Reverse Problem Research Articles

Volleyball premier league algorithm with ACO and ALNS for simultaneous pickup–delivery location routing problem

The reverse logistics problem, which involves customer returns and incurs high additional logistics costs, has become a topic of increasing interest. This problem is modeled as the location routing problem with simultaneous pickup and delivery under time constraints (LRPSPDTW), which is a more complex version of the location routing problem (LRP). Previous studies have shown that existing algorithms are unable to provide satisfactory solution accuracy for this problem. In order to address this, a novel algorithm called the hybrid volleyball premier league (HVPL) algorithm is proposed. Drawing inspiration from the competition mechanism of the original volleyball premier league (VPL) algorithm, the HVPL algorithm incorporates adaptive large neighborhood search (ALNS) and improved ant colony optimization (ACO) as sub-algorithms, allowing them to work together synergistically and strike a balance between exploration and exploitation. The learning and elimination phases of the VPL algorithm have been redesigned to enhance convergence speed. Furthermore, the Bellman’s algorithm has been enhanced to determine depot locations and construct vehicle paths for the solution. Prior to solving the LRPSPDTW problem, benchmark testing was conducted using 35 latest benchmark functions. Experimental results and Friedman mean rank test demonstrated that HVPL exhibits superior exploration and exploitation capabilities. HVPL was subsequently tested on 66 instances based on the modified Solomon’s benchmark and the NEO research group benchmarks, and the results showcased its outperformance over other methods in the majority of cases.

Multi-echelon sustainable reverse logistics network design with incentive mechanism for eco-packages

With the pollution caused by express packaging waste, eco-packages are being commonly used to promote a green supply chain. However, extant research has yet to address the efficacious reverse logistics network design problem while considering both economic and environmental consumption in the recycling process. In this study, a multi-echelon reverse logistics network is designed to collect eco-packages from customers, instead of door-to-door recycling by couriers. This study aims to solve the capacity location-routing problem in a reverse logistics network integrated with the incentive mechanism for customers, which is regarded as NP-hard. To avoid the combinatorial explosion, a multi-objective hybrid genetic algorithm-tabu search (MOHGATS) is developed to reduce search space and improve search speed by changing search strategies. Computational experiments are conducted to verify the proposed model and algorithm based on several test instances and a real-world case study. The impacts of the quantity of eco-packages, the incentive costs for customers, and the quantity and capacity of recycling stations on the reverse logistics network are explored from both economic and environmental perspectives, providing a reference for practical operation and promotion of eco-packages on a large scale.

The reverse selective balance center location problem on trees

The reverse selective balance center location problem on trees

210Pb-based dating of recent sediments with χ-mapping versions of the CFCS, CIC, CF and TERESA models

The 210Pb-based method allows for absolute age determination in recent sediments on the centennial scale. The most common sedimentary scenarios involve ideal deposition without any further redistribution. The conventional models apply to such conditions by adding specific assumptions that allow analytical formulations: constant flux (CF), constant initial concentration (CIC), and constant flux with constant sedimentation (CFCS). The χ-mapping models are presented as a novel methodological approach. They generate a large number (105 to 106) of potential solvers, consisting of sets of n (the number of slices in the core) values of initial activity concentrations, A0, and sedimentation rates, w. Empirical data serve to attract the solver that minimizes a χ function after encountering the best sorting along the core of the A0 and w values. The specific assumptions of the above models are reformulated in terms of the statistical distributions of A0 and w. The performance of the χ-mapping versions is demonstrated with a set of cores from the literature with independent chronologies. The main advantages compared to known analytical formulations are: i) χ-mapping provides a more robust fitting method. ii) It overcomes the problem of age reversals often found in the CIC model. iii) The CF model successfully applies to cores with unsteady and/or incomplete inventories. iv) The TERESA model (time estimates from random entries of sediments and activities), without analytical counterpart, is the only model that can manage continuous trends of change in the fluxes of unsupported 210Pb. The work discusses the conditions for compensating model errors in the chronologies, and the use of the palaeorecords of fluxes, A0 and w. The methodology can be extended to other assumptions (models) and provides novel and insightful views on the 210Pb-based dating of recent sediments.

