Solution of Linear Programming Problems using a Neural Network with Non-Linear Feedback

This paper presents a recurrent neural circuit for solving linear programming problems. The objective is to minimize a linear cost function subject to linear constraints. The proposed circuit employs non-linear feedback, in the form of unipolar comparators, to introduce transcendental terms in the energy function ensuring fast convergence to the solution. The proof of validity of the energy function is also provided. The hardware complexity of the proposed circuit compares favorably with other proposed circuits for the same task. PSPICE simulation results are presented for a chosen optimization problem and are found to agree with the algebraic solution. Hardware test results for a 2–variable problem further serve to strengthen the proposed theory

CoCalc as a Learning Tool for Neural Network Simulation in the Special Course "Foundations of Mathematic Informatics"

The role of neural network modeling in the learning content of the special course "Foundations of Mathematical Informatics" was discussed. The course was developed for the students of technical universities - future IT-specialists and directed to breaking the gap between theoretic computer science and it's applied applications: software, system and computing engineering. CoCalc was justified as a learning tool of mathematical informatics in general and neural network modeling in particular. The elements of technique of using CoCalc at studying topic "Neural network and pattern recognition" of the special course "Foundations of Mathematic Informatics" are shown. The program code was presented in a CoffeeScript language, which implements the basic components of artificial neural network: neurons, synaptic connections, functions of activations (tangential, sigmoid, stepped) and their derivatives, methods of calculating the network's weights, etc. The features of the Kolmogorov-Arnold representation theorem application were discussed for determination the architecture of multilayer neural networks. The implementation of the disjunctive logical element and approximation of an arbitrary function using a three-layer neural network were given as an examples. According to the simulation results, a conclusion was made as for the limits of the use of constructed networks, in which they retain their adequacy. The framework topics of individual research of the artificial neural networks is proposed.Comment: 16 pages, 3 figures, Proceedings of the 13th International Conference on ICT in Education, Research and Industrial Applications. Integration, Harmonization and Knowledge Transfer (ICTERI, 2018

Maximum Resilience of Artificial Neural Networks

The deployment of Artificial Neural Networks (ANNs) in safety-critical applications poses a number of new verification and certification challenges. In particular, for ANN-enabled self-driving vehicles it is important to establish properties about the resilience of ANNs to noisy or even maliciously manipulated sensory input. We are addressing these challenges by defining resilience properties of ANN-based classifiers as the maximal amount of input or sensor perturbation which is still tolerated. This problem of computing maximal perturbation bounds for ANNs is then reduced to solving mixed integer optimization problems (MIP). A number of MIP encoding heuristics are developed for drastically reducing MIP-solver runtimes, and using parallelization of MIP-solvers results in an almost linear speed-up in the number (up to a certain limit) of computing cores in our experiments. We demonstrate the effectiveness and scalability of our approach by means of computing maximal resilience bounds for a number of ANN benchmark sets ranging from typical image recognition scenarios to the autonomous maneuvering of robots.Comment: Timestamp research work conducted in the project. version 2: fix some typos, rephrase the definition, and add some more existing wor

Constraint satisfaction adaptive neural network and heuristics combined approaches for generalized job-shop scheduling

Copyright @ 2000 IEEEThis paper presents a constraint satisfaction adaptive neural network, together with several heuristics, to solve the generalized job-shop scheduling problem, one of NP-complete constraint satisfaction problems. The proposed neural network can be easily constructed and can adaptively adjust its weights of connections and biases of units based on the sequence and resource constraints of the job-shop scheduling problem during its processing. Several heuristics that can be combined with the neural network are also presented. In the combined approaches, the neural network is used to obtain feasible solutions, the heuristic algorithms are used to improve the performance of the neural network and the quality of the obtained solutions. Simulations have shown that the proposed neural network and its combined approaches are efficient with respect to the quality of solutions and the solving speed.This work was supported by the Chinese National Natural Science Foundation under Grant 69684005 and the Chinese National High-Tech Program under Grant 863-511-9609-003, the EPSRC under Grant GR/L81468