GANs generate new designs from an existing dataset utilizing a generator and a discriminator which are usually Deep Generative design has been growing across the Neural Networks (DNNs). The objective function of GANs design community as a viable method for design should be differentiable to utilize gradient-based optimization space exploration. Thermal design is more complex while reward of a deep RL can be defined based on the than mechanical or aerodynamic design because design requirements (Chen & Ahmed, 2021b). of the additional convection-diffusion equation and its pertinent boundary interaction. We Shape and Topology Optimization (TO) play a major role in present a generative thermal design using cooperative Generative models in engineering design (Chen & Ahmed, multi-agent deep reinforcement learning 2021a). Engineering design often require Finite Element and continuous geometric representation of the Analysis (FEA) or Computational Fluid Dynamics (CFD) fluid and solid domain. The proposed framework to assess the performance of the output design (Hoyer et al., consists of a pre-trained neural network surrogate 2019). These numerical approaches are computationally model as an environment to predict heat transfer expensive and require human expertise (Regenwetter et al., and pressure drop of the generated geometries.

Terahertz (THz) wireless networks are expected to catalyze the beyond fifth generation (B5G) era. However, due to the directional nature and the line-of-sight demand of THz links, as well as the ultra-dense deployment of THz networks, a number of challenges that the medium access control (MAC) layer needs to face are created. In more detail, the need of rethinking user association and resource allocation strategies by incorporating artificial intelligence (AI) capable of providing "real-time" solutions in complex and frequently changing environments becomes evident. Moreover, to satisfy the ultra-reliability and low-latency demands of several B5G applications, novel mobility management approaches are required. Motivated by this, this article presents a holistic MAC layer approach that enables intelligent user association and resource allocation, as well as flexible and adaptive mobility management, while maximizing systems' reliability through blockage minimization. In more detail, a fast and centralized joint user association, radio resource allocation, and blockage avoidance by means of a novel metaheuristic-machine learning framework is documented, that maximizes the THz networks performance, while minimizing the association latency by approximately three orders of magnitude. To support, within the access point (AP) coverage area, mobility management and blockage avoidance, a deep reinforcement learning (DRL) approach for beam-selection is discussed. Finally, to support user mobility between coverage areas of neighbor APs, a proactive hand-over mechanism based on AI-assisted fast channel prediction is~reported.

Multiple mobile manipulators show superiority in the tasks requiring mobility and dexterity compared with a single robot, especially when manipulating/transporting bulky objects. When the object and the manipulators are rigidly connected, closed-chain will form and the motion of the whole system will be restricted onto a lower-dimensional manifold. However, current research on multi-robot motion planning did not fully consider the formation of the whole system, the redundancy of the mobile manipulator and obstacles in the environment, which make the tasks challenging. Therefore, this paper proposes a hierarchical framework to efficiently solve the above challenges, where the centralized layer plans the object's motion offline and the decentralized layer independently explores the redundancy of each robot in real-time. In addition, closed-chain, obstacle-avoidance and the lower bound of the formation constraints are guaranteed in the centralized layer, which cannot be achieved simultaneously by other planners. Moreover, capability map, which represents the distribution of the formation constraint, is applied to speed up the two layers. Both simulation and experimental results show that the proposed framework outperforms the benchmark planners significantly. The system could bypass or cross obstacles in cluttered environments, and the framework can be applied to different numbers of heterogeneous mobile manipulators.

What is another way to re-cast this? In the case of Image segmentation, we can think of it as an optimization problem. For any image, you can choose and iterate between a variety of segment configurations, and choose the one where the difference between pixel intensities is the highest. Learning problems are trained by minimizing the error between predictions and actual values across a large data set. In other words, they are trained by optimization methods that are stochastic. Learning and optimization problems have many things in common structurally.

Partial least square regression (PLSR) is a widely-used statistical model to reveal the linear relationships of latent factors that comes from the independent variables and dependent variables. However, traditional methods to solve PLSR models are usually based on the Euclidean space, and easily getting stuck into a local minimum. To this end, we propose a new method to solve the partial least square regression, named PLSR via optimization on bi-Grassmann manifold (PLSRbiGr). Specifically, we first leverage the three-factor SVD-type decomposition of the cross-covariance matrix defined on the bi-Grassmann manifold, converting the orthogonal constrained optimization problem into an unconstrained optimization problem on bi-Grassmann manifold, and then incorporate the Riemannian preconditioning of matrix scaling to regulate the Riemannian metric in each iteration. PLSRbiGr is validated with a variety of experiments for decoding EEG signals at motor imagery (MI) and steady-state visual evoked potential (SSVEP) task. Experimental results demonstrate that PLSRbiGr outperforms competing algorithms in multiple EEG decoding tasks, which will greatly facilitate small sample data learning.

