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Topology optimization of natural convection problems is computationally expensive, due to the large number of degrees of freedom (DOFs) in the model and its two-way coupled nature. Herein, a method is presented to reduce the computational…
Large Language Models (LLMs) have demonstrated remarkable performance across multiple tasks through in-context learning. For complex reasoning tasks that require step-by-step thinking, Chain-of-Thought (CoT) prompting has given impressive…
Decompositions of networks are useful not only for structural exploration. They also have implications and use in analysis and computational solution of processes (such as the Ising model, percolation, SIR model) running on a given network.…
We introduce a new rule-based optimization method for classification with constraints. The proposed method leverages column generation for linear programming, and hence, is scalable to large datasets. The resulting pricing subproblem is…
MPC (Model predictive control)-based motion planning and trajectory generation are essential in applications such as unmanned aerial vehicles, robotic manipulators, and rocket control. However, the real-time implementation of such…
The incorporation of trees on farms can help to improve livelihoods and build resilience among small-holder farmers in developing countries. On-farm trees can help gen- erate additional income from commercial tree harvest as well as…
The discrete Wasserstein barycenter problem is a minimum-cost mass transport problem for a set of discrete probability measures. Although an exact barycenter is computable through linear programming, the underlying linear program can be…
Many decision-making problems in engineering applications such as transportation, power system and operations research require repeatedly solving large-scale linear programming problems with a large number of different inputs. For example,…
We suggest a global perspective on dynamic network flow problems that takes advantage of the similarities to port-Hamiltonian dynamics. Dynamic minimum cost flow problems are formulated as open-loop optimal control problems for general…
Traffic flow forecasting is a crucial task in intelligent transport systems. Deep learning offers an effective solution, capturing complex patterns in time-series traffic flow data to enable the accurate prediction. However, deep learning…
A decomposition principle for nonlinear dynamic compartmental systems is introduced in the present paper. This theory is based on the mutually exclusive and exhaustive, analytical and dynamic, novel system and subsystem partitioning…
Optimal transport has recently been brought forward as a tool for modeling and efficiently solving a variety of flow problems, such as origin-destination problems and multi-commodity flow problems. Although the framework has shown to be…
Long document classification presents challenges in capturing both local and global dependencies due to their extensive content and complex structure. Existing methods often struggle with token limits and fail to adequately model…
In this work, a combined strategy of domain decomposition and the direct-line method is implemented to solve the forward and inverse linear elasticity problems of composite materials in general domains with multiple singularities. Domain…
We propose TD-GEN, a graph generation framework based on tree decomposition, and introduce a reduced upper bound on the maximum number of decisions needed for graph generation. The framework includes a permutation invariant tree generation…
This paper investigates the column generation (CG) for solving cutting stock problems (CSP). Traditional CG method, which repeatedly solves a restricted master problem (RMP), often suffers from two critical issues in practice -- the loss of…
Boosted trees is a dominant ML model, exhibiting high accuracy. However, boosted trees are hardly intelligible, and this is a problem whenever they are used in safety-critical applications. Indeed, in such a context, rigorous explanations…
We study the minimum-concave-cost flow problem on a two-dimensional grid. We characterize the computational complexity of this problem based on the number of rows and columns of the grid, the number of different capacities over all arcs,…
We consider a fashion discounter distributing its many branches with integral multiples from a set of available lot-types. For the problem of approximating the branch and size dependent demand using those lots we propose a tailored exact…
The Discrete Ordered Median Problem (DOMP) is formulated as a set partitioning problem using an exponential number of variables. Each variable corresponds to a set of demand points allocated to the same facility with the information of the…