The quantum approximate optimization algorithm (QAOA) is a general-purpose algorithm for combinatorial optimization. In this paper, we analyze the performance of the QAOA on a statistical estimation problem, namely, the spiked tensor model, which exhibits a statistical-computational gap classically. We prove that the weak recovery threshold of $1$-step QAOA matches that of $1$-step tensor power iteration. Additional heuristic calculations suggest that the weak recovery threshold of $p$-step QAOA matches that of $p$-step tensor power iteration when $p$ is a fixed constant. This further implies that multi-step QAOA with tensor unfolding could achieve, but not surpass, the classical computation threshold $\Theta(n^{(q-2)/4})$ for spiked $q$-tensors. Meanwhile, we characterize the asymptotic overlap distribution for $p$-step QAOA, finding an intriguing sine-Gaussian law verified through simulations. For some $p$ and $q$, the QAOA attains an overlap that is larger by a constant factor than the tensor power iteration overlap. Of independent interest, our proof techniques employ the Fourier transform to handle difficult combinatorial sums, a novel approach differing from prior QAOA analyses on spin-glass models without planted structure.

Recent findings reveal that over-parameterized deep neural networks, trained beyond zero training-error, exhibit a distinctive structural pattern at the final layer, termed as Neural-collapse (NC). These results indicate that the final hidden-layer outputs in such networks display minimal within-class variations over the training set. While existing research extensively investigates this phenomenon under cross-entropy loss, there are fewer studies focusing on its contrastive counterpart, supervised contrastive (SC) loss. Through the lens of NC, this paper employs an analytical approach to study the solutions derived from optimizing the SC loss. We adopt the unconstrained features model (UFM) as a representative proxy for unveiling NC-related phenomena in sufficiently over-parameterized deep networks. We show that, despite the non-convexity of SC loss minimization, all local minima are global minima. Furthermore, the minimizer is unique (up to a rotation). We prove our results by formalizing a tight convex relaxation of the UFM. Finally, through this convex formulation, we delve deeper into characterizing the properties of global solutions under label-imbalanced training data.

Placement is crucial in the physical design, as it greatly affects power, performance, and area metrics. Recent advancements in analytical methods, such as DREAMPlace, have demonstrated impressive performance in global placement. However, DREAMPlace has some limitations, e.g., may not guarantee legalizable placements under the same settings, leading to fragile and unpredictable results. This paper highlights the main issue as being stuck in local optima, and proposes a hybrid optimization framework to efficiently escape the local optima, by perturbing the placement result iteratively. The proposed framework achieves significant improvements compared to state-of-the-art methods on two popular benchmarks.

Over the last decade, Unmanned Aerial Vehicles (UAVs) have been extensively used in many commercial applications due to their manageability and risk avoidance. One of the main problems considered is the Mission Planning for multiple UAVs, where a solution plan must be found satisfying the different constraints of the problem. This problem has multiple variables that must be optimized simultaneously, such as the makespan, the cost of the mission or the risk. Therefore, the problem has a lot of possible optimal solutions, and the operator must select the final solution to be executed among them. In order to reduce the workload of the operator in this decision process, a Decision Support System (DSS) becomes necessary. In this work, a DSS consisting of ranking and filtering systems, which order and reduce the optimal solutions, has been designed. With regard to the ranking system, a wide range of Multi-Criteria Decision Making (MCDM) methods, including some fuzzy MCDM, are compared on a multi-UAV mission planning scenario, in order to study which method could fit better in a multi-UAV decision support system. Expert operators have evaluated the solutions returned, and the results show, on the one hand, that fuzzy methods generally achieve better average scores, and on the other, that all of the tested methods perform better when the preferences of the operators are biased towards a specific variable, and worse when their preferences are balanced. For the filtering system, a similarity function based on the proximity of the solutions has been designed, and on top of that, a threshold is tuned empirically to decide how to filter solutions without losing much of the hypervolume of the space of solutions.

Automated machine learning (AutoML) aims to select and configure machine learning algorithms and combine them into machine learning pipelines tailored to a dataset at hand. For supervised learning tasks, most notably binary and multinomial classification, aka single-label classification (SLC), such AutoML approaches have shown promising results. However, the task of multi-label classification (MLC), where data points are associated with a set of class labels instead of a single class label, has received much less attention so far. In the context of multi-label classification, the data-specific selection and configuration of multi-label classifiers are challenging even for experts in the field, as it is a high-dimensional optimization problem with multi-level hierarchical dependencies. While for SLC, the space of machine learning pipelines is already huge, the size of the MLC search space outnumbers the one of SLC by several orders. In the first part of this thesis, we devise a novel AutoML approach for single-label classification tasks optimizing pipelines of machine learning algorithms, consisting of two algorithms at most. This approach is then extended first to optimize pipelines of unlimited length and eventually configure the complex hierarchical structures of multi-label classification methods. Furthermore, we investigate how well AutoML approaches that form the state of the art for single-label classification tasks scale with the increased problem complexity of AutoML for multi-label classification. In the second part, we explore how methods for SLC and MLC could be configured more flexibly to achieve better generalization performance and how to increase the efficiency of execution-based AutoML systems.

