Search Results (71)

This paper proposes a quantum algorithm, named Dicke state quantum search (DSQS), to set qubits in the Dicke state $|D_k^n⟩$ of D states in superposition to locate the target inputs or solutions of specific patterns among $2^n$ unstructured input instances, where n is the number of input qubits and $D=\left({\displaystyle \genfrac{}{}{0pt}{}{n}{k}}\right)=\mathrm{O}\left(n^k\right)$ for $min(k,n-k)\ll n/2$. Compared to Grover’s algorithm, a famous quantum search algorithm that calls an oracle and a diffuser O($\sqrt{2^n}$) times, DSQS requires no diffuser and calls an oracle only once. Furthermore, DSQS does not need to know the number of solutions in advance. We prove the correctness of DSQS with unitary transformations, and show that each solution can be found by DSQS with an error probability less than 1/3 through O($n^k$) repetitions, as long as $min(k,n-k)\ll n/2$. Additionally, this paper proposes a classical algorithm, named DSQS-VCP, to generate quantum circuits based on DSQS for solving the k-vertex cover problem (k-VCP), a well-known NP-complete (NPC) problem. Complexity analysis demonstrates that DSQS-VCP operates in polynomial time and that the quantum circuit generated by DSQS-VCP has a polynomial qubit count, gate count, and circuit depth as long as $min(k,n-k)\ll n/2$. We thus conclude that the k-VCP can be solved by the DSQS-VCP quantum circuit in polynomial time with an error probability less than 1/3 under the condition of $min(k,n-k)\ll n/2$. Since the k-VCP is NP-complete, NP and NPC problems can be polynomially reduced to the k-VCP. If the reduced k-VCP instance satisfies $min(k,n-k)\ll n/2$, then both the instance and the original NP/NPC problem instance to which it corresponds can be solved by the DSQS-VCP quantum circuit in polynomial time with an error probability less than 1/3. All statements of polynomial algorithm execution time in this paper apply only to VCP instances and similar instances of other problems, where $min(k,n-k)\ll n/2$. Thus, they imply neither NP ⊆ BQP nor P = NP. In this restricted regime of $min(k,n-k)\ll n/2$, the Dicke state subspace has a polynomial size of $D=\left({\displaystyle \genfrac{}{}{0pt}{}{n}{k}}\right)=\mathrm{O}\left(n^k\right)$, and our DSQS algorithm samples from it without asymptotic superiority over exhaustive enumeration. Nevertheless, DSQS may be combined with other quantum algorithms to better exploit the strengths of quantum computation in practice. Experimental results using IBM Qiskit packages show that the DSQS-VCP quantum circuit can solve the k-VCP successfully. Full article

Covering problems constitute a central theme in facility location research. This study extends the classical Maximal Covering Location Problem (MCLP) and Partial Set Covering Location Problem (PSCLP) to their generalized variants, in which each demand point must be simultaneously served by multiple facilities. This generalization captures reliability requirements inherent in applications such as emergency response and robust communication networks. We first present integer programming formulations for both generalized problems, followed by equivalent reformulations that facilitate algorithmic development. Building on these, we design exact Benders decomposition algorithms that exploit structural properties of the problems to achieve enhanced scalability and computational efficiency. Computational experiments on large-scale synthetic instances with up to 200,000 demand points demonstrate that our method attains more than a threefold speedup over CPLEX. We further validate the effectiveness of the proposed approach through experiments on a real-world dataset. In addition, we compare our method with a tabu search heuristic, and the numerical results show that within a fixed time limit, our method is generally able to identify higher-quality feasible solutions. These results collectively demonstrate both the effectiveness and the practical applicability of our approach for large-scale generalized covering problems. Full article

