Sparse Principal Component Analysis (sPCA) is a cardinal technique for obtaining combinations of features, or principal components (PCs), that explain the variance of high-dimensional datasets in an interpretable manner. This involves solving a sparsity and orthogonality constrained convex maximization problem, which is extremely computationally challenging. Most existing works address sparse PCA via methods-such as iteratively computing one sparse PC and deflating the covariance matrix-that do not guarantee the orthogonality, let alone the optimality, of the resulting solution when we seek multiple mutually orthogonal PCs. We challenge this status by reformulating the orthogonality conditions as rank constraints and optimizing over the sparsity and rank constraints simultaneously. We design tight semidefinite relaxations to supply high-quality upper bounds, which we strengthen via additional second-order cone inequalities when each PC's individual sparsity is specified. Further, we derive a combinatorial upper bound on the maximum amount of variance explained as a function of the support. We exploit these relaxations and bounds to propose exact methods and rounding mechanisms that, together, obtain solutions with a bound gap on the order of 0%-15% for real-world datasets with p = 100s or 1000s of features and r \in {2, 3} components. Numerically, our algorithms match (and sometimes surpass) the best performing methods in terms of fraction of variance explained and systematically return PCs that are sparse and orthogonal. In contrast, we find that existing methods like deflation return solutions that violate the orthogonality constraints, even when the data is generated according to sparse orthogonal PCs. Altogether, our approach solves sparse PCA problems with multiple components to certifiable (near) optimality in a practically tractable fashion.

Recently, spam on online social networks has attracted attention in the research and business world. Twitter has become the preferred medium to spread spam content. Many research efforts attempted to encounter social networks spam. Twitter brought extra challenges represented by the feature space size, and imbalanced data distributions. Usually, the related research works focus on part of these main challenges or produce black-box models. In this paper, we propose a modified genetic algorithm for simultaneous dimensionality reduction and hyper parameter optimization over imbalanced datasets. The algorithm initialized an eXtreme Gradient Boosting classifier and reduced the features space of tweets dataset; to generate a spam prediction model. The model is validated using a 50 times repeated 10-fold stratified cross-validation, and analyzed using nonparametric statistical tests. The resulted prediction model attains on average 82.32\% and 92.67\% in terms of geometric mean and accuracy respectively, utilizing less than 10\% of the total feature space. The empirical results show that the modified genetic algorithm outperforms $Chi^2$ and $PCA$ feature selection methods. In addition, eXtreme Gradient Boosting outperforms many machine learning algorithms, including BERT-based deep learning model, in spam prediction. Furthermore, the proposed approach is applied to SMS spam modeling and compared to related works.

Cut-generating linear programs (CGLPs) play a key role as a separation oracle to produce valid inequalities for the feasible region of mixed-integer programs. When incorporated inside branch-and-bound, the cutting planes obtained from CGLPs help to tighten relaxations and improve dual bounds. However, running the CGLPs at the nodes of the branch-and-bound tree is computationally cumbersome due to the large number of node candidates and the lack of a priori knowledge on which nodes admit useful cutting planes. As a result, CGLPs are often avoided at default settings of branch-and-cut algorithms despite their potential impact on improving dual bounds. In this paper, we propose a novel framework based on machine learning to approximate the optimal value of a CGLP class that determines whether a cutting plane can be generated at a node of the branch-and-bound tree. Translating the CGLP as an indicator function of the objective function vector, we show that it can be approximated through conventional data classification techniques. We provide a systematic procedure to efficiently generate training data sets for the corresponding classification problem based on the CGLP structure. We conduct computational experiments on benchmark instances using classification methods such as logistic regression. These results suggest that the approximate CGLP obtained from classification can improve the solution time compared to that of conventional cutting plane methods. Our proposed framework can be efficiently applied to a large number of nodes in the branch-and-bound tree to identify the best candidates for adding a cut.

This paper presents a distributed rule-based Lloyd algorithm (RBL) for multi-robot motion planning and control. The main limitations of the basic Loyd-based algorithm (LB) concern deadlock issues and the failure to address dynamic constraints effectively. Our contribution is twofold. First, we show how RBL is able to provide safety and convergence to the goal region without relying on communication between robots, nor neighbors control inputs, nor synchronization between the robots. We considered both case of holonomic and non-holonomic robots with control inputs saturation. Second, we show that the Lloyd-based algorithm (without rules) can be successfully used as a safety layer for learning-based approaches, leading to non-negligible benefits. We further prove the soundness, reliability, and scalability of RBL through extensive simulations, an updated comparison with the state of the art, and experimental validations on small-scale car-like robots.