PGSL: A probabilistic graph diffusion model for source localization

Source localization, as a reverse problem of the graph diffusion, bears paramount significance for a multitude of applications, such as tracking social rumors, detecting computer viruses, and finding epidemic spreaders. However, the innate uncertainty of the diffusion process complicates this task — different source nodes can result in similar or identical diffusions over time, making the source localization task a complex, ill-posed problem. Most existing solutions utilize deterministic techniques and therefore cannot model the diffusion uncertainty of source nodes. Moreover, current probabilistic approaches are inefficient to conduct smooth transformations with variational inference. To overcome these limitations, we propose a probabilistic framework using normalizing flows with invertible transformations and novel objective optimization methods to explicitly model the uncertainty of the diffusion sources. Moreover, graph neural networks are leveraged to encapsulate propagation patterns between the observed diffusion and sources of high uncertainty. Extensive experiments conducted on six distinct networks demonstrate the effectiveness of our model over strong baselines, up to 11.8% and 8.2% improvements in terms of F1 and AUC, respectively, on Twitter dataset under real-world diffusion.

A static memory sparse spectral method for time-fractional PDEs

We discuss a method which provides accurate numerical solutions to fractional-in-time partial differential equations posed on [0,T]×Ω with Ω⊂Rd without the excessive memory requirements associated with the nonlocal fractional derivative operator. Our approach combines recent advances in the development and utilization of multivariate sparse spectral methods as well as fast methods for the computation of Gauss quadrature nodes with recursive non-classical methods for the Caputo fractional derivative of general fractional order α>0. An attractive feature of the method is that it has minimal theoretical overhead when using it on any domain Ω⊂Rd on which an orthogonal polynomial basis is available. We discuss the memory requirements of the method, present several numerical experiments demonstrating the method's performance in solving time-fractional PDEs on intervals, triangles and disks and derive error bounds which suggest sensible convergence strategies. As an important model problem for this approach we consider a type of wave equation with time-fractional dampening related to acoustic waves in viscoelastic media with applications in the physics of medical ultrasound and outline future research steps required to use such methods for the reverse problem of image reconstruction from sensor data.

Numerical simulation of the distribution of reverse currents in a practical alkaline water electrolysis stack immediately after electrolysis

In alkaline water electrolysis, reverse currents are reported to occur after rapid cell voltage change due to the electrodes oxidation state difference and such currents lead to electrodes degradation. The reverse current problems can be more severe in practical applications with larger electrode sizes and larger numbers of cells. In this study, reverse current with changes in the oxidation state of electrodes and potential distribution after sudden shutdown were analyzed based on a multi-physical simulation considering an electronic and ionic conduction in practical-scale. The effects of stack height, number of cells, and ionic resistance through the manifold on the reverse current distribution were investigated. The numerical results reveal that, especially under the condition of low manifold resistance and higher stack height, the discharge current extremely concentrated near the bottom of the edge electrode. This information is important for future stack development because this current concentration can cause severe stack degradation.

Integrated Approach to Obtain Gas Flow Velocity in Convection Reflow Soldering Oven

The nozzle-matrix gas flow velocity has a great influence on the accuracy of the temperature field of a printed circuit board assembly (PCBA) during the hot air convection reflow soldering process. This paper proposes a new approach that integrates the theoretical calculation, numerical simulation and an experimental test to accurately determine the nozzle-matrix gas flow velocity. First, the temperature profile of the aluminum alloy thin plate in convection reflow ovens is measured using a Wiken tester. Second, the nozzle-matrix gas flow velocity is theoretically calculated with the Martin formula. The computational fluid dynamic (CFD)simulation is performed according to the Icepak code, where a single oven chamber model is established to represent the 10 zones of soldering ovens to reduce computational resources considering the supry of the soldering ovens. The simulated temperature profile of the aluminum alloy thin plate is obtained and the specific response surface model (RSM) is established to represent the deviation between the simulated temperature and the measured temperature. Finally, based on reverse problem analysis, non-linear programming by quadratic Lagrangian (NLPQL) is used to solve the mathematical optimization model with the objective of minimizing the temperature deviation to obtain the corrected nozzle-matrix gas flow velocity. To validate the accuracy, the temperature test and the modeling using the corrected gas flow velocity for a new PCBA component for the soldering ovens is conducted separately. The temperature comparison between the simulation and the test shows that the maximum temperature deviation is within 10 °C. This provides evidence that the nozzle-matrix gas flow velocity obtained by the new approach is accurate and effective.

