Air taxis are poised to be an additional mode of transportation in major cities suffering from ground transportation congestion. Among several potential applications of air taxis, we focus on their use within a city to transport passengers to nearby airports. Specifically, we consider the problem of determining optimal locations for skyports (enabling pick-up of passengers to airport) within a city. Our approach is inspired from hub location problems, and our proposed method optimizes for aggregate travel time to multiple airports while satisfying the demand (trips to airports) either via (i) ground transportation to skyport followed by an air taxi to the airport, or (ii) direct ground transportation to the airport. The number of skyports is a constraint, and the decision to go via the skyport versus direct ground transportation is a variable in the optimization problem. Extensive experiments on publicly available airport trips data from New York City (NYC) show the efficacy of our optimization method implemented using Gurobi. In addition, we share insightful results based on the NYC data set on how ground transportation congestion can impact the demand and service efficiency in such skyports; this emerges as yet another factor in deciding the optimal number of skyports and their locations for a given city.

Metaheuristics are general methods that guide application of concrete heuristic(s) to problems that are too hard to solve using exact algorithms. However, even though a growing body of literature has been devoted to their statistical evaluation, the approaches proposed so far are able to assess only coupled effects of metaheuristics and heuristics. They do not reveal us anything about how efficient the examined metaheuristic is at guiding its subordinate heuristic(s), nor do they provide us information about how much the heuristic component of the combined algorithm contributes to the overall performance. In this paper, we propose a simple yet effective methodology of doing so by deriving a naive, placebo metaheuristic from the one being studied and comparing the distributions of chosen performance metrics for the two methods. We propose three measures of difference between the two distributions. Those measures, which we call BER values (benefit, equivalence, risk) are based on a preselected threshold of practical significance which represents the minimal difference between two performance scores required for them to be considered practically different. We illustrate usefulness of our methodology on the example of Simulated Annealing, Boolean Satisfiability Problem, and the Flip heuristic.

For sampling from a log-concave density, we study implicit integrators resulting from $\theta$-method discretization of the overdamped Langevin diffusion stochastic differential equation. Theoretical and algorithmic properties of the resulting sampling methods for $ \theta \in [0,1] $ and a range of step sizes are established. Our results generalize and extend prior works in several directions. In particular, for $\theta\ge1/2$, we prove geometric ergodicity and stability of the resulting methods for all step sizes. We show that obtaining subsequent samples amounts to solving a strongly-convex optimization problem, which is readily achievable using one of numerous existing methods. Numerical examples supporting our theoretical analysis are also presented.

Optical scatterometry is a method to measure the size and shape of periodic micro- or nanostructures on surfaces. For this purpose the geometry parameters of the structures are obtained by reproducing experimental measurement results through numerical simulations. We compare the performance of Bayesian optimization to different local minimization algorithms for this numerical optimization problem. Bayesian optimization uses Gaussian-process regression to find promising parameter values. We examine how pre-computed simulation results can be used to train the Gaussian process and to accelerate the optimization.

The intelligent Processing technique is more and more attractive to researchers due to its ability to deal with key problems in Vehicular Ad hoc networks. However, several problems in applying intelligent processing technologies in VANETs remain open. The existing applications are comprehensively reviewed and discussed, and classified into different categories in this paper. Their strategies, advantages/disadvantages, and performances are elaborated. By generalizing different tactics in various applications related to different scenarios of VANETs and evaluating their performances, several promising directions for future research have been suggested.

