In this paper, we study a new Workforce Scheduling and Routing Problem, denoted Multiperiod Workforce Scheduling and Routing Problem with Dependent Tasks. In this problem, customers request services from a company. Each service is composed of dependent tasks, which are executed by teams of varying skills along one or more days. Tasks belonging to a service may be executed by different teams, and customers may be visited more than once a day, as long as precedences are not violated. The objective is to schedule and route teams so that the makespan is minimized, i.e., all services are completed in the minimum number of days. In order to solve this problem, we propose a Mixed-Integer Programming model, a constructive algorithm and heuristic algorithms based on the Ant Colony Optimization (ACO) metaheuristic. The presence of precedence constraints makes it difficult to develop efficient local search algorithms. This motivates the choice of the ACO metaheuristic, which is effective in guiding the construction process towards good solutions. Computational results show that the model is capable of consistently solving problems with up to about 20 customers and 60 tasks. In most cases, the best performing ACO algorithm was able to match the best solution provided by the model in a fraction of its computational time.

Deep models, while being extremely flexible and accurate, are surprisingly vulnerable to "small, imperceptible" perturbations known as adversarial attacks. While the majority of existing attacks focus on measuring perturbations under the $\ell_p$ metric, Wasserstein distance, which takes geometry in pixel space into account, has long been known to be a suitable metric for measuring image quality and has recently risen as a compelling alternative to the $\ell_p$ metric in adversarial attacks. However, constructing an effective attack under the Wasserstein metric is computationally much more challenging and calls for better optimization algorithms. We address this gap in two ways: (a) we develop an exact yet efficient projection operator to enable a stronger projected gradient attack; (b) we show that the Frank-Wolfe method equipped with a suitable linear minimization oracle works extremely fast under Wasserstein constraints. Our algorithms not only converge faster but also generate much stronger attacks. For instance, we decrease the accuracy of a residual network on CIFAR-10 to $3.4\%$ within a Wasserstein perturbation ball of radius $0.005$, in contrast to $65.6\%$ using the previous Wasserstein attack based on an \emph{approximate} projection operator. Furthermore, employing our stronger attacks in adversarial training significantly improves the robustness of adversarially trained models.

The field development optimization (FDO) problem represents a challenging mixed-integer nonlinear programming (MINLP) problem in which we seek to obtain the number of wells, their type, location, and drilling sequence that maximizes an economic metric. Evolutionary optimization algorithms have been effectively applied to solve the FDO problem, however, these methods provide only a deterministic (single) solution which are generally not robust towards small changes in the problem setup. In this work, the goal is to apply convolutional neural network-based (CNN) deep reinforcement learning (DRL) algorithms to the field development optimization problem in order to obtain a policy that maps from different states or representation of the underlying geological model to optimal decisions. The proximal policy optimization (PPO) algorithm is considered with two CNN architectures of varying number of layers and composition. Both networks obtained policies that provide satisfactory results when compared to a hybrid particle swarm optimization - mesh adaptive direct search (PSO-MADS) algorithm that has been shown to be effective at solving the FDO problem.

Real-valued logics underlie an increasing number of neuro-symbolic approaches, though typically their logical inference capabilities are characterized only qualitatively. We provide foundations for establishing the correctness and power of such systems. For the first time, we give a sound and complete axiomatization for a broad class containing all the common real-valued logics. This axiomatization allows us to derive exactly what information can be inferred about the combinations of real values of a collection of formulas given information about the combinations of real values of several other collections of formulas. We then extend the axiomatization to deal with weighted subformulas. Finally, we give a decision procedure based on linear programming for deciding, under certain natural assumptions, whether a set of our sentences logically implies another of our sentences.

We present two classes of differentially private optimization algorithms derived from the well-known accelerated first-order methods. The first algorithm is inspired by Polyak's heavy ball method and employs a smoothing approach to decrease the accumulated noise on the gradient steps required for differential privacy. The second class of algorithms are based on Nesterov's accelerated gradient method and its recent multi-stage variant. We propose a noise dividing mechanism for the iterations of Nesterov's method in order to improve the error behavior of the algorithm. The convergence rate analyses are provided for both the heavy ball and the Nesterov's accelerated gradient method with the help of the dynamical system analysis techniques. Finally, we conclude with our numerical experiments showing that the presented algorithms have advantages over the well-known differentially private algorithms.

