As modern software systems expand in scale and complexity, the challenges associated with their modeling and formulation grow increasingly intricate. Traditional approaches often fall short in effectively addressing these complexities, particularly in tasks such as design pattern detection for maintenance and assessment, as well as code refactoring for optimization and long-term sustainability. This growing inadequacy underscores the need for a paradigm shift in how such challenges are approached and resolved. This paper presents Analytical Software Engineering (ASE), a novel design paradigm aimed at balancing abstraction, tool accessibility, compatibility, and scalability. ASE enables effective modeling and resolution of complex software engineering problems. The paradigm is evaluated through two frameworks Behavioral-Structural Sequences (BSS) and Optimized Design Refactoring (ODR), both developed in accordance with ASE principles. BSS offers a compact, language-agnostic representation of codebases to facilitate precise design pattern detection. ODR unifies artifact and solution representations to optimize code refactoring via heuristic algorithms while eliminating iterative computational overhead. By providing a structured approach to software design challenges, ASE lays the groundwork for future research in encoding and analyzing complex software metrics.

In embedded systems, robots must perceive and interpret their environment efficiently to operate reliably in real-world conditions. Visual Semantic SLAM (Simultaneous Localization and Mapping) enhances standard SLAM by incorporating semantic information into the map, enabling more informed decision-making. However, implementing such systems on resource-limited hardware involves trade-offs between accuracy, computing efficiency, and power usage. This paper provides a comparative review of recent Semantic Visual SLAM methods with a focus on their applicability to embedded platforms. We analyze three main types of architectures - Geometric SLAM, Neural Radiance Fields (NeRF), and 3D Gaussian Splatting - and evaluate their performance on constrained hardware, specifically the NVIDIA Jetson AGX Orin. We compare their accuracy, segmentation quality, memory usage, and energy consumption. Our results show that methods based on NeRF and Gaussian Splatting achieve high semantic detail but demand substantial computing resources, limiting their use on embedded devices. In contrast, Semantic Geometric SLAM offers a more practical balance between computational cost and accuracy. The review highlights a need for SLAM algorithms that are better adapted to embedded environments, and it discusses key directions for improving their efficiency through algorithm-hardware co-design.

Parameter-efficient fine-tuning (PEFT) is a highly effective approach for adapting large pre-trained models to downstream tasks with minimal computational overhead. At the core, PEFT methods freeze most parameters and only trains a small subset (say $<0.1\%$ of total parameters). Notably, different PEFT methods select different subsets, resulting in varying levels of performance. This variation prompts a key question: how to effectively select the most influential subset to train? We formulate the subset selection as a multi-task problem: maximizing the performance and minimizing the number of trainable parameters. We leverage a series of transformations -- including $ε$-constraint method and second-order Taylor approximation -- to arrive at the classical 0-1 knapsack problem, which we solve through the lens of Pareto optimality. Consequently, we propose AdaPEFT, a Hessian-informed PEFT that adapts to various tasks and models, in which the selected subset empirically transfers across training horizons and model sizes.

Physics-informed machine learning (PIML) is crucial in modern traffic flow modeling because it combines the benefits of both physics-based and data-driven approaches. In conventional PIML, physical information is typically incorporated by constructing a hybrid loss function that combines data-driven loss and physics loss through linear scalarization. The goal is to find a trade-off between these two objectives to improve the accuracy of model predictions. However, from a mathematical perspective, linear scalarization is limited to identifying only the convex region of the Pareto front, as it treats data-driven and physics losses as separate objectives. Given that most PIML loss functions are non-convex, linear scalarization restricts the achievable trade-off solutions. Moreover, tuning the weighting coefficients for the two loss components can be both time-consuming and computationally challenging. To address these limitations, this paper introduces a paradigm shift in PIML by reformulating the training process as a multi-objective optimization problem, treating data-driven loss and physics loss independently. We apply several multi-gradient descent algorithms (MGDAs), including traditional multi-gradient descent (TMGD) and dual cone gradient descent (DCGD), to explore the Pareto front in this multi-objective setting. These methods are evaluated on both macroscopic and microscopic traffic flow models. In the macroscopic case, MGDAs achieved comparable performance to traditional linear scalarization methods. Notably, in the microscopic case, MGDAs significantly outperformed their scalarization-based counterparts, demonstrating the advantages of a multi-objective optimization approach in complex PIML scenarios.

Optimization with orthogonality constraints frequently arises in various fields such as machine learning. Riemannian optimization offers a powerful framework for solving these problems by equipping the constraint set with a Riemannian manifold structure and performing optimization intrinsically on the manifold. This approach typically involves computing a search direction in the tangent space and updating variables via a retraction operation. However, as the size of the variables increases, the computational cost of the retraction can become prohibitively high, limiting the applicability of Riemannian optimization to large-scale problems. To address this challenge and enhance scalability, we propose a novel approach that restricts each update on a random submanifold, thereby significantly reducing the per-iteration complexity. We introduce two sampling strategies for selecting the random submanifolds and theoretically analyze the convergence of the proposed methods. We provide convergence results for general nonconvex functions and functions that satisfy Riemannian Polyak-Lojasiewicz condition as well as for stochastic optimization settings. Additionally, we demonstrate how our approach can be generalized to quotient manifolds derived from the orthogonal manifold. Extensive experiments verify the benefits of the proposed method, across a wide variety of problems.

