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It is well-known that, the classical gradient-descent-based neural network (CGNN) model is used widely for the time-invariant problem solving. However, it is an extremely common problem for the time varying cases in the practical engineering applications, while the CGNN effective neural solver for the time-variant problems. For this reason, in this article, an adaptive GNN (AGNN) is presented for the linear time variant matrix equation (LTVME) on-line solving based on Lyapunov theory. Theoretical analysis already verified that the presented AGNN model could achieve the correct state solution effectively. The simulated experiment results further validate that the state solution of the AGNN model could be convergent to the correct solution of the solved time variant problems in theory. [ABSTRACT FROM AUTHOR]

TSP(1,2) problem is a special case of the travelling salesperson problem which is NP-hard. Many heuristics including evolutionary algorithms (EAs) are proposed to solve the TSP(1,2) problem. However, we know little about the performance of the EAs for the TSP(1,2) problem. This paper presents an approximation analysis of the (1+1) EA on this problem. It is shown that both the (1+1) EA and (µ+ λ) EA can obtain 3/2 approximation ratio for this problem in expected polynomial runtime O(n3) and O((µ/λ)n3+ n) , respectively. Furthermore, we prove that the (1+1) EA can provide a much tighter upper bound than a simple ACO on the TSP(1,2) problem.

Abstract: A new kind of recurrent neural network is presented for solving the Lyapunov equation with time-varying coefficient matrices. Different from other neural-computation approaches, the neural network is developed by following Zhang et al.'s design method, which is capable of solving the time-varying Lyapunov equation. The resultant Zhang neural network (ZNN) with implicit dynamics could globally exponentially converge to the exact time-varying solution of such a Lyapunov equation. Computer-simulation results substantiate that the proposed recurrent neural network could achieve much superior performance on solving the Lyapunov equation with time-varying coefficient matrices, as compared to conventional gradient-based neural networks (GNN). [Copyright &y& Elsevier]

During the process of the general practical applications and scientific researches, time varying issues are an inescapable challenge to be tackled. In this article, a pre-defined finite-time zeroing neural networks (PDFT-ZNN) is devoted to solve the linear time-variant matrix equation (TVME) E (t) X (t) G (t) = D (t) within a finite time (FT), which contrasts with the general ZNN (G-ZNN) models with relatively long global convergence time. Moreover, the proposed PDFT-ZNN model's convergence time could be calculated in advance by adhering to the designed system parameters; this has nothing to do with the model's initial state. Additionally, after the convergence analysis, if the solution error is relative small, the simple and effective method is to introduce a linear item to accelerate the convergence speed, in comparison with only the power-type ZNN models. Theory-based analysis and simulation-based results further validate that, the neural state solved by the presented FT-ZNN model can reach the theory-based solution of E (t) X (t) G (t) = D (t) within the pre-defined finite time. • Th presented PDFT-ZNN model can predict the convergence time for the control system in advance. • A detailed theoretical analysis are carried out for the proposed PDFT-ZNN model. • The illustrative example is computed and examined for the proposed PDFT-ZNN model. [ABSTRACT FROM AUTHOR]