Constraints Of Problem Research Articles

Quantum Distance Approximation for Persistence Diagrams

Abstract Topological Data Analysis methods can be useful for classification and clustering
tasks in many different fields as they can provide two dimensional persistence dia-
grams that summarize important information about the shape of potentially complex
and high dimensional data sets. The space of persistence diagrams can be endowed
with various metrics, which admit a statistical structure and allow to use these summaries for machine learning algorithms, e.g. the Wasserstein distance.

However, computing the distance between two persistence diagrams involves finding an opti-
mal way to match the points of the two diagrams and may not always be an easy
task for classical computers. Recently, quantum algorithms have shown the po-
tential to speedup the process of obtaining the persistence information displayed on
persistence diagrams by estimating the spectra of persistent Dirac operators. So,
in this work we explore the potential of quantum computers to estimate the distance
between persistence diagrams as the next step in the design of a fully quantum frame-
work for TDA. In particular we propose variational quantum algorithms for the
Wasserstein distance as well as the dcp distance. Our implementation is a weighted
version of the Quantum Approximate Optimization Algorithm that relies on control
clauses to encode the constraints of the optimization problem.

A comparative study on BCTW-GIA and T-DW deposition processes

ABSTRACT To address the problem of mutual constraints between heat input and efficiency in arc additive manufacturing, a BCTW-GIA process is proposed. In this paper, components are manufactured using the BCTW-GIA and T-DW methods. The macroscopic morphology, cooling process, microstructure and properties of the components are analysed. According to the results, the BCTW-GIA method achieves a deposition efficiency of 15.46 kg/h, which is a 123% improvement compared to the T-DW method. The addition of the main wire in the BCTW-GIA method consumed some of the heat, resulting in less heat being applied to the member, and the maximum and average temperatures were reduced by 26% and 13%, respectively, compared to the T-DW method. The BCTW-GIA components have a finer grain size and an average microhardness of 197.17 HV. The BCTW-GIA specimens had higher transverse and longitudinal tensile strengths, which increased by 7% and 10% respectively over the T-DW specimens.

Predicting multi-parametric dynamics of an externally forced oscillator using reservoir computing and minimal data

AbstractMechanical systems exhibit complex dynamical behavior from harmonic oscillations to chaotic motion. The dynamics undergo qualitative changes due to changes to internal system parameters like stiffness and changes to external forcing. Mapping out complete bifurcation diagrams numerically or experimentally is resource-consuming, or even infeasible. This study uses a data-driven approach to investigate how bifurcations can be learned from a few system response measurements. Particularly, the concept of reservoir computing (RC) is employed. As proof of concept, a minimal training dataset under the resource constraint problem of a Duffing oscillator with harmonic external forcing is provided as training data. Our results indicate that the RC not only learns to represent the system dynamics for the external forcing seen during training, but it also provides qualitatively accurate and robust system response predictions for completely unknown multi-parameter regimes outside the training data. Particularly, while being trained solely on regular period-2 cycle dynamics, the proposed framework correctly predicts higher-order periodic and even chaotic dynamics for out-of-distribution forcing signals.

Distributionally robust CVaR optimization for refinery integrated production–maintenance scheduling under uncertainty

In the petroleum refining industry, efficient production planning and maintenance scheduling are crucial for economic performance and operational efficiency. Moreover, the production processes face significant uncertainties stemming from market fluctuations and equipment failures. However, traditional optimization methods often treat production and maintenance independently and neglect the risk management associated with uncertainties in the production process, leading to unreliable plans and suboptimal execution. To address these issues, this paper proposes an innovative data-driven distributionally robust conditional value-at-risk (DRCVaR) method to tackle the integrated production–maintenance optimization problem under crude oil price uncertainty. By constructing confidence sets with L2 norm constraints based on historical data, our approach directly links the model’s conservatism to the amount of available data, effectively managing risk. In addition, we propose robust linear transformation to simplify the min–max nonlinear problem into a conic constraint problem, enhancing solution efficiency and ensuring better operational stability. Refinery case studies demonstrate that the proposed DRCVaR consistently achieves a practical and acceptable solution, significantly outperforming state-of-the-art approaches.

