematical relationships between crop yields and actual crop evapotranspiration (or irrigation water applied). Then, to demonstrate its applicability and feasibility, the INDFCCP approach is applied in the Yingke Irrigation District (YID), northwest China for allocating irrigation water to three crops in three subareas under uncertainty. Finally, more flexible decision solutions regarding optimal irrigation water allocation have been generated and analyzed under different predetermined confidence levels, showing several advantages of the INDFCCP approach with respect to the deterministic one. Under the same confidence level, system benefits under the minimum reliability scenario (e.g. [499.6, 909.7] × 106 Yuan, α = 0.5) are higher than that under the maximum reliability scenario (e.g. [498.7, 908.9] × 106 Yuan, α = 0.5). From above outcomes, the INDFCCP approach provides more appropriate results and reliable scientific bases needed for better managing irrigation water in irrigated agricultural areas.

Electricity market clearing algorithms: A case study of the Bulgarian power system

ABSTRACT This work presents a generic optimization framework (ANNEX model), including three alternative algorithms for the electricity market-clearing process in order to optimally determine the annual energy mix of a power system. The effectiveness of the ANNEX model has been tested on an illustrative case study of the Bulgarian power system to investigate the impacts of each market design on the system’s technical and economic aspects. The results highlight the influences of each market-clearing algorithm on the technology selection in the resulting electricity mix, as well as the effects on the system’s marginal price, capturing both the annual dynamics and the short-term challenges of critical days. The developed methodological framework can provide useful insights on the determination of the optimal electricity mixes, highlighting the system’s requirements to address the future market operating challenges of modern energy markets, subject to several technical, economic, and regulatory constraints.

Scalable and Parallel Deep Bayesian Optimization on Attributed Graphs.

We propose a general and scalable global optimization framework directly operating on annotated graph data by introducing a Bayesian graph neural network to approximate the expensive-to-evaluate objectives. It prevents the cubical complexity of Gaussian processes and can scale linearly with the number of observations. Its parallelized variant makes it scalable. We provide strict theoretical support on its convergence. Intensive experiments conducted on both artificial and real-world problems, including molecular discovery and urban road network design, demonstrate the effectiveness of the proposed methods compared with the current state of the art.

Event-based optimization with random packet dropping

Event-based optimization (EBO) provides a general framework for policy optimization in many discrete event dynamic systems where decision making is triggered by events that represent state transitions with common features. Because the number of events can be defined by the user and usually increases linearly with respect to the system scale, EBO has good potential to address large-scale problems where the state space grows exponentially. However, in many practical systems, sensors are geographically distributed and connected to a central controller through imperfect communication channels. Therefore, events observed by the sensors may not reach the controller. Optimization methods of event-based policies in these cases have not yet been identified. In this paper, we consider this important problem and make three major contributions. First, we formulate a mathematical EBO model in which the communication between sensors and controllers is subject to random packet dropping. Second, we show that this EBO model can be converted to another EBO model with perfect communication. Then, the performance difference equation and the performance derivative equation for event-based policies are straightforward to develop. One gradient-based policy iteration algorithm is developed for problems where the state transition probabilities are explicitly known, while another for problems where they are unknown. Third, the performance of the algorithms and the impact of the packet dropping probability on policy performance are numerically demonstrated on a single-zone occupant level estimation problem in buildings.

Human Perception-Optimized Planning for Comfortable VR-Based Telepresence

This paper introduces an emerging motion planning problem by considering a human that is immersed into the viewing perspective of a remote robot. The challenge is to make the experience both effective (such as delivering a sense of presence) and comfortable (such as avoiding adverse sickness symptoms, including nausea). We refer to this challenging new area as human perception-optimized planning and propose a general multiobjective optimization framework that can be instantiated in many envisioned scenarios. We then consider a specific VR telepresence task as a case of human perception-optimized planning, in which we simulate a robot that sends 360 video to a remote user to be viewed through a head-mounted display. In this particular task, we plan trajectories that minimize VR sickness (and thereby maximize comfort). An A* type method is used to create a Pareto-optimal collection of piecewise linear trajectories while taking into account criteria that improve comfort. We conducted a study with human subjects touring a virtual museum, in which paths computed by our algorithm are compared against a reference RRT-based trajectory. Generally, users suffered less from VR sickness and preferred the paths created by the presented algorithm.

Truncated Robust Principle Component Analysis With A General Optimization Framework.

