Due to the practical importance of vehicle routing problems (VRP), there exists an ever-growing body of research in algorithms and (meta)heuristics for solving such problems. However, the diversity of VRP domains creates the separate problem of modeling such problems -- describing the domain entities (and, in particular, the planning decisions), the set of valid planning decisions, and the preferences between different plans. In this paper, we review the approaches for modeling vehicle routing problems. To make the comparison more straightforward, we formulate several criteria for evaluating modeling methods reflecting the practical requirements of the development of optimization algorithms for such problems. Finally, as a result of this comparison, we discuss several future research avenues in the field of modeling VRP domains.

The Nearly Autonomous Management and Control System (NAMAC) is a comprehensive control system that assists plant operations by furnishing control recommendations to operators in a broad class of situations. This study refines a NAMAC system for making reasonable recommendations during complex loss-of-flow scenarios with a validated Experimental Breeder Reactor II simulator, digital twins improved by machine-learning algorithms, a multi-attribute decision-making scheme, and a discrepancy checker for identifying unexpected recommendation effects. We assessed the performance of each NAMAC component, while we demonstrated and evaluated the capability of NAMAC in a class of loss-of-flow scenarios.

Policy optimization, which learns the policy of interest by maximizing the value function via large-scale optimization techniques, lies at the heart of modern reinforcement learning (RL). In addition to value maximization, other practical considerations arise commonly as well, including the need of encouraging exploration, and that of ensuring certain structural properties of the learned policy due to safety, resource and operational constraints. These considerations can often be accounted for by resorting to regularized RL, which augments the target value function with a structure-promoting regularization term. Focusing on an infinite-horizon discounted Markov decision process, this paper proposes a generalized policy mirror descent (GPMD) algorithm for solving regularized RL. As a generalization of policy mirror descent Lan (2021), the proposed algorithm accommodates a general class of convex regularizers as well as a broad family of Bregman divergence in cognizant of the regularizer in use. We demonstrate that our algorithm converges linearly over an entire range of learning rates, in a dimension-free fashion, to the global solution, even when the regularizer lacks strong convexity and smoothness. In addition, this linear convergence feature is provably stable in the face of inexact policy evaluation and imperfect policy updates. Numerical experiments are provided to corroborate the applicability and appealing performance of GPMD.

The learning rate (LR) schedule is one of the most important hyper-parameters needing careful tuning in training DNNs. However, it is also one of the least automated parts of machine learning systems and usually costs significant manual effort and computing. Though there are pre-defined LR schedules and optimizers with adaptive LR, they introduce new hyperparameters that need to be tuned separately for different tasks/datasets. In this paper, we consider the question: Can we automatically tune the LR over the course of training without human involvement? We propose an efficient method, AutoLRS, which automatically optimizes the LR for each training stage by modeling training dynamics. AutoLRS aims to find an LR applied to every $\tau$ steps that minimizes the resulted validation loss. We solve this black-box optimization on the fly by Bayesian optimization (BO). However, collecting training instances for BO requires a system to evaluate each LR queried by BO's acquisition function for $\tau$ steps, which is prohibitively expensive in practice. Instead, we apply each candidate LR for only $\tau'\ll\tau$ steps and train an exponential model to predict the validation loss after $\tau$ steps. This mutual-training process between BO and the loss-prediction model allows us to limit the training steps invested in the BO search. We demonstrate the advantages and the generality of AutoLRS through extensive experiments of training DNNs for tasks from diverse domains using different optimizers. The LR schedules auto-generated by AutoLRS lead to a speedup of $1.22\times$, $1.43\times$, and $1.5\times$ when training ResNet-50, Transformer, and BERT, respectively, compared to the LR schedules in their original papers, and an average speedup of $1.31\times$ over state-of-the-art heavily-tuned LR schedules.

Neural Linear Models (NLM) are deep Bayesian models that produce predictive uncertainty by learning features from the data and then performing Bayesian linear regression over these features. Despite their popularity, few works have focused on formally evaluating the predictive uncertainties of these models. Furthermore, existing works point out the difficulties of encoding domain knowledge in models like NLMs, making them unsuitable for applications where interpretability is required. In this work, we show that traditional training procedures for NLMs can drastically underestimate uncertainty in data-scarce regions. We identify the underlying reasons for this behavior and propose a novel training method that can both capture useful predictive uncertainties as well as allow for incorporation of domain knowledge.