We develop a novel data-driven robust model predictive control (DDRMPC) approach for automatic control of irrigation systems. The fundamental idea is to integrate both mechanistic models, which describe dynamics in soil moisture variations, and data-driven models, which characterize uncertainty in forecast errors of evapotranspiration and precipitation, into a holistic systems control framework. To better capture the support of uncertainty distribution, we take a new learning-based approach by constructing uncertainty sets from historical data. For evapotranspiration forecast error, the support vector clustering-based uncertainty set is adopted, which can be conveniently built from historical data. As for precipitation forecast errors, we analyze the dependence of their distribution on forecast values, and further design a tailored uncertainty set based on the properties of this type of uncertainty. In this way, the overall uncertainty distribution can be elaborately described, which finally contributes to rational and efficient control decisions. To assure the quality of data-driven uncertainty sets, a training-calibration scheme is used to provide theoretical performance guarantees. A generalized affine decision rule is adopted to obtain tractable approximations of optimal control problems, thereby ensuring the practicability of DDRMPC. Case studies using real data show that, DDRMPC can reliably maintain soil moisture above the safety level and avoid crop devastation. The proposed DDRMPC approach leads to a 40\% reduction of total water consumption compared to the fine-tuned open-loop control strategy. In comparison with the carefully tuned rule-based control and certainty equivalent model predictive control, the proposed DDRMPC approach can significantly reduce the total water consumption and improve the control performance.

Spatial perception is the backbone of many robotics applications, and spans a broad range of research problems, including localization and mapping, point cloud alignment, and relative pose estimation from camera images. Robust spatial perception is jeopardized by the presence of incorrect data association, and in general, outliers. Although techniques to handle outliers do exist, they can fail in unpredictable manners (e.g., RANSAC, robust estimators), or can have exponential runtime (e.g., branch-and-bound). In this paper, we advance the state of the art in outlier rejection by making three contributions. First, we show that even a simple linear instance of outlier rejection is inapproximable: in the worst-case one cannot design a quasi-polynomial time algorithm that computes an approximate solution efficiently. Our second contribution is to provide the first per-instance sub-optimality bounds to assess the approximation quality of a given outlier rejection outcome. Our third contribution is to propose a simple general-purpose algorithm, named adaptive trimming, to remove outliers. Our algorithm leverages recently-proposed global solvers that are able to solve outlier-free problems, and iteratively removes measurements with large errors. We demonstrate the proposed algorithm on three spatial perception problems: 3D registration, two-view geometry, and SLAM. The results show that our algorithm outperforms several state-of-the-art methods across applications while being a general-purpose method.

Sparse principal component analysis (PCA) and sparse canonical correlation analysis (CCA) are two essential techniques from high-dimensional statistics and machine learning for analyzing large-scale data. Both problems can be formulated as an optimization problem with nonsmooth objective and nonconvex constraints. Since non-smoothness and nonconvexity bring numerical difficulties, most algorithms suggested in the literature either solve some relaxations or are heuristic and lack convergence guarantees. In this paper, we propose a new alternating manifold proximal gradient method to solve these two high-dimensional problems and provide a unified convergence analysis. Numerical experiment results are reported to demonstrate the advantages of our algorithm.

With the development of computational intelligence [1, 2, 19, 26], nature-inspired algorithms have been shown to be effective and thus become widely used for various optimization problems [15, 17, 2]. However, there is still a significant gap between theory and practice. Though the applications of algorithms are very successful, the relevant fundamental theory lacks behind or no theory at all. For example, the bat algorithm (BA), developed by Xin-She Yang in 2010 [3, 4], has been shown to very efficient in practice, but there is no mathematical theory for analyzing this algorithm. In fact, most of the swarm intelligence based algorithms for computational intelligence have no or little theoretical analyses, except for a few algorithms, such as the well known particle swarm optimization [10, 12, 25, 27] and genetic algorithms [16, 34]. Though we know these algorithms can work well in practice, we rarely understand why they work so well and under what conditions or parameter ranges. These key challenges require further in-depth theoretical studies.

Search-based procedural content generation uses stochastic global optimization algorithms to search spaces of game content. However, it has been found that tree search can be competitive with evolution on certain optimization problems. We investigate the applicability of several tree search methods to map generation and compare them systematically with several optimization algorithms, including evolutionary algorithms. For purposes of comparison, we use a simplified map generation problem where only passable and impassable tiles exist, three different map representations, and a set of objectives that are representative of those commonly found in actual level generation problem. While the results suggest that evolutionary algorithms produce good maps faster, several tree search methods can perform very well given sufficient time, and there are interesting differences in the character of the generated maps depending on the algorithm chosen, even for the same representation and objective.