Multiple Feasible Solutions Research Articles

A training-free non-intrusive air conditioning load monitoring method based on fuzzy comprehensive evaluation

Air conditioner (AC) is a grid friendly load, monitoring its operating status plays a key role in evaluating user side potential for participation in demand response. With continuous innovations in AC technology, the AC operation characteristics have shown increasing complexity, which poses significant challenges for non-intrusive AC load monitoring. Furthermore, obtaining labeled training data for target scenarios is often challenging, which hinders deployment of many Non-Intrusive Load Monitoring (NILM) methods in practice. In this regard, this article proposes a training-free non-intrusive AC load monitoring method based on fuzzy comprehensive evaluation (FCE), which is very easy to deploy and has good robustness. Firstly, considering various influence factors, a FCE model is constructed based on common knowledge about AC. This model simulates the manual labeling process to locate AC operation periods. Secondly, an AC power estimation method based on weighted filtering is established, in which weighted filter is used to eliminate the non-AC load components that may overlap during AC operation periods. Specifically, an optimization model is constructed to make the cumulative power of the AC events in its working cycle approach zero, with the filter weight vector as the objective variable, in which a heuristic greedy algorithm is used to find the optimal filter weight vector. When multiple feasible solutions with similar objective function values are derived in the solving process, the probability of load events appearing in AC and non-AC operation periods are compared. The final solution is selected, taking into account the likelihood of each feasible solution corresponding to a load event sequence belonging to AC load. The testing results on the PecanStreet dataset and multiple real-world measured datasets prove the effectiveness of the proposed method in monitoring complex ACs with poor waveform consistency.

MH‐HMR: Human mesh recovery from monocular images via multi‐hypothesis learning

AbstractRecovering 3D human meshes from monocular images is an inherently ill‐posed and challenging task due to depth ambiguity, joint occlusion, and truncation. However, most existing approaches do not model such uncertainties, typically yielding a single reconstruction for one input. In contrast, the ambiguity of the reconstruction is embraced and the problem is considered as an inverse problem for which multiple feasible solutions exist. To address these issues, the authors propose a multi‐hypothesis approach, multi‐hypothesis human mesh recovery (MH‐HMR), to efficiently model the multi‐hypothesis representation and build strong relationships among the hypothetical features. Specifically, the task is decomposed into three stages: (1) generating a reasonable set of initial recovery results (i.e., multiple hypotheses) given a single colour image; (2) modelling intra‐hypothesis refinement to enhance every single‐hypothesis feature; and (3) establishing inter‐hypothesis communication and regressing the final human meshes. Meanwhile, the authors take further advantage of multiple hypotheses and the recovery process to achieve human mesh recovery from multiple uncalibrated views. Compared with state‐of‐the‐art methods, the MH‐HMR approach achieves superior performance and recovers more accurate human meshes on challenging benchmark datasets, such as Human3.6M and 3DPW, while demonstrating the effectiveness across a variety of settings. The code will be publicly available at https://cic.tju.edu.cn/faculty/likun/projects/MH‐HMR.

Non-invasive calibration of a Stewart platform by photogrammetry

AbstractAccurate calibration of a Stewart platform is important for their precise and efficient operation. However, the calibration of these platforms using forward kinematics is a challenge for researchers because forward kinematics normally generates multiple feasible and unfeasible solutions for any pose of the moving platform. The complex kinematic relations among the six actuator paths connecting the fixed base to the moving platform further compound the difficulty in establishing a straightforward and efficient calibration method. The authors developed a new forward kinematics-based calibration method using Denavit-Hartenberg (DH) convention and used the Stewart platform “Tiger 66.1” developed in their lab for experimenting with the photogrammetry-based calibration strategies described in this paper. This system became operational upon completion of construction, marking its inaugural use. The authors used their calibration model for estimating the errors in the system and adopted three compensation options or strategies as per least-square method to improve the accuracy of the system. These strategies leveraged a high-resolution digital camera and off-the-shelf software to capture the poses of the moving platform’s center. This process is non-invasive and does not need any additional equipment to be attached to the hexapod or any alteration of the hexapod hardware. This photogrammetry-based calibration process involves multiple high-resolution images from different angles to measure the position and orientation of the platform center in the three-dimensional space. The target poses and actual poses are then compared, and the error compensations are estimated using the least-square methods to calculate the predicted poses. Results from each of the three compensation approaches demonstrated noticeable enhancements in platform pose accuracies, suggesting room for further improvements. Given that “Tiger 66.1” is based on the general Stewart platform structure, the proposed calibration method holds promise for extension to machines operating on similar principles where non-invasive calibration is desirable. This study contributes to advancing the field of Stewart platform calibration, paving the way for more precise and efficient applications in various domains.