Optimal Lens Design constitutes a fundamental, long-standing real-world optimization challenge. Potentially large number of optima, rich variety of critical points, as well as solid understanding of certain optimal designs per simple problem instances, provide altogether the motivation to address it as a niching challenge. This study applies established Niching-CMA-ES heuristic to tackle this design problem (6-dimensional Cooke triplet) in a simulation-based fashion. The outcome of employing Niching-CMA-ES `out-of-the-box' proves successful, and yet it performs best when assisted by a local searcher which accurately drives the search into optima. The obtained search-points are corroborated based upon concrete knowledge of this problem-instance, accompanied by gradient and Hessian calculations for validation. We extensively report on this computational campaign, which overall resulted in (i) the location of 19 out of 21 known minima within a single run, (ii) the discovery of 540 new optima. These are new minima similar in shape to 21 theoretical solutions, but some of them have better merit function value (unknown heretofore), (iii) the identification of numerous infeasibility pockets throughout the domain (also unknown heretofore). We conclude that niching mechanism is well-suited to address this problem domain, and hypothesize on the apparent multidimensional structures formed by the attained new solutions.

In many real-world problems, complex dependencies are present both among samples and among features. The Kronecker sum or the Cartesian product of two graphs, each modeling dependencies across features and across samples, has been used as an inverse covariance matrix for a matrix-variate Gaussian distribution, as an alternative to a Kronecker-product inverse covariance matrix, due to its more intuitive sparse structure. However, the existing methods for sparse Kronecker-sum inverse covariance estimation are limited in that they do not scale to more than a few hundred features and samples and that the unidentifiable parameters pose challenges in estimation. In this paper, we introduce EiGLasso, a highly scalable method for sparse Kronecker-sum inverse covariance estimation, based on Newton's method combined with eigendecomposition of the two graphs for exploiting the structure of Kronecker sum. EiGLasso further reduces computation time by approximating the Hessian based on the eigendecomposition of the sample and feature graphs. EiGLasso achieves quadratic convergence with the exact Hessian and linear convergence with the approximate Hessian. We describe a simple new approach to estimating the unidentifiable parameters that generalizes the existing methods. On simulated and real-world data, we demonstrate that EiGLasso achieves two to three orders-of-magnitude speed-up compared to the existing methods.

Stochastic Gradient Descent (SGD) and its variants are the main workhorses of modern machine learning. Distributed implementations of SGD on a cluster of machines with a central server and a large number of workers are frequently used in practice due to the massive size of the data. In distributed SGD each machine holds a copy of the model and the computation proceeds in rounds. In every round, each worker finds a stochastic gradient based on its batch of examples, the server averages these stochastic gradients to obtain the gradient of the entire batch, makes an SGD step, and broadcasts the updated model parameters to the workers. With a large number of workers, computation parallelizes efficiently while communication becomes the main bottleneck [Chilimbi et al., 2014, Strom, 2015], since each worker needs to send its gradients to the server and receive the updated model parameters. Common solutions for this problem include: local SGD and its variants, when each machine performs multiple local steps before communication [Stich, 2018]; decentralized architectures which allow pairwise communication between the workers [McMahan et al., 2017] and gradient compression, when a compressed version of the gradient is communicated instead of the full gradient [Bernstein et al., 2018, Stich et al., 2018, Karimireddy et al., 2019]. In this work, we consider the latter approach, which we refer to as compressed SGD. Most machine learning models can be described by a d-dimensional vector of parameters x and the model quality can be estimated as a function f(x).

This study aims to optimize Deep Feedforward Neural Networks (DFNNs) training using nature-inspired optimization algorithms, such as PSO, MTO, and its variant called MTOCL. We show how these algorithms efficiently update the weights of DFNNs when learning from data. We evaluate the performance of DFNN fused with optimization algorithms using three Wisconsin breast cancer datasets, Original, Diagnostic, and Prognosis, under different experimental scenarios. The empirical analysis demonstrates that MTOCL is the most performing in most scenarios across the three datasets. Also, MTOCL is comparable to past weight optimization algorithms for the original dataset, and superior for the other datasets, especially for the challenging Prognostic dataset.

In its most traditional setting, the main concern of optimization theory is the search for optimal solutions for instances of a given computational problem. A recent trend of research in artificial intelligence, called solution diversity, has focused on the development of notions of optimality that may be more appropriate in settings where subjectivity is essential. The idea is that instead of aiming at the development of algorithms that output a single optimal solution, the goal is to investigate algorithms that output a small set of sufficiently good solutions that are sufficiently diverse from one another. In this way, the user has the opportunity to choose the solution that is most appropriate to the context at hand. It also displays the richness of the solution space. When combined with techniques from parameterized complexity theory, the paradigm of diversity of solutions offers a powerful algorithmic framework to address problems of practical relevance. In this work, we investigate the impact of this combination in the field of Kemeny Rank Aggregation, a well-studied class of problems lying in the intersection of order theory and social choice theory and also in the field of order theory itself. In particular, we show that the Kemeny Rank Aggregation problem is fixed-parameter tractable with respect to natural parameters providing natural formalizations of the notions of diversity and of the notion of a sufficiently good solution. Our main results work both when considering the traditional setting of aggregation over linearly ordered votes, and in the more general setting where votes are partially ordered.