In Japan, natural disasters occur frequently. Serious disasters may cause damage to traffic networks and telecommunication infrastructures, leading to the occurrence of isolated disaster areas. In this article, unmanned aerial vehicles (UAVs) are used for data collection instead of unavailable ground-based stations in isolated disaster areas. Detailed information about the damage situation will be collected from the user equipment (UE) by a UAV through a fly–hover–fly procedure, and then will be sent to the disaster response headquarters for disaster relief. However, mission completion time minimization becomes a crucial task, considering the requirement of rapid response and the battery constraint of UAVs. Therefore, the author proposed a three-dimensional UAV flight trajectory, discussing the optimal flight altitude and placement of hovering points by transforming the original problem of K-means clustering into a location set cover problem (LSCP) that can be solved via a genetic algorithm (GA) approach. The simulation results have shown the feasibility of the proposed method to reduce the mission completion time. Full article

This paper addresses the maximum coverage location problem in a generalized setting, where both facilities (service areas) and regional demand are modeled as continuous entities. Unlike traditional formulations, our approach allows for arbitrary shapes for both service areas and demand regions, with additional constraints on facility placement. The key novelty of this work is its ability to handle complex, irregularly shaped service areas, including approximating them as unions of centrally symmetric shapes. This enables the use of an analytical approach based on spatial symmetry, which allows for efficient estimation of the covered area. The problem is formulated as a nonlinear optimization task. We analyze the properties of the objective function and leverage the Shapely library in Python 3.13.3 for efficient geometric computations. To improve computational efficiency, we develop an extended elastic model that significantly reduces processing time. This model generalizes the well-known quasi-physical, quasi-human algorithm for circle packing, extending its applicability to more complex spatial configurations. The effectiveness of the proposed approach is validated through test cases in which service areas take the form of circles, ellipses, and irregular polygons. Our method provides a robust and adaptable solution for various settings of practically interesting continuous maximum coverage location problems involving irregular regional demand and service areas. Full article

In recent years, there has been a call for a shift to transportation with lower greenhouse gas (GHG) emissions in order to combat global warming. One of the ecofriendly transportation methods is an electric moped scooter (e-moped)-sharing service that does not emit GHG when it runs. It is necessary to plan the location of charging stations and the material procurement through the manufacturing of e-mopeds in order to reduce the cost and GHG emissions and to improve the accessibility of the service. In this study, a two-stage design on the e-moped-sharing services is proposed to allocate charging stations and select material suppliers for e-mopeds using integer programming. The analysis method to determine the suitable charging station locations and sizes and supplier selection are also presented. Numerical experiments are conducted to illustrate the proposed design and analysis method by assuming Kumpan’s 1954 i model installation in Bochum city, Germany. In the numerical experiments, set covering and maximal covering location problems with small coverage radius of charging stations would be better by evaluating accessibility, GHG emissions, and cost comprehensively. Moreover, 11 prioritized demand points were picked out by introducing new indexes such as geographical and demand importance. Full article

Urban air mobility (UAM) has recently emerged as a promising new transportation mode, with various potential use cases. Facility location problems are well studied and of significant importance for various transportation modes. This work introduces a vertiport location identification framework, focusing on demand coverage and infrastructure accessibility. An Agglomerative Hierarchical Clustering (AHC) model was utilized for the identification of candidate vertiport locations, along with a k-means algorithm, for comparison and validation purposes, based on an estimated UAM demand pattern. A genetic algorithm (GA) was then formulated, for the solution of the proposed Uncapacitated and Capacitated Vertiport Location Problems (UVLP and CVLP, respectively), variations of the Uncapacitated and Capacitated Facility Location Problems. To evaluate and compare the introduced methodology, different existing facility location problems (FLPs) were considered and solved exactly using integer and linear programming. These are the Location Set Covering Problem (LSCP), the Maximal Coverage Location Problem (MCLP), and the p-median problem. The p-center problem was also considered and solved via a heuristic approach. The proposed framework is illustrated through applications in the Chicago Metropolitan Area, with the demand estimated on the basis of existing taxi and Transportation Network Company (TNC) data. Full article

