Related papers: MIPaaL: Mixed Integer Program as a Layer
We present strong mixed-integer programming (MIP) formulations for high-dimensional piecewise linear functions that correspond to trained neural networks. These formulations can be used for a number of important tasks, such as verifying…
Conflict analysis has been successfully generalized from Boolean satisfiability (SAT) solving to mixed integer programming (MIP) solvers, but although MIP solvers operate with general linear inequalities, the conflict analysis in MIP has…
We introduce a mixed integer program (MIP) for assigning importance scores to each neuron in deep neural network architectures which is guided by the impact of their simultaneous pruning on the main learning task of the network. By…
Binary (0-1) integer programming (BIP) is pivotal in scientific domains requiring discrete decision-making. As the advance of AI computing, recent works explore neural network-based solvers for integer linear programming (ILP) problems.…
In this work, we develop an adaptive, multivariate partitioning algorithm for solving mixed-integer nonlinear programs (MINLP) with multi-linear terms to global optimality. This iterative algorithm primarily exploits the advantages of…
We consider the problem of learning optimal binary classification trees. Literature on the topic has burgeoned in recent years, motivated both by the empirical suboptimality of heuristic approaches and the tremendous improvements in…
The problem of computing an exact experimental design that is optimal for the least-squares estimation of the parameters of a regression model is considered. We show that this problem can be solved via mixed-integer linear programming…
In this work, we address a task allocation problem for human multi-robot settings. Given a set of tasks to perform, we formulate a general Mixed-Integer Linear Programming (MILP) problem aiming at minimizing the overall execution time while…
Mixed-integer linear programs (MILPs) are extensively used to model practical problems such as planning and scheduling. A prominent method for solving MILPs is large neighborhood search (LNS), which iteratively seeks improved solutions…
This paper presents a model predictive control (MPC) for dynamic systems whose nonlinearity and uncertainty are modelled by deep neural networks (NNs), under input and state constraints. Since the NN output contains a high-order complex…
Multi-instance partial-label learning (MIPL) is an emerging learning framework where each training sample is represented as a multi-instance bag associated with a candidate label set. Existing MIPL algorithms often overlook the margins for…
Mixed-Integer Linear Programming (MILP) is a fundamental and powerful framework for modeling complex optimization problems across diverse domains. Recently, learning-based methods have shown great promise in accelerating MILP solvers by…
Mixed-integer linear programming (MILP) plays a crucial role in artificial intelligence, biochemistry, finance, cryptography, etc. Notwithstanding popular for decades, the researches of MILP solvers are still limited by the resource…
Mixed Integer Linear Programming (MILP) is a fundamental class of NP-hard problems that has garnered significant attention from both academia and industry. The Branch-and-Bound (B\&B) method is the dominant approach for solving MILPs and…
Recent advances in mathematical programming have made Mixed Integer Optimization a competitive alternative to popular regularization methods for selecting features in regression problems. The approach exhibits unquestionable foundational…
Machine learning interatomic potentials (MLIPs) enable efficient molecular dynamics (MD) simulations with ab initio accuracy and have been applied across various domains in physical science. However, their performance often relies on…
This study introduces a mixed-integer linear programming (MILP) model, effectively co-optimizing patrolling, damage assessment, fault isolation, repair, and load re-energization processes. The model is designed to solve a vital operational…
Sequential quadratic programming and sequential convex programming efficiently solve nonlinear programs (NLPs) by linearizing inner nonlinearities while preserving the outer convex structure. This paper introduces a sequential mixed-integer…
Finding the most probable (MAP) model in SRL frameworks such as Markov logic and Problog can, in principle, be solved by encoding the problem as a `grounded-out' mixed integer program (MIP). However, useful first-order structure disappears…
This work focuses on support vector machine (SVM) with feature selection. A MILP formulation is proposed for the problem. The choice of suitable features to construct the separating hyperplanes has been modelled in this formulation by…