REHAS: Robust and Efficient Hyperelliptic Curve‐Based Authentication Scheme for Internet of Drones

ABSTRACTInternet of Drones (IoD) is one of the most beneficial and has many versatile applications like Surveillance and Security, Delivery and Logistics, Environmental Monitoring, Agriculture, and so forth. The IoD network is crucial for collecting sensitive data like geo‐coordinates, vehicle traffic data, and property details while surveying the various deployment locations in smart cities. The communication between users and drones can be compromised over insecure wireless channels by multiple attacks such as Man‐in‐the‐middle‐attack, Denial of Service, and so forth. Many schemes have already been propounded in the field of IoD. Still, many of them cannot address the resource constraints problem of drones, and existing protocols have higher computation and communication costs. Therefore, this paper has proposed a robust and efficient Hyper‐Elliptic Curve‐based authentication scheme (REHAS), which provides a session key for secure communication. Artificial Identities are generated using a hash function and random numbers. Fuzzy Extractor is used for user biometric authentication, which makes the smart device secure when lost. HECC is used with a smaller bit size of 80 bits rather than ECC of 160 bits. The security of the REHAS has been ensured using Scyther simulation. Furthermore, the resilience, safety, and robustness of REHAS are ensured by Informal security analysis. Lastly, a comparative study of the REHAS has been performed with other related Authentication and key agreement (AKA) protocols regarding communication cost, Computation cost, and security features, demonstrating that REHAS incurred less computation cost (6.7171 ms), communication overhead (1696 bits), and energy consumption (22.5 mJ) than other existing AKA schemes.

Multiple-Input Multiple-Output Synthetic Aperture Radar Waveform and Filter Design in the Presence of Uncertain Interference Environment

Multiple-input multiple-output synthetic aperture radar (MIMO-SAR) anti-jamming waveform design relies on accurate prior information about the interference. However, it is difficult to obtain accurate prior knowledge about uncertain intermittent sampling repeater jamming (ISRJ), leading to a severe decline in the detection performance of MIMO-SAR systems. Therefore, this article studies the robust joint design problem of MIMO radar transmit waveform and filter against uncertain ISRJ. We characterize two categories of uncertain interference, including sample length uncertainty and sample-time uncertainty, modeled as Gaussian distribution in different range bins. Based on the uncertain interference model, we formulate the maximizing SINR as a figure of merit, which is a non-convex quadratic optimization problem under specific waveform constraints. Based on the alternating direction method of multipliers (ADMM) framework, a novel joint design algorithm of waveform and filter is proposed. In order to improve the convergence performance of ADMM, the difference in convex functions (DC) programming is applied to the ADMM iterations framework to solve the problem of waveform energy inequality constraint. Finally, numerical results demonstrate the effectiveness and robustness of the proposed method, compared to the existing methods that utilize deterministic interference models in the uncertain ISRJ environment. Moreover, the spaceborne SAR real scene imaging simulations are conducted to evaluate the anti-ISRJ performance.

A Case Study on the Application of Evolutionary Algorithms for Solving Non-linear Programming Problems in Water Resource Management

Evolutionary algorithms have been proposed and used in this case study for the solution to non-linear programming problems related to water resources. Heuristic, a type of optimization algorithm characterized by population-based search as well as using the genetic algorithms, are used to model and determine the optimal distribution and utilization of aquatic resources based on environmental and demand factors. These materials include examples based on water distribution networks, managing a reservoir, and forecasting demands of customers, demonstrating the effectiveness of the aforementioned algorithms in solving non-linear constraint problems and in dealing with multiple objectives. The comparative analysis is based on a number of simulation experiments to examine the efficiency of such microevolutionary algorithms as Genetic Algorithm, Particle Swarm Optimization, and Differential Evolution in contrast to the traditional optimization algorithms. These results show that there is significant value in using evolutionary algorithms as a basis for managing and modelling water resources as it offers a pragmatic approach and has the potential to meet the demands of the water industry in terms of sustainability, cost and resource requirements. There seems to be considerable scope for extension of these algorithms to a wide range of natural resources management and administration.

Robust Semi-Infinite Interval Equilibrium Problem Involving Data Uncertainty: Optimality Conditions and Duality

In this paper, we model uncertainty in both the objective function and the constraints for the robust semi-infinite interval equilibrium problem involving data uncertainty. We particularize these conditions for the robust semi-infinite mathematical programming problem with interval-valued functions by extending the results from the literature. We introduce the dual robust version of the above problem, prove the Mond–Weir-type weak and strong duality theorems, and illustrate our results with an example.

