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Memristor Neural Networks for Linear and Quadratic programming problems

IEEE TRANSACTIONS ON CYBERNETICS 2022年第3期52卷 1822-1835页

作者： Di Marco, Mauro Forti, Mauro Pancioni, Luca Innocenti, Giacomo Tesi, Alberto Univ Siena Dept Informat Engn & Math I-53100 Siena Italy Univ Florence Dept Informat Engn I-50139 Florence Italy

This article introduces a new class of memristor neural networks (NNs) for solving, in real-time, quadratic programming (QP) and linear programming (LP) problems. The networks, which are called memristor programming NNs (MPNNs), use a set of filamentary-type memristors with sharp memristance transitions for constraint satisfaction and an additional set of memristors with smooth memristance transitions for memorizing the result of a computation. The nonlinear dynamics and global optimization capabilities of MPNNs for QP and LP problems are thoroughly investigated via a recently introduced technique called the flux-charge analysis method. One main feature of MPNNs is that the processing is performed in the fluxcharge domain rather than in the conventional voltage-current domain. This enables exploiting the unconventional features of memristors to obtain advantages over the traditional NNs for QP and LP problems operating in the voltage-current domain. One advantage is that operating in the flux-charge domain allows for reduced power consumption, since in an MPNN, voltages, currents, and, hence, power vanish when the quick analog transient is over. Moreover, an MPNN works in accordance with the fundamental principle of in-memory computing, that is, the nonlinearity of the memristor is used in the dynamic computation, but the same memristor is also used to memorize in a nonvolatile way the result of a computation.

关键词： Global optimization memristor neural networks (NNs) nonsmooth analysis programming problems stability

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Convergence of neural networks for programming problems via a nonsmooth Lojasiewicz inequality

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IEEE TRANSACTIONS ON NEURAL NETWORKS 2006年第6期17卷 1471-1486页

作者： Forti, Mauro Nistri, Paolo Quincampoix, Marc Univ Siena Dipartimento Ingn Informaz I-53100 Siena Italy Univ Bretagne Occidentale Math Lab F-29285 Brest France

This paper considers a class of neural networks (NNs) for solving linear programming (LP) problems, convex quadratic programming (QP) problems, and nonconvex QP problems where an indefinite quadratic objective function is subject to a set of affine constraints. The NNs are characterized by constraint neurons modeled by ideal diodes with vertical segments in their characteristic, which enable to implement an exact penalty method. A new method is exploited to address convergence of trajectories, which is based on a nonsmooth Lojasiewicz inequality for the generalized gradient vector field describing the NN dynamics. The method permits to prove that each forward trajectory of the NN has finite length, and as a consequence it converges toward a singleton. Furthermore, by means of a quantitative evaluation of the Lojasiewicz exponent at the equilibrium points, the following results on convergence rate of trajectories are established: 1) for nonconvex QP problems, each trajectory is either exponentially convergent, or convergent in finite time, toward a singleton belonging to the set of constrained critical points;2) for convex QP problems, the same result as in 1) holds;moreover, the singleton belongs to the set of global minimizers;and 3) for LP problems, each trajectory converges in finite time to a singleton belonging to the set of global minimizers. These results, which improve previous results obtained via the Lyapunov approach, are true independently of the nature of the set of equilibrium points, and in particular they hold even when the NN possesses infinitely many nonisolated equilibrium points.

关键词： convergence in finite time exponential convergence generalized gradient Lojasiewicz inequality neural networks (NNs) programming problems

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THE SADDLE THEOREM FOR MULTIOBJECTIVE GENERALIZED FRACTIONAL programming problems WITH SET FUNCTIONS

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JOURNAL OF APPLIED MATHEMATICS AND COMPUTING 2006年第1-2期22卷 181-191页

作者： Liu, Sanming Feng, Enmin Jiangsu Univ Sci & Technol Dept Math & Phys Zhenjiang 212003 Peoples R China Dalian Univ Technol Dept Appl Math Dalian 116023 Peoples R China

In this paper, multiobjective generalized fractional programming problems with set functions are considered, in which objective functions are maximum of finite fractional set functions. At first, optimality conditions... 详细信息

关键词： Set functions multiobjective generalized fractional programming problems efficient solution Geoffrion properly efficient solution optimality conditions saddle theorem

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An Effective Approach of Evaluating Cognitive Weight and Equivalent Distribution of programming problems 2

An Effective Approach of Evaluating Cognitive Weight and Equ...

