Related papers: Mixed-integer linear representability, disjunction…
Integer Linear Programming (ILP) has a broad range of applications in various areas of artificial intelligence. Yet in spite of recent advances, we still lack a thorough understanding of which structural restrictions make ILP tractable.…
Mixed integer nonlinear programming (MINLP) problems are encountered in modeling a physical/industrial process consisting both nonlinearity and discrete selective parameters. There are variety of algorithms for solving MINLP problems most…
Interior point methods (IPMs) are a common approach for solving linear programs (LPs) with strong theoretical guarantees and solid empirical performance. The time complexity of these methods is dominated by the cost of solving a linear…
A standard approach to solving optimistic bilevel linear programs (BLPs) is to replace the lower-level problem with its Karush-Kuhn-Tucker (KKT) optimality conditions and reformulate the resulting complementarity constraints using auxiliary…
Cutting planes (cuts) are important for solving mixed-integer linear programs (MILPs), which formulate a wide range of important real-world applications. Cut selection -- which aims to select a proper subset of the candidate cuts to improve…
A novel framework has recently been proposed for designing the molecular structure of chemical compounds with a desired chemical property, where design of novel drugs is an important topic in bioinformatics and chemo-informatics. The…
Decentralized planning in uncertain environments is a complex task generally dealt with by using a decision-theoretic approach, mainly through the framework of Decentralized Partially Observable Markov Decision Processes (DEC-POMDPs).…
We propose a framework for the stability verification of Mixed-Integer Linear Programming (MILP) representable control policies. This framework compares a fixed candidate policy, which admits an efficient parameterization and can be…
Many vision-related tasks benefit from reasoning over multiple modalities to leverage complementary views of data in an attempt to learn robust embedding spaces. Most deep learning-based methods rely on a late fusion technique whereby…
The analysis of infeasible subproblems plays an import role in solving mixed integer programs (MIPs) and is implemented in most major MIP solvers. There are two fundamentally different concepts to generate valid global constraints from…
We present a bounded model checking algorithm for signal temporal logic (STL) that exploits mixed-integer linear programming (MILP). A key technical element is our novel MILP encoding of the STL semantics; it follows the idea of stable…
Mixed-Integer Linear Programming (MILP) lies at the core of many real-world combinatorial optimization (CO) problems, traditionally solved by branch-and-bound (B&B). A key driver influencing B&B solvers efficiency is the variable selection…
Designing faster algorithms for solving Mixed-Integer Linear Programming (MILP) problems is highly desired across numerous practical domains, as a vast array of complex real-world challenges can be effectively modeled as MILP formulations.…
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…
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…
We study a mixed integer linear program with m integer variables and k non-negative continuous variables in the form of the relaxation of the corner polyhedron that was introduced by Andersen, Louveaux, Weismantel and Wolsey [Inequalities…
We study the mixed-integer optimization (MIO) approach to feature subset selection in nonlinear kernel support vector machines (SVMs) for binary classification. First proposed for linear regression in the 1970s, this approach has recently…
We introduce a relaxed-projection splitting algorithm for solving variational inequalities in Hilbert spaces for the sum of nonsmooth maximal monotone operators, where the feasible set is defined by a nonlinear and nonsmooth continuous…
A mathematical programming model for a class of single machine family scheduling problem is described in this technical report, with the aim of comparing the performance in solving the scheduling problem by means of mathematical programming…
A scoring system is a linear classifier composed of a small number of explanatory variables, each assigned a small integer coefficient. This system is highly interpretable and allows predictions to be made with simple manual calculations…