Related papers: On MIP Formulations for Logit-Based Multi-Purchase…
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…
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…
Mixed-integer linear programming (MILP) has been a fundamental problem in combinatorial optimization. Conventional MILP solving mainly relies on carefully designed heuristics embedded in the branch-and-bound framework. Driven by the strong…
We consider an assortment optimization problem under the multinomial logit choice model with general covering constraints. In this problem, the seller offers an assortment that should contain a minimum number of products from multiple…
Given a nonlinear, univariate, bounded, and differentiable function $f(x)$, this article develops a sequence of Mixed Integer Linear Programming (MILP) and Linear Programming (LP) relaxations that converge to the graph of $f(x)$ and its…
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…
In this paper we deal with a network of agents seeking to solve in a distributed way Mixed-Integer Linear Programs (MILPs) with a coupling constraint (modeling a limited shared resource) and local constraints. MILPs are NP-hard problems and…
In this paper, we propose an efficient algorithm for the network slicing problem which attempts to map multiple customized virtual network requests (also called services) to a common shared network infrastructure and allocate network…
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 an ML-based model that automates and expedites the solution of MIPs by predicting the values of variables. Our approach is motivated by the observation that many problem instances share salient features and solution structures…
Although the use of metric fluents is fundamental to many practical planning problems, the study of heuristics to support fully automated planners working with these fluents remains relatively unexplored. The most widely used heuristic is…
Mixed integer nonlinear programs (MINLPs) are arguably among the hardest optimization problems, with a wide range of applications. MINLP solvers that are based on linear relaxations and spatial branching work similar as mixed integer…
This paper introduces the logitr R package for fast maximum likelihood estimation of multinomial logit and mixed logit models with unobserved heterogeneity across individuals, which is modeled by allowing parameters to vary randomly over…
Graph matching is an important problem that has received widespread attention, especially in the field of computer vision. Recently, state-of-the-art methods seek to incorporate graph matching with deep learning. However, there is no…
By exploiting the correlation between the structure and the solution of Mixed-Integer Linear Programming (MILP), Machine Learning (ML) has become a promising method for solving large-scale MILP problems. Existing ML-based MILP solvers…
We study mixed-integer programming (MIP) relaxation techniques for the solution of non convex mixed-integer quadratically constrained quadratic programs (MIQCQPs). We present MIP relaxation methods for non convex continuous variable…
Integer linear programming (ILP) is an elegant approach to solve linear optimization problems, naturally described using integer decision variables. Within the context of physics-inspired machine learning applied to chemistry, we…
We solve large-scale mixed-integer linear programs (MILPs) via distributed asynchronous saddle point computation. This is motivated by the MILPs being able to model problems in multi-agent autonomy, e.g., task assignment problems and…
This paper proposes a Heaviside composite optimization approach and presents a progressive (mixed) integer programming (PIP) method for solving multi-class classification and multi-action treatment problems with constraints. A Heaviside…
We address the optimal design of a large scale multi-agent system where each agent has discrete and/or continuous decision variables that need to be set so as to optimize the sum of linear local cost functions, in presence of linear local…