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2nd International Conference on Sustainable Technologies for Industry 4.0 (STI)

作者： Bashir, Golam Md Muradul Muhtasim, Muhammad Ahmed, Md Monsur Patuakhali Sci & Technol Univ Fac Comp Sci & Engn Patuakhali Bangladesh

ISBN: (纸本)9781665404891

Equal distribution of programming problems among the students is so significant during the examination within limited times. But how could we determine that how student feels about whether a given program is either easy or difficult? So Complexity measurement according to their brain thinking capability is necessary. In this article, we have improved the approach of complexity measurement procedure that gives us more accurate value of cognitive weight which contract the constraints of existing measures. The idea of cognitive weight of any basic control structure is ethically based on the logical capacity of the human brain. As per our cognitive data gathering from various level of students, we have built up a new software tool using Java Standard Edition and MySQL for equivalent distribution of programming problems dependent on our developed algorithm. The problems is categorized according to three difficulty level (simple, medium, hard) for each level of students. This will help instructor allocate problems while maintaining an equivalent level of problems for students.

关键词： Cognitive Weights Basic Control Structures Weight Measurement Equivalent Distribution programming problems Java SE MySQL Database

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Classification of Strategies for Solving programming problems using AoI Sequence Analysis 19

Classification of Strategies for Solving Programming Problem...

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11th ACM Symposium On Eye Tracking Research and Applications (ETRA)

作者： Obaidellah, Unaizah Raschke, Michael Blascheck, Tanja Univ Malaya Kuala Lumpur Malaysia Blickshift Gmbh Stuttgart Germany INRIA Saclay France

ISBN: (纸本)9781450367097

This eye tracking study examines participants' visual attention when solving algorithmic problems in the form of programming problems. The stimuli consisted of a problem statement, example output, and a set of multiple-choice questions regarding variables, data types, and operations needed to solve the programming problems. We recorded eye movements of students and performed an Area of Interest (AoI) sequence analysis to identify reading strategies in terms of participants' performance and visual effort. Using classical eye tracking metrics and a visual AoI sequence analysis we identified two main groups of participants-effective and ineffective problem solvers. This indicates that diversity of participants' mental schemas leads to a difference in their performance. Therefore, identifying how participants' reading behavior varies at a finer level of granularity warrants further investigation.

关键词： Eye tracking visual analytics reading strategies programming problems

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Some programming problems for teaching foundations of group theory

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INTERNATIONAL JOURNAL OF MATHEMATICAL EDUCATION IN SCIENCE AND TECHNOLOGY 2014年第3期45卷 438-445页

作者： Shilin, I. A. Sholokhov Moscow State Univ Humanities Dept Math & Phys Moscow Russia Moscow Inst Aviat Technol Dept Math Simulat Moscow Russia

This paper contains some programming problems which can be suggested for students starting to learn group theory. These problems are related to important notations such as subgroup, coset, normal divisor, symmetric group, normalizer, centralizer, homomorphism and automorphism. Carefully selected problems provide a successful understanding of the basic themes of finite group theory.

关键词： finite group theory programming programming problems

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Cognitive Complexity: A Model for Distributing Equivalent programming problems

Cognitive Complexity: A Model for Distributing Equivalent Pr...

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International Conference on Electrical, Computer and Communication Engineering (ECCE)

作者： Dey, Samrat Kumar Tariq, S. S. M. Islam, Md. Shariful Bashir, Golam Md. Muradul Mil Inst Sci & Technol Dept CSE Dhaka Bangladesh BJIT Ltd Dhaka Bangladesh Dhaka Univ Engn & Technol Dept CSE Dhaka Bangladesh Patuakhali Sci & Technol Univ Dept CSE Patuakhali Bangladesh

ISBN: (纸本)9781509056279

Traditional distribution of programming problems seems to create dissatisfaction among students. To overcome this problem, complexity measurement of programming problems is necessary. Although software is the outcome of human ingenious activity, cognitive informatics plays a significant role in understanding its ultimate characteristics. In this article, we have proposed a software complexity measurement algorithm based on cognitive weight of basic control structure that shrink the limitations of existing measures. Cognitive weight concept of any basic control structure are morally based on the rational capacity of Human Brain. According to cognitive data, we have developed a new software tool using Java Standard Edition and MySQL to measure the cognitive complexity by following our developed algorithm. This software is structured and developed based on the outcome of our research data which is capable of determining the complexity value of several programming languages. This will assist the instructors allocating the problems among the learners by preserving the equivalent level of difficulty. Therefore, the developed complexity measurement tool will ensure the students to get problems with identical difficulty level for assessment.