Symmetry classification and enumeration of square-tile sikku kolams

Pulli kolam is an ancient mathematical art form that is still practiced today in south India by over a quarter million people. ‘Pulli’ in the Tamizh language means ‘dots’. A specific type of pulli kolam is sikku kolam where a series of dots are placed using rice flour and lines are drawn around them following three simple rules. Here we focus on sikku kolams assembled from square tiles. Kolams are classified by their point group symmetry and formulae are derived for counting the number of kolams of each symmetry type. Some interesting constraint problems are posed that could help formulate new games based on this elegant art form.

Data-driven prediction of relevant scenarios for robust combinatorial optimization

We study iterative constraint and variable generation methods for (two-stage) robust combinatorial optimization problems with discrete uncertainty. The goal of this work is to find a set of starting scenarios that provides strong lower bounds early in the process. To this end we define the Relevant Scenario Recognition Problem (RSRP) which finds the optimal choice of scenarios which maximizes the corresponding objective value. We show for classical and two-stage robust optimization that this problem can be solved in polynomial time if the number of selected scenarios is constant and NP-hard if it is part of the input. Furthermore, we derive a linear mixed-integer programming formulation for the problem in both cases.Since solving the RSRP is not possible in reasonable time, we propose a machine-learning-based heuristic to determine a good set of starting scenarios. To this end, we design a set of dimension-independent features, and train a Random Forest Classifier on already solved small-dimensional instances of the problem. Our experiments show that our method is able to improve the solution process even for larger instances than contained in the training set, and that predicting even a small number of good starting scenarios can considerably reduce the optimality gap. Additionally, our method provides a feature importance score which can give new insights into the role of scenario properties in robust optimization.

Modified Noise-Immune Fuzzy Neural Network for Solving the Quadratic Programming With Equality Constraint Problem.

Quadratic programming with equality constraint (QPEC) problems have extensive applicability in many industries as a versatile nonlinear programming modeling tool. However, noise interference is inevitable when solving QPEC problems in complex environments, so research on noise interference suppression or elimination methods is of great interest. This article proposes a modified noise-immune fuzzy neural network (MNIFNN) model and use it to solve QPEC problems. Compared with the traditional gradient recurrent neural network (TGRNN) and traditional zeroing recurrent neural network (TZRNN) models, the MNIFNN model has the advantage of inherent noise tolerance ability and stronger robustness, which is achieved by combining proportional, integral, and differential elements. Furthermore, the design parameters of the MNIFNN model adopt two disparate fuzzy parameters generated by two fuzzy logic systems (FLSs) related to the residual and residual integral term, which can improve the adaptability of the MNIFNN model. Numerical simulations demonstrate the effectiveness of the MNIFNN model in noise tolerance.

Sustainable Water Management Solutions for Urban Areas

The management of water resources is a serious concern in urban areas because of the effects of climate change, aging infrastructure, and rapid population increase. This essay examines the vital significance of sustainable water management in urban settings, emphasizing cutting-edge frameworks for policy and technology that can improve water resilience and efficiency. Successful strategies, such as demand management and diversification of the water supply, are demonstrated by case studies like Windhoek, Namibia. In order to solve the intricate and interrelated problems of urban water scarcity, infrastructure constraints, and environmental repercussions, the essay emphasizes integrated water resources management (IWRM) as a crucial technique that incorporates multidisciplinary viewpoints. In order to guarantee a sustainable urban water future, the importance of inclusive policies and governance is also covered, highlighting the necessity of cooperative and flexible problemsolving techniques.

Multi-Static Radar System Deployment Within a Non-Connected Region Utilising Particle Swarm Optimization

This paper is mainly devoted to studying the deployment problem of a multi-static radar system (MSRS) within a non-connected deployment region using multi-objective particle swarm optimization (MOPSO). By modeling and reformulating the problem, it can be represented as a multi-objective mixed integer programming (MOMIP), which eliminates the need for additional constraints. To enhance the algorithm performance, integer variables and continuous ones are treated separately employing multiple velocity formulas. The velocity formulas for integer variables are modified using the sigmoid function and genetic operation, leading to the proposal of two MSRS deployment algorithms, namely MOPSO-Sigmoid and MOPSO-Gene. To evaluate the performance of the proposed algorithms, they are compared with two existing MOPSO-based algorithms. The first algorithm is the MSRS deployment algorithm for the non-connected deployment region that addresses the additional constraint problem model. The second algorithm is based on an existing conventional MOPSO algorithm and addresses the equivalent MOMIP problem model. A numerical study demonstrates that MOPSO-Sigmoid and MOPSO-Gene exhibit promising efficiency and effectiveness.

