The problem has been excessively studied[1][2][3][4][5][6] and a vast array of methods have been introduced to either find the optimal tour or a good less time consuming approximation. This paper will concentrate onthe second path of meta-heuristics and specifically on genetic algorithms(GA) and the historical association with the TSP. GA's have been around since 1957[7], starting with simulations for biological evolution. GA's are used for optimization problems with large search spaces. The TSP as an optimization problem therefore fits the usage and an application of GA's to the TSP was conceivable. In1975 Holland [8] laid the foundation for the success and the resulting interestin GA's. With his fundamental theorem of genetic algorithms he proclaimed the efficiency of GA's for optimization problems. A generic GA starts with the generation of a population of several different tours.

Conversion optimization tools are estimated to have an average ROI of 223%. And that is totally expected as they're largely responsible for most conversions and revenue. However, CRO tools are more expensive than many other marketing tools, too (as you'll soon see in this article). And there are so many of them out there. But at the end of the day, it's not using these tools that matters but what they do for your business.

As teams apply optimization earlier and more frequently in the modeling process, they develop high-performing models at a faster pace. This virtuous cycle increases the number of models that make it into production, which amplifies the impact of these models on the business. At the Deep Learning Summit in San Francisco, SigOpt will be showcasing their model optimization software and how they automate model tuning to accelerate the model development process and amplify the impact of models in production at scale. We spoke to Nick Payton, B2B Marketing Lead at SigOpt to learn more. SigOpt's mission is to empower experts.

Improving predictive understanding of Earth system variability and change requires data-model integration. Efficient data-model integration for complex models requires surrogate modeling to reduce model evaluation time. However, building a surrogate of a large-scale Earth system model (ESM) with many output variables is computationally intensive because it involves a large number of expensive ESM simulations. In this effort, we propose an efficient surrogate method capable of using a few ESM runs to build an accurate and fast-to-evaluate surrogate system of model outputs over large spatial and temporal domains. We first use singular value decomposition to reduce the output dimensions, and then use Bayesian optimization techniques to generate an accurate neural network surrogate model based on limited ESM simulation samples. Our machine learning based surrogate methods can build and evaluate a large surrogate system of many variables quickly. Thus, whenever the quantities of interest change such as a different objective function, a new site, and a longer simulation time, we can simply extract the information of interest from the surrogate system without rebuilding new surrogates, which significantly saves computational efforts. We apply the proposed method to a regional ecosystem model to approximate the relationship between 8 model parameters and 42660 carbon flux outputs. Results indicate that using only 20 model simulations, we can build an accurate surrogate system of the 42660 variables, where the consistency between the surrogate prediction and actual model simulation is 0.93 and the mean squared error is 0.02. This highly-accurate and fast-to-evaluate surrogate system will greatly enhance the computational efficiency in data-model integration to improve predictions and advance our understanding of the Earth system.

Bayesian optimal design of experiments (BODE) has been successful in acquiring information about a quantity of interest (QoI) which depends on a black-box function. BODE is characterized by sequentially querying the function at specific designs selected by an infill-sampling criterion. However, most current BODE methods operate in specific contexts like optimization, or learning a universal representation of the black-box function. The objective of this paper is to design a BODE for estimating the statistical expectation of a physical response surface. This QoI is omnipresent in uncertainty propagation and design under uncertainty problems. Our hypothesis is that an optimal BODE should be maximizing the expected information gain in the QoI. We represent the information gain from a hypothetical experiment as the Kullback-Liebler (KL) divergence between the prior and the posterior probability distributions of the QoI. The prior distribution of the QoI is conditioned on the observed data and the posterior distribution of the QoI is conditioned on the observed data and a hypothetical experiment. The main contribution of this paper is the derivation of a semi-analytic mathematical formula for the expected information gain about the statistical expectation of a physical response. The developed BODE is validated on synthetic functions with varying number of input-dimensions. We demonstrate the performance of the methodology on a steel wire manufacturing problem.

Topology design optimization offers a tremendous opportunity in design and manufacturing freedoms by designing and producing a part from the ground-up without a meaningful initial design as required by conventional shape design optimization approaches. Ideally, with adequate problem statements, to formulate and solve the topology design problem using a standard topology optimization process, such as SIMP (Simplified Isotropic Material with Penalization) is possible. However, in reality, an estimated over thousands of design iterations is often required for just a few design variables, the conventional optimization approach is, in general, impractical or computationally unachievable for real-world applications significantly diluting the development of the topology optimization technology. There is, therefore, a need for a different approach that will be able to optimize the initial design topology effectively and rapidly. In this study, a novel topology optimization approach based on conditional Wasserstein generative adversarial networks (CWGAN) is developed to replicate the conventional topology optimization algorithms in an extremely computationally inexpensive way. CWGAN consists of a generator and a discriminator, both of which are deep convolutional neural networks (CNN). The limited samples of data, quasi-optimal planar structures, needed for training purposes are generated using the conventional topology optimization algorithms. With CWGANs, the topology optimization conditions can be set to a required value before generating samples.

