Decades of research on the 0-1 knapsack problem led to very efficient algorithms that are able to quickly solve large problem instances to optimality. This prompted researchers to also investigate whether relatively small problem instances exist that are hard for existing solvers and investigate which features characterize their hardness. Previously the authors proposed a new class of hard 0-1 knapsack problem instances and demonstrated that the properties of so-called inclusionwise maximal solutions (IMSs) can be important hardness indicators for this class. In the current paper, we formulate several new computationally challenging problems related to the IMSs of arbitrary 0-1 knapsack problem instances. Based on generalizations of previous work and new structural results about IMSs, we formulate polynomial and pseudopolynomial time algorithms for solving these problems. From this we derive a set of 14 computationally expensive features, which we calculate for two large datasets on a supercomputer in approximately 540 CPU-hours. We show that the proposed features contain important information related to the empirical hardness of a problem instance that was missing in earlier features from the literature by training machine learning models that can accurately predict the empirical hardness of a wide variety of 0-1 knapsack problem instances. Using the instance space analysis methodology, we also show that hard 0-1 knapsack problem instances are clustered together around a relatively dense region of the instance space and several features behave differently in the easy and hard parts of the instance space.

Optimization problems on the generalized Stiefel manifold (and products of it) are prevalent across science and engineering. For example, in computational science they arise in symmetric (generalized) eigenvalue problems, in nonlinear eigenvalue problems, and in electronic structures computations, to name a few problems. In statistics and machine learning, they arise, for example, in various dimensionality reduction techniques such as canonical correlation analysis. In deep learning, regularization and improved stability can be obtained by constraining some layers to have parameter matrices that belong to the Stiefel manifold. Solving problems on the generalized Stiefel manifold can be approached via the tools of Riemannian optimization. However, using the standard geometric components for the generalized Stiefel manifold has two possible shortcomings: computing some of the geometric components can be too expensive and convergence can be rather slow in certain cases. Both shortcomings can be addressed using a technique called Riemannian preconditioning, which amounts to using geometric components derived by a precoditioner that defines a Riemannian metric on the constraint manifold. In this paper we develop the geometric components required to perform Riemannian optimization on the generalized Stiefel manifold equipped with a non-standard metric, and illustrate theoretically and numerically the use of those components and the effect of Riemannian preconditioning for solving optimization problems on the generalized Stiefel manifold.

We derive optimal control policies for a Connected Automated Vehicle (CAV) and cooperating neighboring CAVs to carry out a lane change maneuver consisting of a longitudinal phase where the CAV properly positions itself relative to the cooperating neighbors and a lateral phase where it safely changes lanes. In contrast to prior work on this problem, where the CAV "selfishly" only seeks to minimize its maneuver time, we seek to ensure that the fast-lane traffic flow is minimally disrupted (through a properly defined metric). Additionally, when performing lane-changing maneuvers, we optimally select the cooperating vehicles from a set of feasible neighboring vehicles and experimentally show that the highway throughput is improved compared to the baseline case of human-driven vehicles changing lanes with no cooperation. When feasible solutions do not exist for a given maximal allowable disruption, we include a time relaxation method trading off a longer maneuver time with reduced disruption. Our analysis is also extended to multiple sequential maneuvers. Simulation results show the effectiveness of our controllers in terms of safety guarantees and up to 16% and 90% average throughput and maneuver time improvement respectively when compared to maneuvers with no cooperation.

We study the problem of allocating limited supply of medical resources in developing countries, in particular, Sierra Leone. We address this problem by combining machine learning (to predict demand) with optimization (to optimize allocations). A key challenge is the need to align the loss function used to train the machine learning model with the decision loss associated with the downstream optimization problem. Traditional solutions have limited flexibility in the model architecture and scale poorly to large datasets. We propose a decision-aware learning algorithm that uses a novel Taylor expansion of the optimal decision loss to derive the machine learning loss. Importantly, our approach only requires a simple re-weighting of the training data, ensuring it is both flexible and scalable, e.g., we incorporate it into a random forest trained using a multitask learning framework. We apply our framework to optimize the distribution of essential medicines in collaboration with policymakers in Sierra Leone; highly uncertain demand and limited budgets currently result in excessive unmet demand. Out-of-sample results demonstrate that our end-to-end approach can significantly reduce unmet demand across 1040 health facilities throughout Sierra Leone.

We are at the cusp of a transition from "learning from data" to "learning what data to learn from" as a central focus of artificial intelligence (AI) research. While the first-order learning problem is not completely solved, large models under unified architectures, such as transformers, have shifted the learning bottleneck from how to effectively train our models to how to effectively acquire and use task-relevant data. This problem, which we frame as exploration, is a universal aspect of learning in open-ended domains, such as the real world. Although the study of exploration in AI is largely limited to the field of reinforcement learning, we argue that exploration is essential to all learning systems, including supervised learning. We propose the problem of generalized exploration to conceptually unify exploration-driven learning between supervised learning and reinforcement learning, allowing us to highlight key similarities across learning settings and open research challenges. Importantly, generalized exploration serves as a necessary objective for maintaining open-ended learning processes, which in continually learning to discover and solve new problems, provides a promising path to more general intelligence.