Optical circuit switched three-stage twisted-folded Clos-network design model guaranteeing admissible blocking probability

Some data center networks have already started to use optical circuit switching (OCS) with potential performance benefits, including high capacity, low latency, and energy efficiency. This paper addresses a switching network design to maximize the network radix, i.e., the number of terminals connected to the network under the condition that a specified number of identical switches with the size N×N and the maximum admissible blocking probability are given. Previous work presented a two-stage twisted and folded Clos network (TF-Clos) with a blocking probability guarantee for OCS, which has a larger network radix than TF-Clos with a strict-sense non-blocking condition. Expanding the number of stages allows for enhancing the network radix. This paper proposes a model designing an OCS three-stage TF-Clos structure with a blocking probability guarantee to increase the network radix compared to the two-stage TF-Clos. We formulate the problem of obtaining the network configuration that maximizes the network radix as an optimization problem. We conduct an algorithm based on an exhaustive search to obtain a feasible solution satisfying the constraints of the optimization problem. This algorithm identifies the structure with the largest network radix in non-increasing order to avoid unnecessary searches. Numerical results show that the proposed model achieves a larger network radix than the two-stage model.

A two-layer strategy for sustainable energy management of microgrid clusters with embedded energy storage system and demand-side flexibility provision

The intermittent nature of renewable energy generation and the fluctuating demands pose persistent challenges in microgrid operations. In response, stakeholders and operators have turned to clustering the geographically adjacent microgrids as a solution. In this context, this paper introduces a novel two-layer energy management strategy for microgrid clusters, utilizing demand-side flexibility and the capabilities of shared battery energy storage (SBES) to minimize operational costs and emissions, while ensuring a spinning reserve within individual microgrids to prevent load-shedding. In the lower layer, the proposed approach devises optimal day-ahead operation policies, while the upper layer employs a cooperative strategy to further optimize the operational efficiency across the entire cluster. The energy management problem is accurately formulated as a mixed integer quadratic programming (MIQP) optimization, which incorporates linear terms in the problem's constraints. The formulation accounts for operational costs associated with SBES including expenses of charging/discharging and changes in operating states (CiOS). Real-world case studies with a cluster of three microgrids in Australia validate the effectiveness of this approach. Results show a reduction in operational costs for the base case scenario by 6.96 % compared to conventional microgrid management strategies. Sensitivity analyses further demonstrate the economic benefits of varying SBES capacity and flexibility pricing, with savings ranging from 6.5 % to 8.1 %. The proposed strategy also reduces CO2 emissions by up to 11.6 %, while improving system reliability. This strategy holds promise for integration into distributed energy systems with high renewable penetration and clustered local grids, offering significant advantages for utility operators and end-users through improved energy efficiency and reduced emissions.

Optimizing Virtual Network Embedding for Avionics with Time-Triggered Traffic Scheduling

Network virtualization technology abstracts the nodes and links resources in the physical network, and enables multiple virtual networks (VNs) to share the substrate network (SN) resources through the Virtual Netw ork Embedding (VNE) method. For time-triggered Ethernet (TTE) used in avionics, a time-triggered traffic scheduling oriented virtual network embedding (TT-VNE) method is proposed. While meeting the total resource constraints of traditional VNE problem, it ensures the strict periodicity of time-triggered (TT) traffic. During the solution process, the method sorts the virtual nodes according to the TT traffic bandwidth requirements and the total bandwidth requirements of the links connected to the virtual nodes, embeds the virtual nodes using the breadth first search algorithm, and plans the virtual links in candidate shortest path aggregation. If the TT traffic in the current virtual link is not schedulable, the iterative design of local virtual node re embedding and path planning is carried out. The simulation shows that the request acceptance rate of TT-VNE is not lower than that of existing methods, and when the number of virtual network requests in the star topology exceeds 30 , its request acceptance rate is about 14.3%higher than the VNE-NTANRC-D method which only considers the network topology and resource attributes.