As the climate crisis progresses, droughts and the seasonal availability of fresh water are becoming increasingly common in different regions of the world. One solution to tackle this problem is the reuse of treated wastewater in agriculture. This study was carried out in two significant hydrographic regions located in the southeast of Brazil (Mogi Guaçu River Water Management Unit—UGRHI-09 and Piracicaba River Basin—PRB) that have notable differences in terms of land use and land cover. The aim of this study was to carry out a multi-criteria analysis of a set of environmental attributes in order to classify the areas under study according to their levels of soil suitability and runoff potential. The integrated analysis made it possible to geospatialize prospective regions for reuse, under two specified conditions. In the UGRHI-09, condition 1 corresponds to 3373.24 km², while condition 2 comprises 286.07 km², located mainly in the north-western and central-eastern portions of the unit. In the PRB, condition 1 was also more expressive in occupational terms, corresponding to 1447.83 km²; and condition 2 was perceptible in 53.11 km², predominantly in the central region of the basin. The physical characteristics of the areas studied were decisive in delimiting the areas suitable for the reuse of treated wastewater. Full article

This study was aimed at improving the energy efficiency of the distribution of liquefied natural gas (LNG) as shipping fuel in the southern Baltic Sea. The objective of this study was to determine the demand for LNG for maritime shipping by analyzing the distribution of the resource from the water side (ship-to-ship). LNG was chosen due to the location of the LNG terminal in Świnoujście within the analyzed water area, where a problem has arisen in the southern part of the Baltic Sea regarding fuel supply for vessels due to the lack of developed infrastructure along the coast. An analysis was conducted to optimize the size of the LNG fleet and infrastructure facilities. Seeking compliance with Annex VI to the MARPOL 73/78 Convention, adopted by the International Maritime Organization (IMO), shipowners see potential in the switch from conventional fuels to LNG. As one of the alternative solutions, it will contribute to reducing harmful emissions. Determination of the LNG distribution volume requires the identification of LNG storage facility locations, specifying the number of LNG-powered ships (broken down by type) and the number of LNG bunkering ships. The first part of this study contains a detailed analysis of the number of sea-going ships that provide services in the southern part of the Baltic Sea and the world’s number of LNG bunkering ships. The database contains a set of the characteristics required to determine the optimal demand for LNG, where LNG bunkering vessels are capable of supplying fuel within the shortest possible time and covering the shortest possible distance to LNG-powered ships. The characteristics include the type of ship, requested LNG volume, the speed of LNG bunkering ships, the distance between LNG facilities, and the loading rate (the volume of fuel received per time unit). Based on the collected data, the volume of LNG distribution was determined using MATLAB R2019a software. The remainder of this study contains a description of the conducted research and results of an analysis of the traffic density in the Baltic Sea. The results were obtained on the basis of data from the Statistical Yearbook of Maritime Economy and IALA IWRAP Mk2 2020 software. The number of LNG-powered ships and number of LNG bunkering ships were specified, and the demand for LNG for the area under analysis was determined. Full article

In this paper, the quadratic p-median optimization problem is discussed, where the goal is to connect users to a selected group of facilities (emergency services, telecommunications servers, healthcare facilities) at the lowest possible cost. The problem is aimed at minimizing the cost of connecting these selected facilities. The costs are symmetric, meaning connecting two different points is the same in both directions. This problem extends the traditional p-median problem, a combinatorial problem used in various fields like facility location, network design, transportation, supply chain networks, emergency services, healthcare, and education planning. Surprisingly, the quadratic version has not been thoroughly considered in the literature. The paper highlights the formulation of two mixed-integer quadratic programming models to find optimal solutions to this problem. One model is a classic formulation, and the other is based on set cover theory. Linear versions and Bender’s decomposition formulations for each model are also derived. A Bender’s decomposition is solved using an algorithm that adds constraints during each iteration to improve the solution. Lazy constraints in the Gurobi solver’s branch and cut algorithm are dynamically added whenever a mixed-integer programming solution is found. Additionally, an efficient local search meta-heuristic is proposed that usually finds optimal solutions for tested instances. Challenging instances with up to 60 facilities and 2000 users are successfully solved. Our results show that Bender’s models with lazy constraints are the most effective for Euclidean and random test cases, achieving optimal solutions in less CPU time. The meta-heuristic also finds near-optimal solutions rapidly for these cases. Full article