Hence, the use of efficient search methods has experienced a significant growth in the last years, specially for those engineering problems where there are multiple objectives that require to be simultaneously optimized (Marler and Arora, 2004). A recurrent situation in engineering is the need of jointly optimizing energy consumption, cost or time, among others. All these factors constitute a paramount concern to the expert, and represent conflicting objectives, each one having a deep impact on the final solution (Marler and Arora, 2004). Initially applied to single-objective problems, metaheuristics like evolutionary algorithms (EAs) have been successfully applied to the resolution of multi-objective problems (MOPs) in engineering, such as the design of efficient transport systems (Domínguez et al., 2014) or safe civil structures (Zavala et al., 2014). The presence of a large number of objectives has been recently pointed out as an intrinsic characteristic of engineering problems (Singh, 2016), for which the currently applied techniques might not be efficient enough. It is noteworthy that other communities are also demanding novel techniques to face increasingly complex problems, what has led to the appearance of the many-objective optimization approach(von Lücken et al., 2014; Li et al., 2015). This variant of the more general multi-objective optimization (MOO) is specifically devoted to overcome the limits of existing algorithms when problems having 4 or more objectives, known as many-objective problems (MaOPs), have to be faced. Even though each metaheuristic follows different principles to conduct the search, their adaptation to deal with either MOPs or MaOPs share some similarities, such as the presence of new diversity preservation mechanisms or the use of indicators (Li et al., 2015; Mishra et al., 2015). The resulting many-objective algorithms have proven successful in the engineering field too (Li and Hu, 2014; López-Jaimes and Coello Coello, 2014; Cheng et al., 2017), where specialized software tools have begun to appear (Hadka et al., 2015).

Point cloud maps generated via LiDAR sensors using extensive remotely sensed data are commonly used by autonomous vehicles and robots for localization and navigation. However, dynamic objects contained in point cloud maps not only downgrade localization accuracy and navigation performance but also jeopardize the map quality. In response to this challenge, we propose in this paper a novel semantic SLAM approach for dynamic scenes based on LiDAR point clouds, referred to as SD-SLAM hereafter. The main contributions of this work are in three aspects: 1) introducing a semantic SLAM framework dedicatedly for dynamic scenes based on LiDAR point clouds, 2) Employing semantics and Kalman filtering to effectively differentiate between dynamic and semi-static landmarks, and 3) Making full use of semi-static and pure static landmarks with semantic information in the SD-SLAM process to improve localization and mapping performance. To evaluate the proposed SD-SLAM, tests were conducted using the widely adopted KITTI odometry dataset. Results demonstrate that the proposed SD-SLAM effectively mitigates the adverse effects of dynamic objects on SLAM, improving vehicle localization and mapping performance in dynamic scenes, and simultaneously constructing a static semantic map with multiple semantic classes for enhanced environment understanding.

Pareto front profiling in multi-objective optimization (MOO), i.e. finding a diverse set of Pareto optimal solutions, is challenging, especially with expensive objectives like neural network training. Typically, in MOO neural architecture search (NAS), we aim to balance performance and hardware metrics across devices. Prior NAS approaches simplify this task by incorporating hardware constraints into the objective function, but profiling the Pareto front necessitates a search for each constraint. In this work, we propose a novel NAS algorithm that encodes user preferences for the trade-off between performance and hardware metrics, and yields representative and diverse architectures across multiple devices in just one search run. To this end, we parameterize the joint architectural distribution across devices and multiple objectives via a hypernetwork that can be conditioned on hardware features and preference vectors, enabling zero-shot transferability to new devices. Extensive experiments with up to 19 hardware devices and 3 objectives showcase the effectiveness and scalability of our method. Finally, we show that, without additional costs, our method outperforms existing MOO NAS methods across qualitatively different search spaces and datasets, including MobileNetV3 on ImageNet-1k and a Transformer space on machine translation.

Energy Internet (EI) is emerging as new share economy platform for flexible local energy supplies in smart cities. Empowered by the Internet-of-Things (IoT) and Artificial Intelligence (AI), EI aims to unlock peer-to-peer energy trading and sharing among prosumers, who can adeptly switch roles between providers and consumers in localized energy markets with rooftop photovoltaic panels, vehicle-to-everything technologies, packetized energy management, etc. The integration of prosumers in EI, however, will encounter many challenges in modelling, analyzing, and designing an efficient, economic, and social-optimal platform for energy sharing, calling for advanced AI/IoT-based solutions to resource optimization, information exchange, and interaction protocols in the context of the share economy. In this study, we aim to introduce a recently emerged paradigm, Machina Economicus, to investigate the economic rationality in modelling, analysis, and optimization of AI/IoT-based EI prosumer behaviors. The new paradigm, built upon the theory of machine learning and mechanism design, will offer new angles to investigate the selfishness of AI through a game-theoretic perspective, revealing potential competition and collaborations resulting from the self-adaptive learning and decision-making capacity. This study will focus on how the introduction of AI will reshape prosumer behaviors on the EI, and how this paradigm will reveal new research questions and directions when AI meets the share economy. With an extensive case analysis in the literature, we will also shed light on potential solutions for advancements of AI in future smart cities.

Network systems form the foundation of modern society, playing a critical role in various applications. However, these systems are at significant risk of being adversely affected by unforeseen circumstances, such as disasters. Considering this, there is a pressing need for research to enhance the robustness of network systems. Recently, in reinforcement learning, the relationship between acquiring robustness and regularizing entropy has been identified. Additionally, imitation learning is used within this framework to reflect experts' behavior. However, there are no comprehensive studies on the use of a similar imitation framework for optimal transport on networks. Therefore, in this study, imitation-regularized optimal transport (I-OT) on networks was investigated. It encodes prior knowledge on the network by imitating a given prior distribution. The I-OT solution demonstrated robustness in terms of the cost defined on the network. Moreover, we applied the I-OT to a logistics planning problem using real data. We also examined the imitation and apriori risk information scenarios to demonstrate the usefulness and implications of the proposed method.