Research on Intellectualized Location of Coal Gangue Logistics Nodes Based on Particle Swarm Optimization and Quasi-Newton Algorithm

The optimization of an integrated coal gangue system of mining, dressing, and backfilling in deep underground mining is a multi-objective and complex decision-making process, and the factors such as spatial layout, node location, and transportation equipment need to be considered comprehensively. In order to realize the intellectualized location of the nodes for the logistics and transportation system of underground mining and dressing coal and gangue, this paper establishes the model of the logistics and transportation system of underground mining and dressing coal gangue, and analyzes the key factors of the intellectualized location for the logistics and transportation system of coal and gangue, and the objective function of the node transportation model is deduced. The PSO–QNMs algorithm is proposed for the solution of the objective function, which improves the accuracy and stability of the location selection and effectively avoids the shortcomings of the PSO algorithm with its poor local detailed search ability and the quasi-Newton algorithm with its sensitivity to the initial value. Comparison of the particle swarm and PSO–QNMs algorithm outputs for the specific conditions of the New Julong coal mine, as an example, shows that the PSO–QNMs algorithm reduces the complexity of the calculation, increases the calculation efficiency by eight times, saves 42.8% of the cost value, and improves the efficiency of the node selection of mining–dressing–backfilling systems in a complex underground mining environment. The results confirm that the method has high convergence speed and solution accuracy, and provides a fundamental basis for optimizing the underground coal mine logistics system. Based on the research results, a node siting system for an integrated underground mining, dressing, and backfilling system in coal mines (referred to as MSBPS) was developed.

Accelerating Symmetric Rank-1 Quasi-Newton Method with Nesterov’s Gradient for Training Neural Networks

Gradient-based methods are popularly used in training neural networks and can be broadly categorized into first and second order methods. Second order methods have shown to have better convergence compared to first order methods, especially in solving highly nonlinear problems. The BFGS quasi-Newton method is the most commonly studied second order method for neural network training. Recent methods have been shown to speed up the convergence of the BFGS method using the Nesterov’s acclerated gradient and momentum terms. The SR1 quasi-Newton method, though less commonly used in training neural networks, is known to have interesting properties and provide good Hessian approximations when used with a trust-region approach. Thus, this paper aims to investigate accelerating the Symmetric Rank-1 (SR1) quasi-Newton method with the Nesterov’s gradient for training neural networks, and to briefly discuss its convergence. The performance of the proposed method is evaluated on a function approximation and image classification problem.

One-Step Estimation with Scaled Proximal Methods

We study statistical estimators computed using iterative optimization methods that are not run until completion. Classical results on maximum likelihood estimators (MLEs) assert that a one-step estimator (OSE), in which a single Newton-Raphson iteration is performed from a starting point with certain properties, is asymptotically equivalent to the MLE. We further develop these early-stopping results by deriving properties of one-step estimators defined by a single iteration of scaled proximal methods. Our main results show the asymptotic equivalence of the likelihood-based estimator and various one-step estimators defined by scaled proximal methods. By interpreting OSEs as the last of a sequence of iterates, our results provide insight on scaling numerical tolerance with sample size. Our setting contains scaled proximal gradient descent applied to certain composite models as a special case, making our results applicable to many problems of practical interest. Additionally, our results provide support for the utility of the scaled Moreau envelope as a statistical smoother by interpreting scaled proximal descent as a quasi-Newton method applied to the scaled Moreau envelope.

A new limited memory method for unconstrained nonlinear least squares

This paper suggests a new limited memory trust region algorithm for large unconstrained black box least squares problems, called LMLS. Main features of LMLS are a new non-monotone technique, a new adaptive radius strategy, a new Broyden-like algorithm based on the previous good points, and a heuristic estimation for the Jacobian matrix in a subspace with random basis indices. Our numerical results show that LMLS is robust and efficient, especially in comparison with solvers using traditional limited memory and standard quasi-Newton approximations.