Analysis of Middle School Mathematics Applications Textbook Activities Based on Model-Eliciting Principles

Model-eliciting activities (MEA) represent a distinct form of problem-solving exercises that deviate from conventional problem-solving approaches. They encompass complex real-life scenarios characterized by multiple feasible solutions, demanding non-routine thinking with open-ended possibilities. Lesh and Doerr (2003) posit that MEA conform to specific principles, encompassing model construction, reality, self-evaluation, model externalization (construct certification), model generalization, and effective prototype principles. This study examines the compatibility of tasks in Turkey's middle school mathematics applications textbooks (grades 5-8) with the principles of model-eliciting activities (MEA). The analysis focuses on five principles: reality, model construction, self-evaluation, model documentation, and model generalization. The findings reveal varying degrees of compatibility across different grades. The reality and model generalization principles show more robust compatibility, while the model construction and model documentation principles have mixed levels of compatibility. The self-evaluation principle demonstrates varied compatibility. The study highlights strengths and areas for improvement in the tasks' alignment with MEA principles and emphasizes the importance of real-life relevance and model application. Suggestions are made to enhance explicit guidance in model construction and documentation. The study provides implications for curriculum design, teacher professional development, instructional strategies, student engagement, assessment practices, and future research in mathematics education. However, limitations, such as the absence of student perspectives and contextual factors, should be considered when interpreting the findings.

A Study on a New Way of Thinking Based on Linear Programming to Analyze Civic Education in Colleges and Universities

Abstract This paper intends to construct a new multi-dimensional preference analysis model for learners by using the improved linear programming method of multi-dimensional preference analysis (LINMAP) to get the weight vector of attributes under the situation that the weights of attributes are completely unknown and for the uncertain multi-attribute decision-making problem that the elements of decision-making matrix are triangular fuzzy numbers, and the preference information is ordered pairs. The data of subjective or objective Civics education learning preferences are aggregated, and the statistical analysis of the data is carried out using SPSS.21 to generate the Civics education learning preference input degree weighting system. The results show that the offline behavioral input weight in the college Civics course is 0.5769, which is greater compared to the online input. And the attribute weights of course Civics preference are calculated to get Z max = 2.29, Z min = 0.73. Multiple feasible solutions can be obtained by taking any value between [0,1]. Based on the development law of the times, this paper makes a new thinking on ideological and political education and actively explores a new road suitable for the development of ideological and political education in colleges and universities.

A Geometric Knowledge Oriented Single-Frame 2D-to-3D Human Absolute Pose Estimation Method

As a critical part of the 3D human pose estimation (HPE), establishing the 2D-to-3D lifting mapping is limited by depth ambiguity. Most current works generally lack the quantitative analysis of the relative depth expression and the depth ambiguity error expression in lifting mapping, resulting in low prediction efficiency and poor interpretability. To this end, this paper mines and leverages prior geometric knowledge of these expressions based on the pinhole imaging principle, decoupling the 2D-to-3D lifting mapping and simplifying the model training. Specifically, this paper proposes a prior geometric knowledge oriented pose estimation model with two-branch transformer architectures, explicitly introducing high-dimensional prior geometric features to improve model efficiency and interpretability. It converts the regression of spatial coordinates into the prediction of spatial direction vectors between joints to generate multiple feasible solutions further alleviate the depth ambiguity. Moreover, this paper raises a novel non-learning-based absolute depth estimation algorithm based on prior geometric relationship decoupling from relative depth expression for the first time. It establishes multiple independent depth mapping from non-root nodes to the root node to calculate the absolute depth candidate, which is parameter-free, plug-and-play, and interpretable. Experiments show that the proposed pose estimation model achieves state-of-the-art performance on Human 3.6M and MPI-INF-3DHP benchmarks with lower parameters and faster inference speed, and the proposed absolute depth estimation algorithm achieves similar performance to traditional methods without any network parameters. The source code are available at https://github.com/Humengxian/GKONet.

