The updating rule of the original discrete Hopfield neural network (DHNN) is based on gradient descent dynamics, which always leads to the local minima problem. In this paper, by introducing the idea of the simulated ...
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The updating rule of the original discrete Hopfield neural network (DHNN) is based on gradient descent dynamics, which always leads to the local minima problem. In this paper, by introducing the idea of the simulated annealing (SA) into the DHNN, we first propose an annealing HNN (AHNN) that permits temporary energy ascent to help the DHNN escape from local minima. Then, from a cooperative perspective, a population of the AHNN processes are simultaneously implemented and coupled by their acceptance probabilities, and thus a cooperative AHNN (CoAHNN) is proposed. The primary objective of the coupling in the CoAHNN is to create cooperative behavior via information exchange among neural networks. This objective helps in the decision of whether uphill moves will be accepted. In addition, coupling can provide information used online to guide the networks toward the global optimum. The CoAHNN is tested on 21 unconstrained binary quadratic programming problems (UBQP) with the size ranging from 3000 to 7000, and 48 maximum cut benchmark problems, a special case of the UBQP, with the size ranging from 512 to 3375. The UBQP consists in maximizing a quadratic 0-1 function. It is a well known NP-hard problem and is considered as a unified model for a variety of combinatorial optimization problems. Simulation results show that the CoAHNN is better than or competitive with other HNN based algorithms, metaheuristicalgorithms and state-of-the-art algorithms. (C) 2011 Elsevier Ltd. All rights reserved.
Certain shortcomings are described in the second order converse duality results in the recent work of (J. Zhang and B. Mond, Bull. Austral. Math. Soc. 55(1997) 29-44). Appropriate modifications are suggested.
Certain shortcomings are described in the second order converse duality results in the recent work of (J. Zhang and B. Mond, Bull. Austral. Math. Soc. 55(1997) 29-44). Appropriate modifications are suggested.
This paper deals with a regularity assumption for the mathematical programming problem in Banach spaces. The attractive feature of our constraint qualification is the fact that it can be considered as a condition on t...
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This paper deals with a regularity assumption for the mathematical programming problem in Banach spaces. The attractive feature of our constraint qualification is the fact that it can be considered as a condition on the active part only of the constraint, and that it is preserved under small perturbations. Moreover, we show that our condition is “almost” equivalent to the existence of a non-empty and weakly compact set of Lagrange multipliers. The main step in the proof of our results is a generalization of the open mapping theorem.
This paper explores the consequences for the l(1)-optimal controller of the dual linear programming problem having multiple solutions, for linear time-invariant single-input/single-output systems. When the dual proble...
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This paper explores the consequences for the l(1)-optimal controller of the dual linear programming problem having multiple solutions, for linear time-invariant single-input/single-output systems. When the dual problem has multiple solutions, all solutions yield the same set of optimal controllers. If these multiple solutions comprise an entire face of the constraint region, there is a single optimal controller. Thus, if the constraint region is two-dimensional, the primal and dual problems cannot both have multiple solutions. An example is given with a three-dimensional constraint region where both problems have multiple solutions.
In ITS, for students' success in carrying out their activities, it is essential to provide scaffolding, such as hints and feedback. Although using the ITS has increased student engagement and effort in the classro...
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ISBN:
(纸本)9783031328824;9783031328831
In ITS, for students' success in carrying out their activities, it is essential to provide scaffolding, such as hints and feedback. Although using the ITS has increased student engagement and effort in the classroom, some students have responded to the ITS's support facilities with an inappropriate behavior called gaming the system. Thus, in this article, we explore the phenomenon of gaming the system behavior, studying underlying factors related to automatically detecting when students game the system. We aim to develop a model for detecting gaming the system behavior in a computer programming student during problem-solving activities. Particularly, we have had special attention on testing the influence of variables such as (i) the student's level of belief and the system's level of belief in the difficulty level of the problem in detecting gaming the system;and (ii) partial submission of the problem associated with complete submission, in program form, in the detection of system manipulation. To conduct the detector's development, we developed an appropriate environment for data collection and preparation of these data to be used by supervised machine learning algorithms, allowing the detection of the behavior. The development of the detector involved training single and ensemble machine learning algorithms to classify the system's gaming behavior and obtain models with the best accuracy, including exploring, evaluating, and comparing different algorithms. The results show, considering the average of all algorithm results concerning all measures, the XGBoost ensemble classifier achieved the best performance.
In this work, we address automatic evaluation of the difficulty of programming problems or exercises. Typically the problems consist of both text description and accompanying figures. We collect a suitable dataset, in...
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ISBN:
(纸本)9783030883041;9783030883034
In this work, we address automatic evaluation of the difficulty of programming problems or exercises. Typically the problems consist of both text description and accompanying figures. We collect a suitable dataset, investigate the evaluation based on the text and the image data separately, as well as a combination of the two. The first results of this investigation are reported, together with the discussion and future work.
programming story problems requires an understanding of the requirements of the problem statement and how to write source code that satisfies them. However, some learners are unable to write source code that meets the...
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ISBN:
(纸本)9783031601248;9783031601255
programming story problems requires an understanding of the requirements of the problem statement and how to write source code that satisfies them. However, some learners are unable to write source code that meets the requirements of the problem statement. Therefore, we modeled the problem-solving process in programming story problems. The problem-solving process begins by organizing the information in the context of the problem statement, thinking through the abstract operations necessary to find a solution, and defining the solution. In this study, we propose a learning support method and develop a learning support system that follows this problem-solving process.
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