In his work published in (Ann. Probab. 19, No. 2 (1991), 812–825), W. Stute introduced the notion of conditional U-statistics, expanding upon the Nadaraya–Watson estimates used for regression functions. Stute illustrated the pointwise consistency and asymptotic normality of these statistics. Our research extends these concepts to a broader scope, establishing, for the first time, an asymptotic framework for single-index conditional U-statistics applicable to locally stationary random fields $\{{\mathbf{X}}_{s,A_n}:sin{R}_n\}$ observed at irregularly spaced locations in $R_n$, a subset of ${\mathbb{R}}^d$. We introduce an estimator for the single-index conditional U-statistics operator that accommodates the nonstationary nature of the data-generating process. Our method employs a stochastic sampling approach that allows for the flexible creation of irregularly spaced sampling sites, covering both pure and mixed increasing domain frameworks. We establish the uniform convergence rate and weak convergence of the single conditional U-processes. Specifically, we examine weak convergence under bounded or unbounded function classes that satisfy specific moment conditions. These findings are established under general structural conditions on the function classes and underlying models. The theoretical advancements outlined in this paper form essential foundations for potential breakthroughs in functional data analysis, laying the groundwork for future research in this field. Moreover, in the same context, we show the uniform consistency for the nonparametric inverse probability of censoring weighted (I.P.C.W.) estimators of the regression function under random censorship, which is of its own interest. Potential applications of our findings encompass, among many others, the set-indexed conditional U-statistics, the Kendall rank correlation coefficient, and the discrimination problems. Full article

Battlefield surveillance radar is usually 2-D radar, which cannot realize target three-dimensional localization, leading to poor resolution for the air target in the elevation dimension. Previous researchers have used the Traditional Height Finder Radar (HFR) or multiple 2-D radar networking to estimate the target three-dimensional location. However, all of them face the problems of high cost, poor real-time performance and high requirement of space–time registration. In this paper, Reconfigurable Intelligent Surfaces (RISs) with low cost are introduced into the 2-D radar to realize the target three-dimensional localization. Taking advantage of the wide beam of 2-D radar in the elevation dimension, several Unmanned Aerial Vehicles (UAVs) carrying RISs are set in the receiving beam to form multiple auxiliary measurement channels. In addition, the traditional 2-D radar measurements combined with the auxiliary channel measurements are used to realize the target three-dimensional localization by solving a nonlinear least square problem with a convex optimization method. For the proposed RIS-assisted target three-dimensional localization problem, the Cramer–Rao Lower Bound (CRLB) is derived to measure the target localization accuracy. Simulation results verify the effectiveness of the proposed 3-D localization method, and the influences of the number, the positions and the site errors of the RISs on the localization accuracy are covered. Full article

Phasor measurement units (PMUs) are deployed at power grid nodes around the transmission grid, determining precise power system monitoring conditions. In real life, it is not realistic to place a PMU at every power grid node; thus, the lowest PMU number is optimally selected for the full observation of the entire network. In this study, the PMU placement model is reconsidered, taking into account single- and multi-capacity placement models rather than the well-studied PMU placement model with an unrestricted number of channels. A restricted number of channels per monitoring device is used, instead of supposing that a PMU is able to observe all incident buses through the transmission connectivity lines. The optimization models are declared closely to the power dominating set and minimum edge cover problem in graph theory. These discrete optimization problems are directly related with the minimum set covering problem. Initially, the allocation model is declared as a constrained mixed-integer linear program implemented by mathematical and stochastic algorithms. Then, the $0/1$ integer linear problem is reformulated into a non-convex constraint program to find optimality. The mathematical models are solved either in binary form or in the continuous domain using specialized optimization libraries, and are all implemented in YALMIP software in conjunction with MATLAB. Mixed-integer linear solvers, nonlinear programming solvers, and heuristic algorithms are utilized in the aforementioned software packages to locate the global solution for each instance solved in this application, which considers the transformation of the existing power grids to smart grids. Full article