3D Human Pose Estimation Based on Transformer

Currently, 3D human pose estimation has gradually been a well-liked subject. Although various models based on the deep neural network have produced an excellent performance, they still suffer from the ignorance of multiple feasible pose solutions and the problem of the relatively-fixed input length. To solve these issues, a coordinate transformer encoder based on a 2D pose is constructed to generate multiple feasible pose solutions, and multi-to-one pose mapping is employed to generate a reliable pose. A temporal transformer encoder is used to exploit the temporal dependencies of consecutive pose sequences, which avoids the issue of relatively-fixed input length caused by temporal dilated convolution. Adequate experiments indicate that our model achieves a promising performance.

Multi-hypothesis representation learning for transformer-based 3D human pose estimation

Despite significant progress, estimating 3D human poses from monocular videos remains a challenging task due to depth ambiguity and self-occlusion. Most existing works attempt to solve both issues by exploiting spatial and temporal relationships. However, those works ignore the fact that it is an inverse problem where multiple feasible solutions (i.e., hypotheses) exist. To relieve this limitation, we propose a Multi-Hypothesis Transformer that learns spatio-temporal representations of multiple plausible pose hypotheses. In order to effectively model multi-hypothesis dependencies and build strong relationships across hypothesis features, we introduce a one-to-many-to-one three-stage framework: (i) Generate multiple initial hypothesis representations; (ii) Model self-hypothesis communication, merge multiple hypotheses into a single converged representation and then partition it into several diverged hypotheses; (iii) Learn cross-hypothesis communication and aggregate the multi-hypothesis features to synthesize the final 3D pose. Through the above processes, the final representation is enhanced and the synthesized pose is much more accurate. Extensive experiments show that the proposed method achieves state-of-the-art results on two challenging datasets: Human3.6M and MPI-INF-3DHP. The code and models are available at https://github.com/Vegetebird/MHFormer.

Stress-field driven conformal lattice design using circle packing algorithm

Reliable extreme lightweight is the pursuit in many high-end manufacturing areas. Aided by additive manufacturing (AM), lattice material has become a promising candidate for lightweight optimization. Configuration of lattice units at the material level and the distribution of lattice units at the structure level are the two main research directions recently. This paper proposes a generative strategy for lattice infilling optimization using organic strut-based lattices. A sphere packing algorithm driven by von Mises stress fields determines the lattice distribution density. Two typical configurations, Voronoi polygons and Delaunay triangles, are adopted to constitute the frames, respectively. Based on finite element analysis, a simplified truss model is utilized to evaluate the lattice distribution in terms of mechanical properties. Optimization parameters, including node number, mapping gradient, and the range of varying circle size, are investigated through the genetic algorithm (GA). Multiple feasible solutions are obtained for further solidification modelling. To avoid the stress concentration, the organic strut-based lattice units are created by the iso-surface modelling method. The effectiveness of the proposed generative approach is illustrated through a classical 3-point bending beam. The stiffness of the optimized structure, verified through experimental testing, has increased 80% over the one using the traditional uniform body center cubic (BCC) lattice distribution.

