Analysis-of-marginal-Tail-Means (ATM): a robust method for discrete black-box optimization

We present a new method, called Analysis-of-marginal-Tail-Means (ATM), for effective robust optimization of discrete black-box problems. ATM has important applications to many real-world engineering problems (e.g., manufacturing optimization, product design, molecular engineering), where the objective to optimize is black-box and expensive, and the design space is inherently discrete. One weakness of existing methods is that they are not robust: these methods perform well under certain assumptions, but yield poor results when such assumptions (which are difficult to verify in black-box problems) are violated. ATM addresses this via the use of marginal tail means for optimization, which combines both rank-based and model-based methods. The trade-off between rank- and model-based optimization is tuned by first identifying important main effects and interactions, then finding a good compromise which best exploits additive structure. By adaptively tuning this trade-off from data, ATM provides improved robust optimization over existing methods, particularly in problems with (i) a large number of factors, (ii) unordered factors, or (iii) experimental noise. We demonstrate the effectiveness of ATM in simulations and in two real-world engineering problems: the first on robust parameter design of a circular piston, and the second on product family design of a thermistor network

Labeling and denoising geometrically parameterized data with applications to Cryo-EM

textMany data sets encountered in practice depend continuously on a geometric parameter. An important example of this is image collections from Cryo-EM experiments, where the images depend continuously on the orientation of molecules. The first part of the thesis considers the problem of labeling geometrically parameterized data sets. It shows that for this problem the popular method of spectral clustering is sensitive to noise. It then presents a categorical optimization solution which is unbiased and robust to noise. The second part of the thesis presents a method to denoise collections of Cryo-EM images. The method represents Cryo-EM image collections as a single vector in a high dimensional space, and computes a low dimensional subspace which well contains the signal of the vector. By projecting the vector of images onto this subspace, the image collection is denoised. The thesis shows that the output images are centered, and that their SNR grows linearly with the number of input images.Mathematic

A Method for Finding a Design Space as Linear Combinations of Parameter Ranges for Biopharmaceutical Control Strategies

According to ICH Q8 guidelines, the biopharmaceutical manufacturer submits a design space (DS) definition as part of the regulatory approval application, in which case process parameter (PP) deviations within this space are not considered a change and do not trigger a regulatory post approval procedure. A DS can be described by non-linear PP ranges, i.e., the range of one PP conditioned on specific values of another. However, independent PP ranges (linear combinations) are often preferred in biopharmaceutical manufacturing due to their operation simplicity. While some statistical software supports the calculation of a DS comprised of linear combinations, such methods are generally based on discretizing the parameter space - an approach that scales poorly as the number of PPs increases. Here, we introduce a novel method for finding linear PP combinations using a numeric optimizer to calculate the largest design space within the parameter space that results in critical quality attribute (CQA) boundaries within acceptance criteria, predicted by a regression model. A precomputed approximation of tolerance intervals is used in inequality constraints to facilitate fast evaluations of this boundary using a single matrix multiplication. Correctness of the method was validated against different ground truths with known design spaces. Compared to stateof-the-art, grid-based approaches, the optimizer-based procedure is more accurate, generally yields a larger DS and enables the calculation in higher dimensions. Furthermore, a proposed weighting scheme can be used to favor certain PPs over others and therefore enabling a more dynamic approach to DS definition and exploration. The increased PP ranges of the larger DS provide greater operational flexibility for biopharmaceutical manufacturers.Comment: 15 pages, 7 figures, 3 tables, research articl

A general mathematical framework for constrained mixed-variable blackbox optimization problems with meta and categorical variables

A mathematical framework for modelling constrained mixed-variable optimization problems is presented in a blackbox optimization context. The framework introduces a new notation and allows solution strategies. The notation framework allows meta and categorical variables to be explicitly and efficiently modelled, which facilitates the solution of such problems. The new term meta variables is used to describe variables that influence which variables are acting or nonacting: meta variables may affect the number of variables and constraints. The flexibility of the solution strategies supports the main blackbox mixed-variable optimization approaches: direct search methods and surrogate-based methods (Bayesian optimization). The notation system and solution strategies are illustrated through an example of a hyperparameter optimization problem from the machine learning community

Tree ensemble kernels for Bayesian optimization with known constraints over mixed-feature spaces

Tree ensembles can be well-suited for black-box optimization tasks such as algorithm tuning and neural architecture search, as they achieve good predictive performance with little or no manual tuning, naturally handle discrete feature spaces, and are relatively insensitive to outliers in the training data. Two well-known challenges in using tree ensembles for black-box optimization are (i) effectively quantifying model uncertainty for exploration and (ii) optimizing over the piece-wise constant acquisition function. To address both points simultaneously, we propose using the kernel interpretation of tree ensembles as a Gaussian Process prior to obtain model variance estimates, and we develop a compatible optimization formulation for the acquisition function. The latter further allows us to seamlessly integrate known constraints to improve sampling efficiency by considering domain-knowledge in engineering settings and modeling search space symmetries, e.g., hierarchical relationships in neural architecture search. Our framework performs as well as state-of-the-art methods for unconstrained black-box optimization over continuous/discrete features and outperforms competing methods for problems combining mixed-variable feature spaces and known input constraints.Comment: 27 pages, 9 figures, 4 table

A Bilevel Optimization Approach for Joint Offloading Decision and Resource Allocation in Cooperative Mobile Edge Computing

This paper studies a multi-user cooperative mobile edge computing offloading (CoMECO) system in a multi-user interference environment, in which delay-sensitive tasks may be executed on local devices, cooperative devices, or the primary MEC server. In this system, we jointly optimize the offloading decision and computation resource allocation for minimizing the total energy consumption of all mobile users under the delay constraint. If this problem is solved directly, the offloading decision and computation resource allocation are generally generated separately at the same time. Note, however, that they are closely coupled. Therefore, under this condition, their dependency is not well considered, thus leading to poor performance. We transform this problem into a bilevel optimization problem, in which the offloading decision is generated in the upper level, and then the optimal allocation of computation resources is obtained in the lower level based on the given offloading decision. In this way, the dependency between the offloading decision and computation resource allocation can be fully taken into account. Subsequently, a bilevel optimization approach, called BiJOR, is proposed. In BiJOR, candidate modes are first pruned to reduce the number of infeasible offloading decisions. Afterward, the upper level optimization problem is solved by ant colony system (ACS). Furthermore, a sorting strategy is incorporated into ACS to construct feasible offloading decisions with a higher probability and a local search operator is designed in ACS to accelerate the convergence. For the lower level optimization problem, it is solved by the monotonic optimization method. In addition, BiJOR is extended to deal with a complex scenario with the channel selection. Extensive experiments are carried out to investigate the performance of BiJOR on two sets of instances with up to 400 mobile users. The experimental results demonstrate the effectiveness of BiJOR and the superiority of the CoMECO system