Many fundamental low-rank optimization problems, such as matrix completion, phase synchronization/retrieval, power system state estimation, and robust PCA, can be formulated as the matrix sensing problem. Two main approaches for solving matrix sensing are based on semidefinite programming (SDP) and Burer-Monteiro (B-M) factorization. The SDP method suffers from high computational and space complexities, whereas the B-M method may return a spurious solution due to the non-convexity of the problem. The existing theoretical guarantees for the success of these methods have led to similar conservative conditions, which may wrongly imply that these methods have comparable performances. In this paper, we shed light on some major differences between these two methods. First, we present a class of structured matrix completion problems for which the B-M methods fail with an overwhelming probability, while the SDP method works correctly. Second, we identify a class of highly sparse matrix completion problems for which the B-M method works and the SDP method fails. Third, we prove that although the B-M method exhibits the same performance independent of the rank of the unknown solution, the success of the SDP method is correlated to the rank of the solution and improves as the rank increases. Unlike the existing literature that has mainly focused on those instances of matrix sensing for which both SDP and B-M work, this paper offers the first result on the unique merit of each method over the alternative approach.

We consider two federated learning algorithms for training partially personalized models, where the shared and personal parameters are updated either simultaneously or alternately on the devices. Both algorithms have been proposed in the literature, but their convergence properties are not fully understood, especially for the alternating variant. We provide convergence analyses of both algorithms in the general nonconvex setting with partial participation and delineate the regime where one dominates the other. Our experiments on real-world image, text, and speech datasets demonstrate that (a) partial personalization can obtain most of the benefits of full model personalization with a small fraction of personal parameters, and, (b) the alternating update algorithm often outperforms the simultaneous update algorithm by a small but consistent margin.

We study first-order optimization algorithms under the constraint that the descent direction is quantized using a pre-specified budget of $R$-bits per dimension, where $R \in (0 ,\infty)$. We propose computationally efficient optimization algorithms with convergence rates matching the information-theoretic performance lower bounds for: (i) Smooth and Strongly-Convex objectives with access to an Exact Gradient oracle, as well as (ii) General Convex and Non-Smooth objectives with access to a Noisy Subgradient oracle. The crux of these algorithms is a polynomial complexity source coding scheme that embeds a vector into a random subspace before quantizing it. These embeddings are such that with high probability, their projection along any of the canonical directions of the transform space is small. As a consequence, quantizing these embeddings followed by an inverse transform to the original space yields a source coding method with optimal covering efficiency while utilizing just $R$-bits per dimension. Our algorithms guarantee optimality for arbitrary values of the bit-budget $R$, which includes both the sub-linear budget regime ($R < 1$), as well as the high-budget regime ($R \geq 1$), while requiring $O\left(n^2\right)$ multiplications, where $n$ is the dimension. We also propose an efficient relaxation of this coding scheme using Hadamard subspaces that requires a near-linear time, i.e., $O\left(n \log n\right)$ additions.Furthermore, we show that the utility of our proposed embeddings can be extended to significantly improve the performance of gradient sparsification schemes. Numerical simulations validate our theoretical claims. Our implementations are available at https://github.com/rajarshisaha95/DistOptConstrComm.

This is one of the most applied courses on Genetic Algorithms (GA), which presents an integrated framework to solve real-world optimization problems in the most simple way. For the first time, we have presented a practical course in the domain of metaheuristics algorithms required for students, researchers and practitioners. Firstly, we will introduce the basic theory of GA, then implement the simplest version of GA, namely Binary GA, into Matlab, and then present the continuous version, real GA, of it. Therefore, the main focus will be on the Genetic Algorithm as the most well-regarded optimization algorithm in the literature. In the following sections, we will introduce some well-known operation research problems, including transportation problems, hub location problems (HLP), quadratic assignment problems and travelling salesman problems (TSP) and try to solve them via GA.

The phenomenon of adversarial examples has been revealed in variant scenarios. Recent studies show that well-designed adversarial defense strategies can improve the robustness of deep learning models against adversarial examples. However, with the rapid development of defense technologies, it also tends to be more difficult to evaluate the robustness of the defensed model due to the weak performance of existing manually designed adversarial attacks. To address the challenge, given the defensed model, the efficient adversarial attack with less computational burden and lower robust accuracy is needed to be further exploited. Therefore, we propose a multi-objective memetic algorithm for auto adversarial attack optimization design, which realizes the automatical search for the near-optimal adversarial attack towards defensed models. Firstly, the more general mathematical model of auto adversarial attack optimization design is constructed, where the search space includes not only the attacker operations, magnitude, iteration number, and loss functions but also the connection ways of multiple adversarial attacks. In addition, we develop a multi-objective memetic algorithm combining NSGA-II and local search to solve the optimization problem. Finally, to decrease the evaluation cost during the search, we propose a representative data selection strategy based on the sorting of cross entropy loss values of each images output by models. Experiments on CIFAR10, CIFAR100, and ImageNet datasets show the effectiveness of our proposed method.