Hybrid quantum-classical multi-cut Benders approach with a power system application

Leveraging the current generation of quantum devices to solve optimization problems of practical interest necessitates the development of hybrid quantum-classical (HQC) solution approaches. In this paper, a multi-cut Benders decomposition (BD) approach that exploits multiple feasible solutions of the master problem (MP) to generate multiple valid cuts is adapted, so as to be used as an HQC solver for general mixed-integer linear programming (MILP) problems. The use of different cut selection criteria and strategies to manage the size of the MP by eliciting a subset of cuts to be added in each iteration of the BD scheme using quantum computing is discussed. The HQC optimization algorithm is applied to the Unit Commitment (UC) problem. UC is a prototypical use case of optimization applied to electrical power systems, a critical sector that may benefit from advances in quantum computing. The proposed approach is demonstrated using the D-Wave Advantage 4.1 quantum annealer.

Solving airline crew pairing problems through constraint partitioning

In this paper, a decomposition technique based on constraint partitioning is developed to solve the crew pairing problem (CPP) which has an overriding importance in the airline industry as it determines the crew cost. The method is based on the observation that in large-scale problems, the constraints can be partitioned to some sub-problems which involve special subsets of variables. The resultant structure is called the 'partitioned structure'. Therefore, in the proposed method, first, a feasible solution is generated for a reduced CPP with a 'partitioned structure' through the optimal solutions of its sub-problems. Then, at each step, the feasible solution is improved through adding/removing some pairings to/from it. The proposed algorithm is applied to a case study from the literature as well as some randomly generated test problems. One advantage of the proposed method is finding multiple feasible solutions with lower time than the method used to solve the case. [Submitted: 8 May 2020; Accepted: 29 December 2021]

Integrated thermal modeling, analysis, and sequential design of heat exchanger surfaces of a natural circulation RDF boiler including evaporator tubes

Although the design methodology of individual heat transfer surfaces in a natural circulation boiler such as evaporator tubes, convective and radiative superheaters are available in the literature, the multiple feasible design solutions of boiler heat exchanger surfaces coupled with drift flux based model of evaporator tube and cost-based optimal solution of the surfaces is not common. The present study proposes a sequential iterative design methodology for all heat transfer surfaces (from the evaporator to air preheater) in a single boiler to bridge the gap between industrial needs and academia. The salient temperature points in different locations are used in the design, alternate solutions are considered, and the overall cost is minimized. The evaporator tubes are designed based on a two-phase flow drift flux model and fixed volume constraint. The radiant and radiative-convective superheaters are modeled using weighted average flue gas temperature. The models of evaporator section and other heat exchangers are validated extensively with data of natural circulation loop and components integrated into real plants, respectively. The feasible and optimal design solutions of all heat transfer surfaces are proposed for a medium-scale (35 MW) Refused-Derived Fuel-fired Boiler (RDFB). The variation of mass flux through the evaporator tubes with the fuel feed rate is observed to be gravity-driven initially followed by friction-dominated. It is observed that for lowering the exit flue gas temperature of 14.93% below 150 °C, the required area of air preheater is 21.83% higher, while for a reduction of temperature of 21.42%, the area increment is 55.8%, which increases the investment cost rapidly. Results also indicate that the radiative heat exchangers require less heat transfer surface for a higher pitch to diameter ratio while the opposite characteristic is observed for the convective heat exchangers.

Out of the Niche: Using Direct Search Methods to Find Multiple Global Optima

Multimodal optimization deals with problems where multiple feasible global solutions coexist. Despite sharing a common objective function value, some global optima may be preferred to others for various reasons. In such cases, it is paramount to devise methods that are able to find as many global optima as possible within an affordable computational budget. Niching strategies have received an overwhelming attention in recent years as the most suitable technique to tackle these kinds of problems. In this paper we explore a different approach, based on a systematic yet versatile use of traditional direct search methods. When tested over reference benchmark functions, our proposal, despite its apparent simplicity, noticeably resists the comparison with state-of-the-art niching methods in most cases, both in the number of global optima found and in the number of function evaluations required. However, rather than trying to outperform niching methods—far more elaborated—our aim is to enrich them with the knowledge gained from exploiting the distinctive features of direct search methods. To that end, we propose two new performance measures that can be used to evaluate, compare and monitor the progress of optimization algorithms of (possibly) very different nature in their effort to find as many global optima of a given multimodal objective function as possible. We believe that adopting these metrics as reference criteria could lead to more sophisticated and computationally-efficient algorithms, which could benefit from the brute force of derivative-free local search methods.

