Model and Algorithm for Container Allocation Problem with Random Freight Demands in Synchromodal Transportation

This paper aims to investigate container allocation problem with random freight demands in synchromodal transportation network from container carriers’ perspective. Firstly, the problem is formulated as a stochastic integer programming model where the overall objective is to determine a container capacity allocation plan at operational level, so that the expected total transportation profit is maximized. Furthermore, by integrating simulated annealing with genetic algorithm, a problem-oriented hybrid algorithm with a novel gene encode method is designed to solve the optimization model. Some numerical experiments are carried out to demonstrate the effectiveness and efficiency of the proposed model and algorithm

Large Trajectory Models are Scalable Motion Predictors and Planners

Motion prediction and planning are vital tasks in autonomous driving, and recent efforts have shifted to machine learning-based approaches. The challenges include understanding diverse road topologies, reasoning traffic dynamics over a long time horizon, interpreting heterogeneous behaviors, and generating policies in a large continuous state space. Inspired by the success of large language models in addressing similar complexities through model scaling, we introduce a scalable trajectory model called State Transformer (STR). STR reformulates the motion prediction and motion planning problems by arranging observations, states, and actions into one unified sequence modeling task. With a simple model design, STR consistently outperforms baseline approaches in both problems. Remarkably, experimental results reveal that large trajectory models (LTMs), such as STR, adhere to the scaling laws by presenting outstanding adaptability and learning efficiency. Qualitative results further demonstrate that LTMs are capable of making plausible predictions in scenarios that diverge significantly from the training data distribution. LTMs also learn to make complex reasonings for long-term planning, without explicit loss designs or costly high-level annotations

Covariance Estimation for High Dimensional Data Vectors Using the Sparse Matrix Transform

Many problems in statistical pattern recognition and analysis require the classifcation and analysis of high dimensional data vectors. However, covariance estimation for high dimensional vectors is a classically difficult problem because the number of coefficients in the covariance grows as the dimension squared [1, 2, 3]. This problem, sometimes referred to as the curse of dimensionality [4], presents a classic dilemma in statistical pattern analysis and machine learning. In a typical application, one measures M versions of an N dimensional vector. If M \u3c N, then the sample covariance matrix will be singular with N - M eigenvalues equal to zero. Over the years, a variety of techniques have been proposed for computing a nonsingular estimate of the covariance. For example, regularized and shrinkage covariance estimators [5, 6, 7, 8, 9, 10] are examples of such techniques. In this paper, we propose a new approach to covariance estimation, which is based on constrained maximum likelihood (ML) estimation of the covariance. In particular, the covariance is constrained to have an eigen decomposition which can be represented as a sparse matrix transform (SMT) [11]. The SMT is formed by a product of pairwise coordinate rotations known as Givens rotations [12]. Using this framework, the covariance can be efficiently estimated using greedy minimization of the log likelihood function, and the number of Givens rotations can be efficiently computed using a cross-validation procedure. The estimator obtained using this method is always positive definite and well-conditioned even with limited sample size. In order to validate our model, we perform experiments using a standard set of hyperspectral data [13]. Our experiments show that SMT covariance estimation results in consistently better estimates of the covariance for a variety of different classes and sample sizes. Also, we show that the SMT method has a particular advantage over traditional methods when estimating small eigenvalues and their associated eigenvectors

Modeling and processing of high dimensional signals and systems using the sparse matrix transform

In this work, a set of new tools is developed for modeling and processing of high dimensional signals and systems, which we refer to as the sparse matrix transform (SMT). The SMT can be viewed as a generalization of the FFT and wavelet transforms in that it uses butterflies for efficient implementation. However, unlike the FFT and wavelet transforms, the design of the SMT is adapted to data, and therefore it can be used to process more general non-stationary signals. To demonstrate the potential of the SMT, it is first shown how the non-iterative maximum a posteriori (MAP) reconstruction can be made possible for tomographic systems using the SMT and a novel matrix source coding theory. In fact, for a class of difficult optical tomography problems, this non-iterative MAP reconstruction can reduce both computation and storage by well over two orders of magnitude. The SMT can also be used for accurate covariance estimation of high dimensional data vectors from a limited number of samples ( small n, large p ). Experiments on standard hyperspectral data and face image sets show that the SMT covariance estimation is consistently more accurate than alternative methods. This has also resulted in successful applications of the SMT for weak signal detection in hyperspectral imagery and eigen-image analysis. This work is concluded with a novel approach to high dimensional regression using the SMT, and it is demonstrated that the new approach can significantly improve prediction accuracy as compared to traditional regression methods