Energy saving in wireless networks is growing in importance due to increasing demand for evolving new-gen cellular networks, environmental and regulatory concerns, and potential energy crises arising from geopolitical tensions. In this work, we propose an approximate dynamic programming (ADP)-based method coupled with online optimization to switch on/off the cells of base stations to reduce network power consumption while maintaining adequate Quality of Service (QoS) metrics. We use a multilayer perceptron (MLP) given each state-action pair to predict the power consumption to approximate the value function in ADP for selecting the action with optimal expected power saved. To save the largest possible power consumption without deteriorating QoS, we include another MLP to predict QoS and a long short-term memory (LSTM) for predicting handovers, incorporated into an online optimization algorithm producing an adaptive QoS threshold for filtering cell switching actions based on the overall QoS history. The performance of the method is evaluated using a practical network simulator with various real-world scenarios with dynamic traffic patterns.

Evolutionary Computation (EC) has emerged as a powerful field of Artificial Intelligence, inspired by nature's mechanisms of gradual development. However, EC approaches often face challenges such as stagnation, diversity loss, computational complexity, population initialization, and premature convergence. To overcome these limitations, researchers have integrated learning algorithms with evolutionary techniques. This integration harnesses the valuable data generated by EC algorithms during iterative searches, providing insights into the search space and population dynamics. Similarly, the relationship between evolutionary algorithms and Machine Learning (ML) is reciprocal, as EC methods offer exceptional opportunities for optimizing complex ML tasks characterized by noisy, inaccurate, and dynamic objective functions. These hybrid techniques, known as Evolutionary Machine Learning (EML), have been applied at various stages of the ML process. EC techniques play a vital role in tasks such as data balancing, feature selection, and model training optimization. Moreover, ML tasks often require dynamic optimization, for which Evolutionary Dynamic Optimization (EDO) is valuable. This paper presents the first comprehensive exploration of reciprocal integration between EDO and ML. The study aims to stimulate interest in the evolutionary learning community and inspire innovative contributions in this domain.

Optimization problems are pervasive across various sectors, from manufacturing and distribution to healthcare. However, most such problems are still solved heuristically by hand rather than optimally by state-of-the-art solvers, as the expertise required to formulate and solve these problems limits the widespread adoption of optimization tools and techniques. We introduce OptiMUS, a Large Language Model (LLM)-based agent designed to formulate and solve MILP problems from their natural language descriptions. OptiMUS is capable of developing mathematical models, writing and debugging solver code, developing tests, and checking the validity of generated solutions. To benchmark our agent, we present NLP4LP, a novel dataset of linear programming (LP) and mixed integer linear programming (MILP) problems. Our experiments demonstrate that OptiMUS solves nearly twice as many problems as a basic LLM prompting strategy. OptiMUS code and NLP4LP dataset are available at \href{https://github.com/teshnizi/OptiMUS}{https://github.com/teshnizi/OptiMUS}

Complex engineering design problems, such as those involved in aerospace, civil, or energy engineering, require the use of numerically costly simulation codes in order to predict the behavior and performance of the system to be designed. To perform the design of the systems, these codes are often embedded into an optimization process to provide the best design while satisfying the design constraints. Recently, new approaches, called Quality-Diversity, have been proposed in order to enhance the exploration of the design space and to provide a set of optimal diversified solutions with respect to some feature functions. These functions are interesting to assess trade-offs. Furthermore, complex engineering design problems often involve mixed continuous, discrete, and categorical design variables allowing to take into account technological choices in the optimization problem. In this paper, a new Quality-Diversity methodology based on mixed continuous, discrete and categorical Bayesian optimization strategy is proposed. This approach allows to reduce the computational cost with respect to classical Quality - Diversity approaches while dealing with discrete choices and constraints. The performance of the proposed method is assessed on a benchmark of analytical problems as well as on an industrial design optimization problem dealing with aerospace systems.

To that aim we introduce new g-convex optimization results, of independent interest: we show global linear convergence for metric-projected Riemannian gradient descent and improve existing accelerated methods by reducing geometric constants. Additionally, we complete the analysis of two previous works applying to the Riemannian min-max case by removing an assumption about iterates staying in a pre-specified compact set.

Actor-critic (AC) methods are widely used in reinforcement learning (RL) and benefit from the flexibility of using any policy gradient method as the actor and value-based method as the critic. The critic is usually trained by minimizing the TD error, an objective that is potentially decorrelated with the true goal of achieving a high reward with the actor. We address this mismatch by designing a joint objective for training the actor and critic in a decision-aware fashion. We use the proposed objective to design a generic, AC algorithm that can easily handle any function approximation. We explicitly characterize the conditions under which the resulting algorithm guarantees monotonic policy improvement, regardless of the choice of the policy and critic parameterization. Instantiating the generic algorithm results in an actor that involves maximizing a sequence of surrogate functions (similar to TRPO, PPO) and a critic that involves minimizing a closely connected objective. Using simple bandit examples, we provably establish the benefit of the proposed critic objective over the standard squared error. Finally, we empirically demonstrate the benefit of our decision-aware actor-critic framework on simple RL problems.