Modeling and control of complex dynamic systems: Applied mathematical aspects

The concept of complex dynamic systems arises in many varieties, including the areas of energy generation, storage and distribution, ecosystems, gene regulation and health delivery, safety and security systems, telecommunications, transportation networks, and the rapidly emerging research topics seeking to understand and analyse. Such systems are often concurrent and distributed, because they have to react to various kinds of events, signals, and conditions. They may be characterized by a system with uncertainties, time delays, stochastic perturbations, hybrid dynamics, distributed dynamics, chaotic dynamics, and a large number of algebraic loops. This special issue provides a platform for researchers to report their recent results on various mathematical methods and techniques for modelling and control of complex dynamic systems and identifying critical issues and challenges for future investigation in this field. This special issue amazingly attracted one-hundred-and eighteen submissions, and twenty-eight of them are selected through a rigorous review procedure

Improved formulations of the joint order batching and picker routing problem

Order picking is the process of retrieving ordered products from storage locations in warehouses. In picker-to-parts order picking systems, two or more customer orders may be grouped and assigned to a single picker. Then routing decision regarding the visiting sequence of items during a picking tour must be made. (J.Won and S.Olafsson 2005) found that solving the integrated problem of batching and routing enables warehouse managers to organize order picking operations more efficiently compared with solving the two problems separately and sequentially. We therefore investigate the mathematical programming formulation of this integrated problem. We present several improved formulations for the problem based on the findings of (Valle, Beasley, and da Cunha 2017), that can significantly improve computational results. More specifically, we reconstruct the connectivity constraints and generate new cutting planes in our branch-and-cut framework. We also discuss some problem properties by studying the structure of the graphical representation, and we present two types of additional constraints. We also consider the no-reversal case of this problem. We present efficient formulations by building different auxiliary graphs. Finally, we present computational results for publicly available test problems for single-block and multiple-block warehouse configurationsComment: 37 pages, 11 figures, 7 table

An adaptive dimension reduction algorithm for latent variables of variational autoencoder

Constructed by the neural network, variational autoencoder has the overfitting problem caused by setting too many neural units, we develop an adaptive dimension reduction algorithm that can automatically learn the dimension of latent variable vector, moreover, the dimension of every hidden layer. This approach not only apply to the variational autoencoder but also other variants like Conditional VAE(CVAE), and we show the empirical results on six data sets which presents the universality and efficiency of this algorithm. The key advantages of this algorithm is that it can converge the dimension of latent variable vector which approximates the dimension reaches minimum loss of variational autoencoder(VAE), also speeds up the generating and computing speed by reducing the neural units.Comment: 11 pages 12 figure