A Penalized Likelihood Method for Classification With Matrix-Valued Predictors

We propose a penalized likelihood method to fit the linear discriminant analysis model when the predictor is matrix valued. We simultaneously estimate the means and the precision matrix, which we assume has a Kronecker product decomposition. Our penalties encourage pairs of response category mean matrix estimators to have equal entries and also encourage zeros in the precision matrix estimator. To compute our estimators, we use a blockwise coordinate descent algorithm. To update the optimization variables corresponding to response category mean matrices, we use an alternating minimization algorithm that takes advantage of the Kronecker structure of the precision matrix. We show that our method can outperform relevant competitors in classification, even when our modeling assumptions are violated. We analyze three real datasets to demonstrate our method’s applicability. Supplementary materials, including an R package implementing our method, are available online.     

An Asynchronous Distributed Expectation Maximization Algorithm for Massive Data: The DEM Algorithm

The family of expectation--maximization (EM) algorithms provides a general approach to fitting flexible models for large and complex data. The expectation (E) step of EM-type algorithms is time-consuming in massive data applications because it requires multiple passes through the full data. We address this problem by proposing an asynchronous and distributed generalization of the EM called the distributed EM (DEM). Using DEM, existing EM-type algorithms are easily extended to massive data settings by exploiting the divide-and-conquer technique and widely available computing power, such as grid computing. The DEM algorithm reserves two groups of computing processes called workers and managers for performing the E step and the maximization step (M step), respectively. The samples are randomly partitioned into a large number of disjoint subsets and are stored on the worker processes. The E step of DEM algorithm is performed in parallel on all the workers, and every worker communicates its results to the managers at the end of local E step. The managers perform the M step after they have received results from a γ-fraction of the workers, where γ is a fixed constant in (0, 1]. The sequence of parameter estimates generated by the DEM algorithm retains the attractive properties of EM: convergence of the sequence of parameter estimates to a local mode and linear global rate of convergence. Across diverse simulations focused on linear mixed-effects models, the DEM algorithm is significantly faster than competing EM-type algorithms while having a similar accuracy. The DEM algorithm maintains its superior empirical performance on a movie ratings database consisting of 10 million ratings. Supplementary material for this article is available online.     

Improved lower bounds for the Split Delivery Vehicle Routing Problem

This paper presents an algorithm to obtain lower bounds for the Split Delivery Vehicle Routing Problem. An extended formulation over a large set of variables is provided and valid inequalities are identified. The algorithm combined column and cut generation and improved the best known lower bounds for all instances from the literature. Some reasonably sized instances are solved to optimality for the first time.     

Hilbert空间中的不可微最优化问题的基路径增量目标水平算法

主要研究了Hilbert空间中的一类不可微最优化问题的基路径增量目标水平算法.证明了当约束集合为有界集时,问题的最优解集非空,且这时通过算法生成的迭代点列是弱收敛于最优解的..     

Genetic-algorithm-based simulation optimization considering a single stochastic constraint

In this paper, we consider the discrete optimization via simulation problem with a single stochastic constraint. We present two genetic-algorithm-based algorithms that adopt different sampling rules and searching mechanisms, and thus deliver different statistical guarantees. The first algorithm offers global convergence as the simulation effort goes to infinity. However, the algorithm’s finite-time efficiency may be sacrificed to maintain this theoretically appealing property. We therefore propose the second heuristic algorithm that can take advantage of the desirable mechanics of genetic algorithm, and might be better able to find near-optimal solutions in a reasonable amount of time. Empirical studies are performed to compare the efficiency of the proposed algorithms with other existing ones.     

Many-to-many location-routing with inter-hub transport and multi-commodity pickup-and-delivery

In this paper, we consider a variant of the many-to-many location-routing problem, where hub facilities have to be located and customers with either pickup or delivery demands have to be combined in vehicle routes. In addition, several commodities and inter-hub transport processes are taken into account. A practical application of the problem can be found in the timber-trade industry, where companies provide their services using hub-and-spoke networks. We present a mixed-integer linear model for the problem and use CPLEX 12.4 to solve small-scale instances. Furthermore, a multi-start procedure based on a fix-and-optimize scheme and a genetic algorithm are introduced that efficiently construct promising solutions for medium- and large-scale instances. A computational performance analysis shows that the presented methods are suitable for practical application.     

A multi-start algorithm for a balanced real-world Open Vehicle Routing Problem

The aim of this paper is to solve a real-world problem proposed by an international company operating in Spain and modeled as a variant of the Open Vehicle Routing Problem in which the makespan, i.e., the maximum time spent on the vehicle by one person, must be minimized. A competitive multi-start algorithm, able to obtain high quality solutions within reasonable computing time is proposed. The effectiveness of the algorithm is analyzed through computational testing on a set of 19 school-bus routing benchmark problems from the literature, and on 9 hard real-world problem instances.     

基于图论和遗传算法的终端扇区划分方法

为了均衡终端区扇区的工作负荷,保障扇区边界的合理性,研究了终端扇区的划分方法.针对建立的扇区划分数学模型,提出了3阶段的划分方法.首先,采用voronoi图和遗传算法完成初始划分,实现均衡负荷的目标;其次,提出了基于voronoi图和基于maklink图的2种扇区二次划分方法,满足最小飞行时间及最小距离约束;最后,应用分段线性拟合的方法消除扇区边界的锯齿状,以及满足扇区凸形约束.以广州终端为例进行了仿真计算.应用提出的方法,给出了2种划分结果,都能够使得各扇区的工作负荷在2880s以内,差值不超过350s,扇区边界较为平滑,且计算时间明显减少.仿真计算结果说明方法是可行和有效的,也为使用者提供了灵活的选择.     

Bird mating optimizer: An optimization algorithm inspired by bird mating strategies

Thanks to their simplicity and flexibility, evolutionary algorithms (EAs) have attracted significant attention to tackle complex optimization problems. The underlying idea behind all EAs is the same and they differ only in technical details. In this paper, we propose a novel version of EAs, bird mating optimizer (BMO), for continuous optimization problems which is inspired by mating strategies of bird species during mating season. BMO imitates the behavior of bird species metaphorically to breed broods with superior genes for designing optimum searching techniques. On a large set of unimodal and multimodal benchmark functions, BMO represents a competitive performance to other EAs.