Horizontally Aligned Zn Crystals Deposition with 1T VSe2 Functional Layer for Dendrite-Free Zn Metal Anodes

To fulfill the high requirement for high-energy-density storage, Zn ions batteries (ZIBs) has been garnering great scientific attention and considered the promising candidate due to the moderate redox potential, high safety and reasonable cost. However, the problem of the inferior reversibility and limited-service period owing to the issues of side reactions and Zn dendrites hinder its application. In our study, the hexagonal 1T VSe2, owns metallic appearance, was used as the zincophilic film to replace the conventional metal and graphene-based matrix for hexagonal closest packed (HCP) typed Zn metal electrodeposition in ZIBs. Our experimental results discovers that 1T VSe2/Zn anode is beneficial to regulating Zn crystal morphology from randomly oriented to horizontally (002)-oriented plate-like. Combining with computational modelling, the early stage of Zn nucleation and morphological evolution is investigated from atomistic to meso scale. VSe2 substrate exhibits higher adsorption energy (-0.54 eV) with Zn, contrasting with graphene (-0.38 eV) and pure Zn (-0.48 eV) based on the density functional theory (DFT) calculations. And classical molecular dynamic (MD) simulations reveal the plate-like Zn electrodeposits undergo a reorientation transition with a higher fraction of the (002) facet due to the rapid adatom diffusion coefficient, which effectively prohibits the dendrite formation. The symmetric cell with modified electrodes shows an ultra-stable cyclic life with 50 mV overpotential up to 2500 cycles in the condition of 1 mA cm-2 and 1 mAh cm-2.

An improved TOPSIS-based rank preservation approach for hesitant fuzzy information processing

In this study, a novel approach based on the reduction of the attribution and the rank preservation is analyzed, which intends to solve the issue of multi-attribute decision making (MADM) with the hesitant fuzzy information. Firstly, several new concepts are shown to simplify the representation of hesitant fuzzy information, such as single point fuzzification estimated value, and single point fuzzification weighted Euclidean distance. Secondly, a new improved HF-TOPSIS method based on the overall situation and these new concepts are put forward, in which the positive and negative ideal solutions are fixed to calculate the complex hesitant fuzzy decision process. The proposed method in this paper achieves the purpose of compression of the complex hesitant fuzzy information, and the calculation is relatively simple and easy to operate. Finally, two examples are presented to test and verify the credibility and effectiveness of the TOPSIS-Based rank preservation approach, which can achieve the consistency of results before and after evaluation, as well as ensuring rank preservation, while other HF-TOPSIS methods may cause rank reversal problems.

A new high voltage gain DC‐DC converter based on active switched‐inductor technique

SummaryThis article proposes a brand‐new high voltage gain step‐up DC‐DC converter through the amalgamation of active switched‐inductors (A‐SL) and a coupled‐inductor (CL) unit. This topology stands out due to its capacity to achieve noteworthy high voltage amplification employing a lesser amount of components when put in contrast to other comparable topologies. The voltage stress across the switches is low, which enables the utilization of low‐voltage rating switches to elevate efficiency. Moreover, the division of the input current between the switches of the converter enables the power dissipation to be diminished. The CL is utilized in a way that if the turn ratio of its windings is lessened, the voltage boost will be augmented. Furthermore, the leakage energy is recycled through the output diode; therefore, problems such as voltage spikes across the switches do not occur. Moreover, the output diode turns off naturally without reverse recovery problems. The switching pattern of the converter is simple, and both switches are driven simultaneously, and the converter can be controlled using a simple controller in a closed‐loop control method. In addition, the duty cycle range has no limitations. The operation principle and the steady‐state analysis of the proffered converter are discussed in detail for CCM and DCM. The design considerations and efficiency analysis are provided, followed by small‐signal modeling and controller design. Moreover, to evaluate the performance of the proffered converter among other topologies, a comparison study is conducted in terms of voltage gain, total device count, and voltage tension on the power switches and diodes. Finally, a 200–300 W, 28/400 V lab‐based prototype is implemented and tested to validate the analysis.