The proposed article aims at offering a comprehensive tutorial for the computational aspects of structured matrix and tensor factorization. Unlike existing tutorials that mainly focus on {\it algorithmic procedures} for a small set of problems, e.g., nonnegativity or sparsity-constrained factorization, we take a {\it top-down} approach: we start with general optimization theory (e.g., inexact and accelerated block coordinate descent, stochastic optimization, and Gauss-Newton methods) that covers a wide range of factorization problems with diverse constraints and regularization terms of engineering interest. Then, we go `under the hood' to showcase specific algorithm design under these introduced principles. We pay a particular attention to recent algorithmic developments in structured tensor and matrix factorization (e.g., random sketching and adaptive step size based stochastic optimization and structure-exploiting second-order algorithms), which are the state of the art---yet much less touched upon in the literature compared to {\it block coordinate descent} (BCD)-based methods. We expect that the article to have an educational values in the field of structured factorization and hope to stimulate more research in this important and exciting direction.

We study Frank-Wolfe algorithms -- standard, pairwise, and away-steps -- for efficient optimization of Dominant Set Clustering. We present a unified and computationally efficient framework to employ the different variants of Frank-Wolfe methods, and we investigate its effectiveness via several experimental studies. In addition, we provide explicit convergence rates for the algorithms in terms of the so-called Frank-Wolfe gap. The theoretical analysis has been specialized to the problem of Dominant Set Clustering and is thus more easily accessible compared to prior work.

Social choice is the theory about collective decision towards social welfare starting from individual opinions, preferences, interests or welfare. The field of Computational Social Welfare is somewhat recent and it is gaining impact in the Artificial Intelligence Community. Classical literature makes the assumption of single-peaked preferences, i.e. there exist a order in the preferences and there is a global maximum in this order. This year some theoretical results were published about Two-stage Approval Voting Systems (TAVs), Multi-winner Selection Rules (MWSR) and Incomplete (IPs) and Circular Preferences (CPs). The purpose of this paper is three-fold: Firstly, I want to introduced Social Choice Optimisation as a generalisation of TAVs where there is a max stage and a min stage implementing thus a Minimax, well-known Artificial Intelligence decision-making rule to minimize hindering towards a (Social) Goal. Secondly, I want to introduce, following my Open Standardization and Open Integration Theory (in refinement process) put in practice in my dissertation, the Open Standardization of Social Inclusion, as a global social goal of Social Choice Optimization.

In the application of machine learning to real-life decision-making systems, e.g., credit scoring and criminal justice, the prediction outcomes might discriminate against people with sensitive attributes, leading to unfairness. The commonly used strategy in fair machine learning is to include fairness as a constraint or a penalization term in the minimization of the prediction loss, which ultimately limits the information given to decision-makers. In this paper, we introduce a new approach to handle fairness by formulating a stochastic multi-objective optimization problem for which the corresponding Pareto fronts uniquely and comprehensively define the accuracy-fairness trade-offs. We have then applied a stochastic approximation-type method to efficiently obtain well-spread and accurate Pareto fronts, and by doing so we can handle training data arriving in a streaming way.

For supervised classification problems involving design, control, other practical purposes, users are not only interested in finding a highly accurate classifier, but they also demand that the obtained classifier be easily interpretable. While the definition of interpretability of a classifier can vary from case to case, here, by a humanly interpretable classifier we restrict it to be expressed in simplistic mathematical terms. As a novel approach, we represent a classifier as an assembly of simple mathematical rules using a non-linear decision tree (NLDT). Each conditional (non-terminal) node of the tree represents a non-linear mathematical rule (split-rule) involving features in order to partition the dataset in the given conditional node into two non-overlapping subsets. This partitioning is intended to minimize the impurity of the resulting child nodes. By restricting the structure of split-rule at each conditional node and depth of the decision tree, the interpretability of the classifier is assured. The non-linear split-rule at a given conditional node is obtained using an evolutionary bilevel optimization algorithm, in which while the upper-level focuses on arriving at an interpretable structure of the split-rule, the lower-level achieves the most appropriate weights (coefficients) of individual constituents of the rule to minimize the net impurity of two resulting child nodes. The performance of the proposed algorithm is demonstrated on a number of controlled test problems, existing benchmark problems, and industrial problems. Results on two to 500-feature problems are encouraging and open up further scopes of applying the proposed approach to more challenging and complex classification tasks.