Related papers: Mixed-Integer Programming for Change-point Detecti…

Embedding deep neural networks (NNs) into mixed-integer programs (MIPs) is attractive for decision making with learned constraints, yet state-of-the-art monolithic linearisations blow up in size and quickly become intractable. In this…

We propose a dual dynamic integer programming (DDIP) framework for solving multi-scale mixed-integer model predictive control (MPC) problems. Such problems arise in applications that involve long horizons and/or fine temporal…

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…

Linear programming (LP) relaxations are widely employed in exact solution methods for multilinear programs (MLP). One example is the family of Recursive McCormick Linearization (RML) strategies, where bilinear products are substituted for…

We present a technique for neural network verification using mixed-integer programming (MIP) formulations. We derive a \emph{strong formulation} for each neuron in a network using piecewise linear activation functions. Additionally, as in…

Mixed-integer programming (MIP) is a powerful paradigm for modeling and solving various important combinatorial optimization problems. Recently, learning-based approaches have shown a potential to speed up MIP solving via offline training…

In this paper we aim to construct piecewise-linear (PWL) approximations for functions of multiple variables and to build compact mixed-integer linear programming (MILP) formulations to represent the resulting PWL function. On the one hand,…

Indefinite quadratic programs (QPs) are known to be very difficult to be solved to global optimality, so are linear programs with linear complementarity constraints. Treating the former as a subclass of the latter, this paper presents a…

Two-stage stochastic mixed-integer programming (SMIP) problems with general integer variables in the second-stage are generally difficult to solve. This paper develops the theory of integer set reduction for characterizing the subset of the…

There is an increasing need for algorithms that can accurately detect changepoints in long time-series, or equivalent, data. Many common approaches to detecting changepoints, for example based on penalised likelihood or minimum description…

This paper addresses a mixed integer programming (MIP) formulation for the multi-item uncapacitated lot-sizing problem that is inspired from the trailer manufacturer. The proposed MIP model has been utilized to find out the optimum order…

Mixed Integer Linear Programs (MILPs) are essential tools for solving planning and scheduling problems across critical industries such as construction, manufacturing, and logistics. However, their widespread adoption is limited by long…

This paper introduces a novel algorithm for Mixed-Integer Nonlinear Programming (MINLP) problems with multilinear interpolations of look-up tables. These problems arise when objective or constraints contain black-box functions only known at…

Many problems of interest for cyber-physical network systems can be formulated as Mixed-Integer Linear Programs in which the constraints are distributed among the agents. In this paper we propose a distributed algorithmic framework to solve…

Mixed integer linear programming (MILP) solvers expose hundreds of parameters that have an outsized impact on performance but are difficult to configure for all but expert users. Existing machine learning (ML) approaches require training on…

In this paper, we propose a Pre-trained Mixed Integer Optimization framework (PreMIO) that accelerates online mixed integer program (MIP) solving with offline datasets and machine learning models. Our method is based on a data-driven…

Linear Predictive Clustering (LPC) partitions samples based on shared linear relationships between feature and target variables, with numerous applications including marketing, medicine, and education. Greedy optimization methods, commonly…

We present a new mixed integer formulation for the discrete informative path planning problem in random fields. The objective is to compute a budget constrained path while collecting measurements whose linear estimate results in minimum…

We propose a hierarchical architecture for efficiently computing high-quality solutions to structured mixed-integer programs (MIPs). To reduce computational effort, our approach decouples the original problem into a higher level problem and…

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…