Application of multi-criteria decision-making methods in the selection of additive manufacturing materials for solid ankle foot orthoses

The present study aims to focus on material selection using FDM for solid ankle foot orthoses, a problem that has not been adequately addressed in previous studies. To address this issue, the present case study employs, for the first time, a combination of recently developed and other Multi-Criteria Decision-Making (MCDM) methods, including Simple Weighted Sum Product Method (WISP), Measurement Alternatives and Ranking According to Compromise Solution (MARCOS) and Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS). This study evaluates seven different materials based on eleven carefully selected criteria, which reflect the essential properties required for SAFOs fabrication using FDM. The criteria weights are determined based on the analytical hierarchy process (AHP). The results of above methods reveal that the most suitable material selected for SAFOs is polylactic acid (PLA) followed by nylon and polycarbonate. Additionally, the study examines the rank reversal problem and find that AHP-MARCOS is stable in performance while AHP-WISP and AHP-TOPSIS suffer rank reversal problems. This research provides valuable guidance for material selection in SAFOs fabrication using FDM and is expected to assist researchers and clinicians who may lack the necessary expertise in selecting appropriate materials for SAFOs and analysing their outcomes.

Searching for explanations of black-box classifiers in the space of semantic queries

Deep learning models have achieved impressive performance in various tasks, but they are usually opaque with regards to their inner complex operation, obfuscating the reasons for which they make decisions. This opacity raises ethical and legal concerns regarding the real-life use of such models, especially in critical domains such as in medicine, and has led to the emergence of the eXplainable Artificial Intelligence (XAI) field of research, which aims to make the operation of opaque AI systems more comprehensible to humans. The problem of explaining a black-box classifier is often approached by feeding it data and observing its behaviour. In this work, we feed the classifier with data that are part of a knowledge graph, and describe the behaviour with rules that are expressed in the terminology of the knowledge graph, that is understandable by humans. We first theoretically investigate the problem to provide guarantees for the extracted rules and then we investigate the relation of “explanation rules for a specific class” with “semantic queries collecting from the knowledge graph the instances classified by the black-box classifier to this specific class”. Thus we approach the problem of extracting explanation rules as a semantic query reverse engineering problem. We develop algorithms for solving this inverse problem as a heuristic search in the space of semantic queries and we evaluate the proposed algorithms on four simulated use-cases and discuss the results.

A Soft-Switching Bridgeless Buck-Boost Power Factor Correction Converter With Simple Auxiliary Circuit and Low Input Current THD

In this paper, a new bridgeless (BL) buck-boost power factor correction (PFC) converter using pulse width modulation (PWM) control is presented. The introduced structure operates in discontinuous conduction mode (DCM) to achieve the sinusoidal form of the input current inherently. The proposed converter utilizes a simple zero voltage transition (ZVT) circuit in which the auxiliary switch is turned ON and OFF under zero current switching (ZCS) condition, and the main switches turn ON and OFF under zero voltage switching (ZVS). Moreover, all diodes are turned OFF under ZCS condition, and the reverse recovery problem is solved. By reducing the number of semiconductor elements in the current flow path, conduction loss is minimized. Also, the proposed structure utilizes only one magnetic element. The above-mentioned advantages along with a low total harmonic distortion (THD) and high efficiency are the main benefits of the proposed structure compared to previous topologies. In addition, unlike the BL-buck converter, the input current dead angle is omitted without adding any extra components. Finally, a 500 W-100 kHz prototype at 90-265 Vrms input and 96 V output is implemented to verify the theoretical analysis and it illustrates the efficiency of 97.35 % and the input current THD is about 2.7 % at 220Vrms input voltage.

How do students solve reversible thinking problems in mathematics?

Reversible thinking is a cognitive activity in finding a solution to a problem by arranging the direction of logical thinking from the end to the starting point. Reversible thinking requires a student to think logically in two ways. Therefore, reversible thinking influences students' success in solving problems. This study aims to identify students' thinking processes in solving problems that require reversible thinking ability. This research was conducted on junior high school students in Bandung, West Java, Indonesia, using test instruments, interviews, and documentation studies. The tests given consisted of two types of problems, including tests on forward-thinking problems and tests on reversible thinking problems. The research subjects were students with high average mathematics scores in their class. The study found that students could answer the tests on forward-thinking problem-solving very well but could not work on similar questions with the backward-thinking process. Based on the interview results, one of the causes for the need for more backward-thinking ability is the limited learning resources or context when students first learn the concept.