Several problems in modeling and control of stochastically-driven dynamical systems can be cast as regularized semi-definite programs. We examine two such representative problems and show that they can be formulated in a similar manner. The first, in statistical modeling, seeks to reconcile observed statistics by suitably and minimally perturbing prior dynamics. The second seeks to optimally select a subset of available sensors and actuators for control purposes. To address modeling and control of large-scale systems we develop a unified algorithmic framework using proximal methods. Our customized algorithms exploit problem structure and allow handling statistical modeling, as well as sensor and actuator selection, for substantially larger scales than what is amenable to current general-purpose solvers. We establish linear convergence of the proximal gradient algorithm, draw contrast between the proposed proximal algorithms and alternating direction method of multipliers, and provide examples that illustrate the merits and effectiveness of our framework. Index Terms Actuator selection, sensor selection, sparsity-promoting estimation and control, method of multipliers, nonsmooth convex optimization, proximal algorithms, regularization for design, semi-definite programming, structured covariances. I. INTRODUCTION Convex optimization has had tremendous impact on many disciplines, including system identification and control design [1]-[7]. The present paper focuses on two representative control problems, statistical control-oriented modeling and sensor/actuator selection, that are cast as convex programs.

Statistical inference of analytically non-tractable posteriors is a difficult problem because of marginalization of correlated variables and stochastic methods such as MCMC and VI are commonly used. We argue that stochastic KL divergence minimization used by MCMC and VI is noisy, and we propose instead EL_2O, expectation optimization of L_2 distance squared between the approximate log posterior q and the un-normalized log posterior of p. When sampling from q the solutions agree with stochastic KL divergence minimization based VI in the large sample limit, however EL_2O method is free of sampling noise, has better optimization properties, and requires only as many sample evaluations as the number of parameters we are optimizing if q covers p. As a consequence, increasing the expressivity of q improves both the quality of results and the convergence rate, allowing EL_2O to approach exact inference. Use of automatic differentiation methods enables us to develop Hessian, gradient and gradient free versions of the method, which can determine M(M+2)/2+1, M+1 and 1 parameter(s) of q with a single sample, respectively. EL_2O provides a reliable estimate of the quality of the approximating posterior, and converges rapidly on full rank gaussian approximation for q and extensions beyond it, such as nonlinear transformations and gaussian mixtures. These can handle general posteriors, while still allowing fast analytic marginalizations. We test it on several examples, including a realistic 13 dimensional galaxy clustering analysis, showing that it is several orders of magnitude faster than MCMC, while giving smooth and accurate non-gaussian posteriors, often requiring a few to a few dozen of iterations only.

Evolutionarily stable strategy (ESS) is an important solution concept in game theory which has been applied frequently to biological models. Informally an ESS is a strategy that if followed by the population cannot be taken over by a mutation strategy that is initially rare. Finding such a strategy has been shown to be difficult from a theoretical complexity perspective. We present an algorithm for the case where mutations are restricted to pure strategies, and present experiments on several game classes including random and a recently-proposed cancer model. Our algorithm is based on a mixed-integer non-convex feasibility program formulation, which constitutes the first general optimization formulation for this problem. It turns out that the vast majority of the games included in the experiments contain ESS with small support, and our algorithm is outperformed by a support-enumeration based approach. However we suspect our algorithm may be useful in the future as games are studied that have ESS with potentially larger and unknown support size.

Many challenging image processing tasks can be described by an ill-posed linear inverse problem: deblurring, deconvolution, inpainting, compressed sensing, and superresolution all lie in this framework. Traditional inverse problem solvers minimize a cost function consisting of a data-fit term, which measures how well an image matches the observations, and a regularizer, whichreflects prior knowledge and promotes images with desirable properties like smoothness. Recent advances in machine learning and image processing have illustrated that it is often possible to learn a regularizer from training data that can outperform more traditional regularizers.We present an end-to-end, data-driven method of solving inverse problems inspired by the Neumann series, which we call a Neumann network. Rather than unroll an iterative optimization algorithm, we truncate a Neumann series which directly solves the linear inverseproblem with a data-driven nonlinear regularizer. Finally, when the images belong to a union of subspaces and under appropriate assumptions on the forward model, we prove there exists a Neumann network configuration that well-approximates the optimal oracle estimator for the inverse problem and demonstrate empirically that the trained Neumann network has the form predicted by theory. D. Gilton is with the Department of Electrical and Computer Engineering, University of Wisconsin, Madison, WI, 53706 USA (email: gilton@wisc.edu). G. Ongie is with the Department of Statistics, University of Chicago, Chicago, IL, 60637 USA (email: gongie@uchicago.edu). R. Willett is with the Department of Statistics and Computer Science, University of Chicago, Chicago, IL, 60637 USA (email: willett@uchicago.edu). In general, a regularization function r(β) measures the lack of conformity of β to this prior knowledge and β is selected so that r( β) is as small as possible while still providing a good fit to the data. However, recent work in computer vision using deep neural networks has leveraged large collections of"training" images to yield unprecedented image recognition performance [32, 33, 38], and an emerging body of research is exploring whether this training data can also be used to improve thequality of image reconstruction. In other words, can training data be used to learn how to regularize inverse problems? As we detail below, existing methods include using training images to learn a low-dimensional image manifold and constraining β to lie on this manifold [9] or learning a denoising autoencoder that can be treated as a regularization step (i.e., proximal operator) within an iterative reconstruction scheme [47].