Near-surface air temperature (T_a) is a key variable in global climate studies. Global climate models such as ERA5 and CMIP6 predict various parameters at coarse spatial resolution (>9 km). As a result, local phenomena such as the urban heat islands are not reflected in the model’s outputs. In this study, we address this limitation by downscaling the resolution of ERA5 (9 km) and CMIP6 (27 km) T_a to 1 km, employing two different machine learning algorithms (XGBoost and Deep Learning). Our models leverage a diverse set of features, including data from satellites (land surface temperature and normalized difference vegetation index), from ERA5 and CMIP6 climate models (e.g., solar and thermal radiation, wind), and from digital elevation models to develop accurate machine learning prediction models. These models were rigorously validated against observations from 98 meteorological stations in the East Mediterranean (Israel) using a standard cross-validation technique as well as a leave-one-group-out on the station ID evaluation methodology to avoid overfitting and dependence on geographic location. We demonstrate the sensitivity of the downscaled T_a to local land cover and topography, which is missing in the climate models. Our results demonstrate impressive accuracy with the Deep Learning-based models, obtaining Root Mean Squared Error (RMSE) values of 0.98 °C (ERA5) and 1.86 °C (CMIP6) for daily T_a and 2.20 °C (ERA5) for hourly T_a. Additionally, we explore the impact of the various input features and offer an extended application for future climate predictions. Finally, we propose an enhanced evaluation framework, which addresses the problem of model overfitting. This work provides practical tools and insights for building and evaluating T_a downscaling models. The code and data are publicly shared online. Full article

This study introduces an innovative numerical approach for polylinear approximation (polylinearization) of non-self-intersecting compact sensor characteristics (transfer functions) specified either pointwise or analytically. The goal is to partition the sensor characteristic optimally, i.e., to select the vertices of the approximating polyline (approximant) along with their positions, on the sensor characteristics so that the distance (i.e., the separation) between the approximant and the characteristic is rendered below a certain problem-specific tolerance. To achieve this goal, two alternative nonlinear optimization problems are solved, which differ in the adopted quantitative measure of the separation between the transfer function and the approximant. In the first problem, which relates to absolutely integrable sensor characteristics (their energy is not necessarily finite, but they can be represented in terms of convergent Fourier series), the polylinearization is constructed by the numerical minimization of the $L^1$-metric (a distance-based separation measure), concerning the number of polyline vertices and their locations. In the second problem, which covers the quadratically integrable sensor characteristics (whose energy is finite, but they do not necessarily admit a representation in terms of convergent Fourier series), the polylinearization is constructed by numerically minimizing the $L^2$-metric (area- or energy-based separation measure) for the same set of optimization variables—the locations and the number of polyline vertices. Full article

(1) Background: Women in their middle years undergoing perimenopause encounter a range of physical and psychological alterations attributed to hormonal changes. The prominent symptoms among menopausal women are depressive symptoms and sleep-related problems. The aim of this study was to conduct a meta-analysis examining the effects of Cognitive Behavioral Therapy (CBT) on women going through menopause, specifically focusing on depressive symptoms and sleep problems. We analyzed studies conducted both within the country and across international settings over the last decade. (2) Methods: A search of the literature was conducted—a targeted search, exclusively considering randomized controlled trials (RCTs) that were published within the timeframe spanning from 15 June 2013 to 15 June 2023. (3) Findings: Upon reviewing nine studies that satisfied our inclusion criteria and involved a total of 923 participants, it was noted that four of these studies incorporated diverse cognitive-behavioral strategies. Among the nine studies, a total of four were included in the meta-analysis: two measured depressive symptoms, and two measured sleep quality. The combined effect size for depressive symptoms was found to be 3.55 (95% confidence interval: −5.48, −1.61; p < 0.05), and for sleep quality, it was 0.78 (95% confidence interval: −1.32, −0.25; p = 0.004). (4) Conclusions: Our review emphasizes the necessity for conducting larger-scale studies focused on the application of CBT for women experiencing menopausal symptoms. Additionally, it is recommended to approach the interpretation of these results with caution due to discrepancies in methodology and the overall quality of the studies. Further clinical trials are necessary to establish the ideal number of CBT sessions needed for the effective treatment of depression in menopausal women. Future studies should cover a wider range of geographical locations, including more countries, and focus on various outcomes such as depressive symptoms and sleep quality. Full article