Classification and decomposition of quaternionic projective transformations

We consider the projective linear group PSL(3,H). We have investigated the reversibility problem in this group and use the reversibility to offer an algebraic characterization of the dynamical types of PSL(3,H). We further decompose elements of SL(3,H) as products of simple elements, where an element g in SL(3,H) is called simple if it is conjugate to an element of SL(3,R). We have also revisited real projective transformations and following Goldman's ideas, have offered a complete classification for elements of SL(3,R).

A Physically‐Based Reverse‐Stage Routing Model Considering Lateral Flow for Establishing Normal Rating Curves at Ungauged Upstream River Sections

AbstractMany of the world‐rivers are often ungauged or poorly gauged due to inadequate streamflow monitoring networks. Even with the limited available monitoring stations, only a few of them monitor both stage and discharge data. But when there is a need for estimation of discharges at a gauging station, where only stage data is monitored, one may employ a reverse routing technique using the stage data monitored at a nearby downstream gauging station. This study develops a novel single‐parameter reverse‐stage routing (RSR) model based on the second‐order approximate water surface gradient governing equation to estimate stage and discharge at any scantily‐gauged upstream river section using the known stage information available at the downstream section. A novel criterion is also developed for checking the applicability of the RSR model. Reverse routing experiments, carried out by the RSR model using different hypothetical downstream stage hydrographs in a number of hypothetical trapezoidal and rectangular channel reaches to reproduce the benchmark upstream stage and discharge hydrographs, demonstrate the good performance of the RSR model with the Nash–Sutcliffe Efficiency >98%, absolute volume conservation error <1.5%, and an absolute error in peak ≤1%. Subsequently, the RSR model was tested for three real‐river case studies in India and Italy with good reproduction performances, and along with the development of the corresponding normal rating curves at the upstream river sections. The study results reveal that the parsimonious RSR model has good potential for solving reverse routing problems with stable numerical solutions for rivers under ungauged and scantily‐gauged scenarios.

A Probabilistic Graph Diffusion Model for Source Localization (Student Abstract)

Source localization, as a reverse problem of graph diffusion, is important for many applications such as rumor tracking, detecting computer viruses, and finding epidemic spreaders. However, it is still under-explored due to the inherent uncertainty of the diffusion process: after a long period of propagation, the same diffusion process may start with diverse sources. Most existing solutions utilize deterministic models and therefore cannot describe the diffusion uncertainty of sources. Moreover, current probabilistic approaches are hard to conduct smooth transformations with variational inference. To overcome the limitations, we propose a probabilistic framework using continuous normalizing flows with invertible transformations and graph neural networks to explicitly model the uncertainty of the diffusion source. Experimental results on two real-world datasets demonstrate the effectiveness of our model over strong baselines.

Description of K‐spaces by means of J‐spaces and the reverse problem in the limiting real interpolation

AbstractWe establish conditions under which K‐spaces in the limiting real interpolation involving slowly varying functions can be described by means of J‐spaces and we also solve the reverse problem. To this end, we prove several versions of the fundamental lemma of the real interpolation theory. We apply our results to obtain density theorems for the corresponding limiting interpolation spaces.

Controlling the physical field using the shape function technique

Abstract A field is described as a region under the influence of some physical force, such as electricity, magnetism, or heat. It is a continuous distribution in the space of continuous quantities. The characteristics of the field are that the values vary continuously between neighboring points. However, because of the continuous nature of the field, it is possible to approximate a physical field of interpolation operations to reduce the cost of sampling and simplify the calculation. This article introduces the modeling of the parametric intensity of physical fields in a general form based on the interpolation shape function technique. Besides the node points with sample data, there are interpolation points, whose accuracy depends significantly on the type of interpolation function and the number of node points sampled. Therefore, a comparative analysis of theoretical shape functions (TSFs) and experimental shape functions (ESFs) is carried out to choose a more suitable type of shape function when interpolating. Specifically, the temperature field is the quantity selected to apply, analyze, and conduct experiments. Theoretical computations, experiments, and comparisons of results have been obtained for each type of shape function in the same physical model under the same experimental conditions. The results show that ESF has an accuracy (error of 0.66%) much better than TSF (error of 10.34%). Moreover, the field model surveyed by a generalized reduced gradient algorithm allows for identifying points with the required parameter values presented in detail. The illustrated calculations on temperature field control in the article show that the solution for both forward and reverse problems can be determined very quickly with high accuracy and stability. Therefore, this technique is expected to be entirely feasible when applied to thermal control processes such as drying in paint technology, kilns, and heat dissipation in practice.