Recently, several robust principle component analysis (RPCA) models have been proposed to improve the robustness of principle component analysis (PCA). But an important problem that the robustness to outliers affects the discrimination of correct samples has not been solved yet. To solve this problem, we propose a truncated robust principle component analysis (T-RPCA) model which treats correct samples and outliers separately. In fact, the proposed model performs an implicitly truncated weighted learning scheme which is more reasonable for robustness learning respective to previous works. Moreover, we propose a re-weighted (RW) optimization framework to solve a general problem and generalize two sub-frameworks upon it. To be specific, the first sub-framework orients a general truncated loss optimization problem which contains the objective problem of T-RPCA, and the second one focuses on a general singular-value based optimization problem. Besides, we provide rigorously theoretical guarantees for the proposed model, RW framework and sub-frameworks. Empirical studies demonstrate that the proposed T-RPCA model outperforms previous RPCA models on reconstruction and classification tasks.

Topology-Finding of Tensegrity Structures Considering Global Stability Condition

This study proposes a general framework for topology-finding or topology optimization of tensegrity structures. The existing topology-finding formulation of tensegrity structures based on mixed-integer linear programming (MILP) was improved and transformed into a formulation based on mixed-integer semidefinite programming (MISDP) which considers the global stability condition of tensegrity. We illustrated and analyzed two undesirable phenomena, loss of prestress stability and loss of integrity, caused by the missing global stability condition in previous MILP-based approaches. A branch-and-bound algorithm combined with a primal-dual interior-point algorithm is employed to solve the proposed MISDP model. Some numerical examples illustrated the improvements and effectiveness of the proposed approach. The proposed approach successfully can avoid the two undesirable phenomena and ensure the global stability of the found tensegrity structures. By using different stability conditions in the topology-finding process, the proposed approach can find general stable tensegrity structures and superstable tensegrity structures.

Efficient Estimation of Treatment Effects using Neural Networks with A Diverging Number of Confounders

The estimation of causal effects is a primary goal of behavioral, social, economic and biomedical sciences. Under the unconfounded treatment assignment condition, adjustment for confounders requires estimating the nuisance functions relating outcome and/or treatment to confounders. The conventional approaches rely on either a parametric or a nonparametric modeling strategy to approximate the nuisance functions. Parametric methods can introduce serious bias into casual effect estimation due to possible mis-specification, while nonparametric estimation suffers from the ''curse of dimensionality. This paper proposes a new unified approach for efficient estimation of treatment effects using feedforward artificial neural networks (ANN) when the number of covariates is allowed to increase with the sample size. We consider a general optimization framework that includes the average, quantile and asymmetric least squares treatment effects as special cases. Under this unified setup, we develop a generalized optimization estimator for the treatment effect with the nuisance function estimated by ANNs. We further establish the consistency and asymptotic normality of the proposed estimator and show that it attains the semiparametric efficiency bound. The proposed methods are illustrated via simulation studies and a real data application.

Learning Functors using Gradient Descent

Neural networks are a general framework for differentiable optimization which includes many other machine learning approaches as special cases. In this paper we build a category-theoretic formalism around a neural network system called CycleGAN. CycleGAN is a general approach to unpaired image-to-image translation that has been getting attention in the recent years. Inspired by categorical database systems, we show that CycleGAN is a "schema", i.e. a specific category presented by generators and relations, whose specific parameter instantiations are just set-valued functors on this schema. We show that enforcing cycle-consistencies amounts to enforcing composition invariants in this category. We generalize the learning procedure to arbitrary such categories and show a special class of functors, rather than functions, can be learned using gradient descent. Using this framework we design a novel neural network system capable of learning to insert and delete objects from images without paired data. We qualitatively evaluate the system on the CelebA dataset and obtain promising results.

Co-Saliency Detection via a General Optimization Model and Adaptive Graph Learning

Co-saliency detection is an important research problem, and has been widely used in computer vision area. One main challenge for co-saliency detection problem is how to explore both interactive information among different images and individual salient information within each image simultaneously in co-saliency estimation. In this paper, we propose a novel general optimization framework with adaptive graph learning for co-saliency estimation problem. The proposed model integrates multiple cues including background, and foreground priors, structural information of images, and image feature representation together to obtain a uniform, and accurate co-saliency estimation. One main benefit of the proposed co-saliency method is that it conducts co-saliency propagation, and prediction across different images while maintains the individual salient information of each image, which ensures the consistency, and communication across different images effectively in co-saliency estimation. To improve the accuracy of co-saliency estimation, we adaptively learn a neighborhood, and structured graph to conduct co-saliency propagation among superpixels. An effective optimization algorithm has been designed to seek the optimal solution for the proposed co-saliency optimization model. Experimental results on several widely used datasets show that our method outperforms some other related co-saliency detection methods.