The paper proposes a novel adaptive search space decomposition method and a novel gradient-free optimization-based formulation for the pre- and post-buckling analyses of space truss structures. Space trusses are often employed in structural engineering to build large steel constructions, such as bridges and domes, whose structural response is characterized by large displacements. Therefore, these structures are vulnerable to progressive collapses due to local or global buckling effects, leading to sudden failures. The method proposed in this paper allows the analysis of the load-equilibrium path of truss structures to permanent and variable loading, including stable and unstable equilibrium stages and explicitly considering geometric nonlinearities. The goal of this work is to determine these equilibrium stages via optimization of the Lagrangian kinematic parameters of the system, determining the global equilibrium. However, this optimization problem is non-trivial due to the undefined parameter domain and the sensitivity and interaction among the Lagrangian parameters. Therefore, we propose formulating this problem as a nonlinear, multimodal, unconstrained, continuous optimization problem and develop a novel adaptive search space decomposition method, which progressively and adaptively re-defines the search domain (hypersphere) to evaluate the equilibrium of the system using a gradient-free optimization algorithm. We tackle three benchmark problems and evaluate a medium-sized test representing a real structural problem in this paper. The results are compared to those available in the literature regarding displacement-load curves and deformed configurations. The accuracy and robustness of the adopted methodology show a high potential of gradient-free algorithms in analyzing space truss structures.

With the rise of edge computing, various AI services are expected to be available at a mobile side through the inference based on deep neural network (DNN) operated at the network edge, called edge inference (EI). On the other hand, the resulting AI quality (e.g., mean average precision in objective detection) has been regarded as a given factor, and AI quality control has yet to be explored despite its importance in addressing the diverse demands of different users. This work aims at tackling the issue by proposing a feature hierarchical EI (FHEI), comprising feature network and inference network deployed at an edge server and corresponding mobile, respectively. Specifically, feature network is designed based on feature hierarchy, a one-directional feature dependency with a different scale. A higher scale feature requires more computation and communication loads while it provides a better AI quality. The tradeoff enables FHEI to control AI quality gradually w.r.t. communication and computation loads, leading to deriving a near-to-optimal solution to maximize multi-user AI quality under the constraints of uplink \& downlink transmissions and edge server and mobile computation capabilities. It is verified by extensive simulations that the proposed joint communication-and-computation control on FHEI architecture always outperforms several benchmarks by differentiating each user's AI quality depending on the communication and computation conditions.

Quantum computing has gained a lot of attention recently, and scientists have seen potential applications in this field using quantum computing for Cryptography and Communication to Machine Learning and Healthcare. Protein folding has been one of the most interesting areas to study, and it is also one of the biggest problems of biochemistry. Each protein folds distinctively, and the difficulty of finding its stable shape rapidly increases with an increase in the number of amino acids in the chain. A moderate protein has about 100 amino acids, and the number of combinations one needs to verify to find the stable structure is enormous. At some point, the number of these combinations will be so vast that classical computers cannot even attempt to solve them. In this paper, we examine how this problem can be solved with the help of quantum computing using two different algorithms, Variational Quantum Eigensolver (VQE) and Quantum Approximate Optimization Algorithm (QAOA), using Qiskit Nature. We compare the results of different quantum hardware and simulators and check how error mitigation affects the performance. Further, we make comparisons with SoTA algorithms and evaluate the reliability of the method.

Robots with multi-fingered grippers could perform advanced manipulation tasks for us if we were able to properly specify to them what to do. In this study, we take a step in that direction by making a robot grasp an object like a grasping demonstration performed by a human. We propose a novel optimization-based approach for transferring human grasp demonstrations to any multi-fingered grippers, which produces robotic grasps that mimic the human hand orientation and the contact area with the object, while alleviating interpenetration. Extensive experiments with the Allegro and BarrettHand grippers show that our method leads to grasps more similar to the human demonstration than existing approaches, without requiring any gripper-specific tuning. We confirm these findings through a user study and validate the applicability of our approach on a real robot.

We consider control of dynamical systems through the lens of competitive analysis. Most prior work in this area focuses on minimizing regret, that is, the loss relative to an ideal clairvoyant policy that has noncausal access to past, present, and future disturbances. Motivated by the observation that the optimal cost only provides coarse information about the ideal closed-loop behavior, we instead propose directly minimizing the tracking error relative to the optimal trajectories in hindsight, i.e., imitating the clairvoyant policy. By embracing a system level perspective, we present an efficient optimization-based approach for computing follow-the-clairvoyant (FTC) safe controllers. We prove that these attain minimal regret if no constraints are imposed on the noncausal benchmark. In addition, we present numerical experiments to show that our policy retains the hallmark of competitive algorithms of interpolating between classical $\mathcal{H}_2$ and $\mathcal{H}_\infty$ control laws - while consistently outperforming regret minimization methods in constrained scenarios thanks to the superior ability to chase the clairvoyant.