Multi-UAVs task allocation method based on MPSO-SA-DQN

Multi-UAVs play an important role in the battlefield. Although many methods are proposed to solve the Multi-UAV task allocation, there still existing the problems of complex time constraints and uncertain solution space. The reason is that multi-UAVs usually face changing environmental factors. Aiming at solving such problem, this paper proposes a multi-UAV task assignment method based on Deep Q-based evolutionary reinforcement learning algorithms (MPSO-SA-DQN). Specifically, this method builds a multi-agent training framework based on the deep evolutionary reinforcement learning mechanism and SA-DQN. Its aim is to improve the global exploration and optimization capabilities of multi-agents. At the same time, the multi-dimensional particle swarm optimization algorithm is introduced to optimize the state space. Based on task priority mapping, the MPSO-SA-DQN algorithm framework is proposed. As a result, multi-agents can optimize the execution state in real time in the environment interaction. Besides, it also has the ability to reach optimal state and maximum reward. According to the characteristics of multi-UAV global task assignment, this paper designs a priority state space autoencoder strategy and global task feature. A multi-UAVs tasks allocation and iterative optimization method based on MPSO-SA-DQN algorithm is proposed, so as to continuously optimize the task allocation scheme. The simulation results show that the multi-UAV task allocation method based on MPSO-SA-DQN can effectively solve the problem of uncertainty in the optimal solution space of task allocation. At the same time, the algorithm achieves faster convergence result, and a good prospect of promotion in the field of UAV swarm cooperative task planning.

Existence and stability of standing waves for a weakly coupled nonlinear fractional Schrödinger system

We study the system of two weakly coupled nonlinear fractional Schrödinger equations{(−Δ)su+ωu=|u|2p−2u+β|u|p−2u|v|pin RN,(−Δ)sv+ωv=|v|2p−2v+β|u|p|v|p−2vin RN, where N≥2,s∈(0,1],2<2p<2s⁎=2N/(N−2s),ω>0 and β>0. For s∈(0,1] and 1<p<2, by finding a new kind of solution to the above system and comparing its energy level with those of other kinds of solutions, we show that each component of the least energy solution is nontrivial for any β>0, which forms a striking contrast with case p≥2. We emphasize that this result can be viewed as a complement to that of Guo and He (2016) [13] and Maia et al. (2006) [28]. When s∈(0,1),1<p<1+2s/N and ω>0 is fixed, we obtain the orbital stability of standing waves associated with the synchronized solution to the above system. To this end, we introduce an auxiliary mass constraint problem and establish the connection between the orbital stability of standing waves and the stability of ground state set to the auxiliary problem.

Scaling Abstraction Refinement for Program Analyses in Datalog using Graph Neural Networks

Counterexample-guided abstraction refinement (CEGAR) is a popular approach for automatically selecting abstractions with high precision and low time costs. Existing works cast abstraction refinements as constraint-solving problems. Due to the complexity of these problems, they cannot be scaled to large programs or complex analyses. We propose a novel approach that applies graph neural networks to improve the scalability of CEGAR for Datalog-based program analyses. By constructing graphs directly from the Datalog solver’s calculations, our method then uses a neural network to score abstraction parameters based on the information in these graphs. Then we reform the constraint problems such that the constraint solver ignores parameters with low scores. This in turn reduces the solution space and the size of the constraint problems. Since our graphs are directly constructed from Datalog computation without human effort, our approach can be applied to a broad range of parametric static analyses implemented in Datalog. We evaluate our approach on a pointer analysis and a typestate analysis and our approach can answer 2.83× and 1.5× as many queries as the baseline approach on large programs for the pointer analysis and the typestate analysis, respectively.

Modified Double Inertial Extragradient-like Approaches for Convex Bilevel Optimization Problems with VIP and CFPP Constraints

Convex bilevel optimization problems (CBOPs) exhibit a vital impact on the decision-making process under the hierarchical setting when image restoration plays a key role in signal processing and computer vision. In this paper, a modified double inertial extragradient-like approach with a line search procedure is introduced to tackle the CBOP with constraints of the CFPP and VIP, where the CFPP and VIP represent a common fixed point problem and a variational inequality problem, respectively. The strong convergence analysis of the proposed algorithm is discussed under certain mild assumptions, where it constitutes both sections that possess a mutual symmetry structure to a certain extent. As an application, our proposed algorithm is exploited for treating the image restoration problem, i.e., the LASSO problem with the constraints of fractional programming and fixed-point problems. The illustrative instance highlights the specific advantages and potential infect of the our proposed algorithm over the existing algorithms in the literature, particularly in the domain of image restoration.