Fairness in machine learning has become a critical concern, particularly in high-stakes applications. Existing approaches often focus on achieving full fairness across all score ranges generated by predictive models, ensuring fairness in both high and low-scoring populations. However, this stringent requirement can compromise predictive performance and may not align with the practical fairness concerns of stakeholders. In this work, we propose a novel framework for building partially fair machine learning models, which enforce fairness within a specific score range of interest, such as the middle range where decisions are most contested, while maintaining flexibility in other regions. We introduce two statistical metrics to rigorously evaluate partial fairness within a given score range, such as the top 20%-40% of scores. To achieve partial fairness, we propose an in-processing method by formulating the model training problem as constrained optimization with difference-of-convex constraints, which can be solved by an inexact difference-of-convex algorithm (IDCA). We provide the complexity analysis of IDCA for finding a nearly KKT point. Through numerical experiments on real-world datasets, we demonstrate that our framework achieves high predictive performance while enforcing partial fairness where it matters most.

High-stakes decisions in domains such as healthcare, energy, and public policy are often made by human experts using domain knowledge and heuristics, yet are increasingly supported by predictive and optimization-based tools. A dominant approach in operations research is the predict-then-optimize paradigm, where a predictive model estimates uncertain inputs, and an optimization model recommends a decision. However, this approach often lacks interpretability and can fail under distributional uncertainty -- particularly when the outcome distribution is multi-modal or complex -- leading to brittle or misleading decisions. In this paper, we introduce CREDO, a novel framework that quantifies, for any candidate decision, a distribution-free upper bound on the probability that the decision is suboptimal. By combining inverse optimization geometry with conformal prediction and generative modeling, CREDO produces risk certificates that are both statistically rigorous and practically interpretable. This framework enables human decision-makers to audit and validate their own decisions under uncertainty, bridging the gap between algorithmic tools and real-world judgment.

Accurately modeling the friction torque in robotic joints has long been challenging due to the request for a robust mathematical description. Traditional model-based approaches are often labor-intensive, requiring extensive experiments and expert knowledge, and they are difficult to adapt to new scenarios and dependencies. On the other hand, data-driven methods based on neural networks are easier to implement but often lack robustness, interpretability, and trustworthiness--key considerations for robotic hardware and safety-critical applications such as human-robot interaction. To address the limitations of both approaches, we propose the use of symbolic regression (SR) to estimate the friction torque. SR generates interpretable symbolic formulas similar to those produced by model-based methods while being flexible to accommodate various dynamic effects and dependencies. In this work, we apply SR algorithms to approximate the friction torque using collected data from a KUKA LWR-IV+ robot. Our results show that SR not only yields formulas with comparable complexity to model-based approaches but also achieves higher accuracy. Moreover, SR-derived formulas can be seamlessly extended to include load dependencies and other dynamic factors.

Meta-Black-Box Optimization (MetaBBO) garners attention due to its success in automating the configuration and generation of black-box optimizers, significantly reducing the human effort required for optimizer design and discovering optimizers with higher performance than classic human-designed optimizers. However, existing MetaBBO methods conduct one-off training under the assumption that a stationary problem distribution with extensive and representative training problem samples is pre-available. This assumption is often impractical in real-world scenarios, where diverse problems following shifting distribution continually arise. Consequently, there is a pressing need for methods that can continuously learn from new problems encountered on-the-fly and progressively enhance their capabilities. In this work, we explore a novel paradigm of lifelong learning in MetaBBO and introduce LiBOG, a novel approach designed to learn from sequentially encountered problems and generate high-performance optimizers for Black-Box Optimization (BBO). LiBOG consolidates knowledge both across tasks and within tasks to mitigate catastrophic forgetting. Extensive experiments demonstrate LiBOG's effectiveness in learning to generate high-performance optimizers in a lifelong learning manner, addressing catastrophic forgetting while maintaining plasticity to learn new tasks.

This thesis delves into the forefront of wireless communication by exploring the synergistic integration of three transformative technologies: STAR-RIS, CoMP, and NOMA. Driven by the ever-increasing demand for higher data rates, improved spectral efficiency, and expanded coverage in the evolving landscape of 6G development, this research investigates the potential of these technologies to revolutionize future wireless networks. The thesis analyzes the performance gains achievable through strategic deployment of STAR-RIS, focusing on mitigating inter-cell interference, enhancing signal strength, and extending coverage to cell-edge users. Resource sharing strategies for STAR-RIS elements are explored, optimizing both transmission and reflection functionalities. Analytical frameworks are developed to quantify the benefits of STAR-RIS assisted CoMP-NOMA networks under realistic channel conditions, deriving key performance metrics such as ergodic rates and outage probabilities. Additionally, the research delves into energy-efficient design approaches for CoMP-NOMA networks incorporating RIS, proposing novel RIS configurations and optimization algorithms to achieve a balance between performance and energy consumption. Furthermore, the application of Deep Reinforcement Learning (DRL) techniques for intelligent and adaptive optimization in aerial RIS-assisted CoMP-NOMA networks is explored, aiming to maximize network sum rate while meeting user quality of service requirements. Through a comprehensive investigation of these technologies and their synergistic potential, this thesis contributes valuable insights into the future of wireless communication, paving the way for the development of more efficient, reliable, and sustainable networks capable of meeting the demands of our increasingly connected world.