Related papers: Constraint Matters: Multi-Modal Representation for…

Model reduction is a central topic in systems biology and dynamical systems theory, for reducing the complexity of detailed models, finding important parameters, and developing multi-scale models for instance. While perturbation theory is a…

We consider a dynamic pricing problem in network revenue management where customer behavior is predicted by a choice model, i.e., the multinomial logit (MNL) model. The problem, even in the static setting (i.e., customer demand remains…

While Mixed-integer linear programming (MILP) is NP-hard in general, practical MILP has received roughly 100--fold speedup in the past twenty years. Still, many classes of MILPs quickly become unsolvable as their sizes increase, motivating…

Cutting planes are essential for solving mixed-integer linear problems (MILPs), because they facilitate bound improvements on the optimal solution value. For selecting cuts, modern solvers rely on manually designed heuristics that are tuned…

This work introduces a framework to address the computational complexity inherent in Mixed-Integer Programming (MIP) models by harnessing the potential of deep learning. By employing deep learning, we construct problem-specific heuristics…

In this study, we introduce an innovative deep learning framework that employs a transformer model to address the challenges of mixed-integer programs, specifically focusing on the Capacitated Lot Sizing Problem (CLSP). Our approach, to our…

Mixed-integer rounding (MIR) cutting planes (cuts) are effective at improving the strength of a linear relaxation for mixed-integer linear programming (MIP) problems. The cuts in this family are derived by aggregating constraints then…

Recently, diffusion models have been used to solve various inverse problems in an unsupervised manner with appropriate modifications to the sampling process. However, the current solvers, which recursively apply a reverse diffusion step…

In the past few years, there has been an explosive surge in the use of machine learning (ML) techniques to address combinatorial optimization (CO) problems, especially mixed-integer linear programs (MILPs). Despite the achievements, the…

Mixed Integer Linear Programming (MILP) is a pillar of mathematical optimization that offers a powerful modeling language for a wide range of applications. During the past decades, enormous algorithmic progress has been made in solving…

Vision-language pre-trained models have achieved impressive performance on various downstream tasks. However, their large model sizes hinder their utilization on platforms with limited computational resources. We find that directly using…

Lagrangian relaxation stands among the most efficient approaches for solving a Mixed Integer Linear Programs (MILP) with difficult constraints. Given any duals for these constraints, called Lagrangian Multipliers (LMs), it returns a bound…

We consider a discrete optimization formulation for learning sparse classifiers, where the outcome depends upon a linear combination of a small subset of features. Recent work has shown that mixed integer programming (MIP) can be used to…

A standard tool for modelling real-world optimisation problems is mixed-integer programming (MIP). However, for many of these problems, information about the relationships between variables is either incomplete or highly complex, making it…

Projected Gradient Descent denotes a class of iterative methods for solving optimization programs. Its applicability to convex optimization programs has gained significant popularity for its intuitive implementation that involves only…

The goal of survey design is often to minimize the errors associated with inference: the total of bias and variance. Random surveys are common because they allow the use of theoretically unbiased estimators. In practice however, such…

Linear constraints are one of the most fundamental constraints in fields such as computer science, operations research and optimization. Many applications reduce to the task of model counting over integer linear constraints (MCILC). In this…

Cutting planes are crucial in solving mixed integer linear programs (MILP) as they facilitate bound improvements on the optimal solution. Modern MILP solvers rely on a variety of separators to generate a diverse set of cutting planes by…

Increasingly volatile electricity prices make simultaneous scheduling optimization desirable for production processes and their energy systems. Simultaneous scheduling needs to account for both process dynamics and binary on/off-decisions…

We present new models of optimization-based task and motion planning (TAMP) for robotic pick-and-place (P&P), which plan action sequences and motion trajectory with low computational costs. We improved an existing state-of-the-art TAMP…