Design of Real-Valued Wideband Beamformers Using an Adaptive-Array-Theory-Inspired WLS: Theory and Algorithm

The weighted least squares (WLS)-based beamformer design can achieve flexible beampattern control via adjusting the WLS weighting function inspired by the adaptive array theory (AAT). Nevertheless, the weighting function is conventionally adjusted in an <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ad hoc</i> way, and precise beampattern control cannot be guaranteed. Although an analytical solution for the weighting function adjustment was proposed very recently, it is only applicable to complex-valued narrowband beamformers. In some applications such as acoustic/seismic array processing, however, real-valued wideband beamformers are required, since acoustic/seismic signals are usually unmodulated, real-valued and wideband. This paper studies the theory and design of real-valued wideband beamformers using an AAT-inspired WLS, which can achieve precise wideband beampattern control. The main contributions of this paper include: i) we theoretically prove the existence of the WLS weighting function for the real-valued wideband beamformers to achieve precise control of wideband beampatterns, and derive the corresponding analytical solutions; ii) we provide the insights into the impact of the weighting function on the cost function, which is useful to find the optimum solution for the weighting function among multiple feasible solutions; and iii) we propose an algorithm for the design of real-valued wideband beamformers using the proposed AAT-inspired WLS, which does not require to fine-tune any user parameters, and can guarantee precise control of wideband beampatterns as demonstrated by the simulation results.

Learning Based Methods for Traffic Matrix Estimation From Link Measurements

Network traffic matrix (TM) is a critical input for capacity planning, anomaly detection and many other network management related tasks. The TMs are often computed from link load measurements. The TM estimation problem is the determination of the TM from link load measurements. The relationship between the link loads and the TM that generated the link loads can be modeled as an under-determined linear system and has multiple feasible solutions. Therefore, prior knowledge of the traffic demand pattern has to be used in order to find a potentially feasible TM. In this paper, we consider the TM estimation problem with limited prior information. Unlike previous methods that require past measurements of complete TMs, which are hard to obtain or protected by regulations, our method works even if only the distribution of TMs is known. We develop an iterative projection based algorithm to solve this problem. If large number of past TMs can be measured, we propose a Generative Adversarial Network (GAN) based approach for solving the problem. We compare the strengths of the two approaches and evaluate their performance for several networks using varying amounts of past data.

A Model for Intact and Damage Stability Evaluation of CNG Ships during the Concept Design Stage

To face the design of a new ship concept, the evaluation of multiple feasible solutions concerning several aspects of naval architecture and marine engineering is necessary. Compressed natural gas technologies are in continuous development; therefore, there are no available databases for existing ships to use as a basis for the design process of a new unit. In this sense, the adoption of a modern multi-attribute decision-based method can help the designer for the study of a completely new ship prototype. A database of compressed natural gas ships was generated starting from a baseline hull, varying six hull-form parameters by means of the design of experiment technique. Between the attributes involved in the concept design process, stability is for sure one of the most relevant topics, both for intact and damaged cases. This work describes two approaches to identify the compliance of a ship with the intact stability regulations based on the ship main geometrical quantities. Moreover, a metamodel based on the maximum floodable length concept (damage stability) allows determining the main internal subdivision of the ship. The metamodel outcomes were compared with results from direct calculations on a ship external to the database, highlighting the adequate accuracy given by the developed methods.