关键词： cognitive weight complexity measurement equivalent distribution programming problems java SE MySQL database problems bank

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Grey interpolation approach for small time-lag samples based on grey dynamic relation analysis

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Journal of Systems Engineering and Electronics 2018年第1期29卷 105-115页

作者： WANG Junjie DANG Yaoguo XU Ning DING Song College of Economics and Management Nanjing University of Aeronautics and Astronautics College of Management Science and Engineering Nanjing Audit University

Given a non-equidistant sequence or an equidistant series with one or more outliers, a grey interpolation approach considering the time lags is established for producing the missing data or correcting the abnormal values. To accomplish this, a new grey incidence model, called the grey dynamic incidence model GDIM(t), is constructed for determining whether the factors are effective to the known factor and what the time lag is between a useful factor and the specified sequence. Based on the results of the GDIM(t) model, two programming problems are designed to obtain the upper and lower bounds of the unknown or abnormal values which are regarded as grey numbers. The solutions based on the particle swarm optimization(PSO) for the nonlinear programming problems are given. To explain how it can be used in practice, this new grey interpolation approach is applied to correct an abnormal value in the sequence of an agriculture environment problem.

关键词： grey interpolation grey relational analysis time lags programming problems

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A generalized computing paradigm based on artificial dynamic models for mathematical programming

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SOFT COMPUTING 2014年第8期18卷 1561-1573页

作者： Torelli, F. Vaccaro, A. Politecn Bari Dept Elect Engn I-70125 Bari Italy Univ Sannio Dept Engn I-82100 Benevento Italy

In this paper a novel computing paradigm aimed at solving non linear systems of equations and finding feasible solutions and local optima to scalar and multi objective optimizations problems is conceptualized. The underlying principle is to formulate a generic programming problem by a proper set of ordinary differential equations, whose equilibrium points correspond to the problem solutions. Starting from the Lyapunov theory, we will demonstrate that this artificial dynamic system could be designed to be stable with an exponential asymptotic convergence to equilibrium points. This important feature allows the analyst to overcome some of the inherent limitations of the traditional iterative solution algorithms that can fail to converge due to the highly nonlinearities of the first-order conditions. Besides we will demonstrate as the proposed paradigm could be applied to solve non linear equations systems, scalar and multi-objective optimization problems. Extensive numerical studies aimed at assessing the effectiveness of the proposed computing paradigm are presented and discussed.

关键词： Dynamic system theory Artificial models Non linear systems of equations Multiobjective programming problems

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Small-sample size problems solving based on incremental learning: an adaptive Bayesian quadrature approach

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APPLIED INTELLIGENCE 2023年第12期53卷 15174-15187页

作者： Feng, Yiding Feng, Xiang Yu, Huiqun East China Univ Sci & Technol Dept Comp Sci & Engn Shanghai 200237 Peoples R China Shanghai Engn Res Ctr Smart Energy Shanghai 200237 Peoples R China

When solving programming problems with objectives, we are often faced with the challenge of insufficient samples. And when new samples are generated, re-modeling based on historical and incremental samples is costly. Many Bayesian based approaches have been proposed to update the original models using newly coming samples which are called incremental learning. In this paper, we derive a calculation method of information value based on Bayesian quadrature technology, and use multi-start Adaptive Momentum (ADAM) stochastic gradient algorithm to design independent adaptive learning rates by computing the first-order moment and the second-order moment of the gradient then we propose a small-sample size problems solving based on incremental learning called Adaptive Bayesian Quadrature Approach (ABQA) We use a numerical validation experiment to verify the effectiveness of our approach, and then use two programming problems, shared bike system and newsvendor problem, to verify the effectiveness of our approach on incremental learning and small-samples size problems. In all these experiments, ABQA outperforms the benchmarks and state-of-the-art Bayesian algorithms. Performance and speed are improved by 2.8% and 8.6%, respectively.

关键词： Incremental learning Bayesian quadrature Small-sample size problems Multi-startADAM programming problems

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