A note on short-term scheduling of multi-grade polymer plant using DNA computing

Short-term scheduling of batch polymer plant involves the scheduling of different orders in parallel available production lines. The scheduling becomes more challenging due to the presence of sequence-dependent changeover constraints between different orders which lead to combinatorial optimization formulation. Such combinatorial optimization problems have exponential time complexity on the silicon-based computer. DNA computing experiments are found to be promising for such combinatorial optimization problems particularly involving unique feasible optimal solution. However, use of DNA to find a solution to real-life problems involving multiple feasible solutions is an emerging area of research. The present paper illustrates the DNA solutions to the short-term scheduling of a polymer plant involving multiple feasible solutions and parallel production lines. The DNA computer aided with nearest neighbour heuristics and iterative implementation found to be successfully searching the optimal solution in a combinatorial search space for three short-term scheduling problems of multi-grade polymer plant.

Modeling and Simulation for Effectiveness Evaluation of Dynamic Discrete Military Supply Chain Networks

The effectiveness of military supply chain networks is an important reference for logistics decision-making, and it is crucial to evaluate it scientifically and accurately. This paper highlights the problem from the perspective of dynamic and discrete networks. A topological structure model with the characteristics of dynamic and discreteness is used to describe the structure of military supply chain networks (MSCNs). In order to provide a platform for evaluating the effectiveness, simulation algorithms based on topological structure models for MSCNs are presented. Considering military and economic factors, evaluation metrics including supply capability and supply efficiency are proposed. By applying the model and algorithms to a POL supply network in a theater, we obtain the values of supply capability and efficiency metrics in a dynamic environment. We also identify an optimal solution from multiple feasible solutions to help decision-makers to make scientific and rational decisions by using exploratory analysis method. The results show that new evaluation metrics can capture important effectiveness requirements for military supply networks positively. We also find the proposed method in this paper can solve the problem of evaluating the effectiveness of dynamic and discrete network effectiveness evaluation in a feasible and effective manner.

Multi-Objective Sustainable Operation of the Three Gorges Cascaded Hydropower System Using Multi-Swarm Comprehensive Learning Particle Swarm Optimization

Optimal operation of hydropower reservoir systems often needs to optimize multiple conflicting objectives simultaneously. The conflicting objectives result in a Pareto front, which is a set of non-dominated solutions. Non-dominated solutions cannot outperform each other on all the objectives. An optimization framework based on the multi-swarm comprehensive learning particle swarm optimization algorithm is proposed to solve the multi-objective operation of hydropower reservoir systems. Through adopting search techniques such as decomposition, mutation and differential evolution, the algorithm tries to derive multiple non-dominated solutions reasonably distributed over the true Pareto front in one single run, thereby facilitating determining the final tradeoff. The long-term sustainable planning of the Three Gorges cascaded hydropower system consisting of the Three Gorges Dam and Gezhouba Dam located on the Yangtze River in China is studied. Two conflicting objectives, i.e., maximizing hydropower generation and minimizing deviation from the outflow lower target to realize the system’s economic, environmental and social benefits during the drought season, are optimized simultaneously. Experimental results demonstrate that the optimization framework helps to robustly derive multiple feasible non-dominated solutions with satisfactory convergence, diversity and extremity in one single run for the case studied.

Phasing Delta-V for transfers from Sun–Earth halo orbits to the Moon

Inspired by successful extended missions such as the ISEE-3, an investigation for the extended mission that involves a lunar encounter following a Sun-Earth halo orbit mission is considered valuable. Most previous studies present the orbit-to-orbit transfers where the lunar phase is not considered. Intended for extended missions, the present work aims to solve for the minimum phasing ∆V for various initial lunar phases. Due to the solution multiplicity of the two-point boundary value problem, the general constrained optimization algorithm that does not identify multiple feasible solutions is shown to miss minima. A two-step differential corrector with a two-body Lambert solver is developed for identifying multiple solutions. The minimum ∆V associated with the short-way and long-way approaches can be recovered. It is acquired that the required ∆V to cover all initial lunar phases is around 45m/s for the halo orbit with out-of-plane amplitude Az greater than 3.5×105km, and 14m/s for a small halo orbit with Az=1×105km. In addition, the paper discusses the phasing planning based on the ∆V result and the shift of lunar phase with halo orbit revolution.