Related papers: A Survey for Solving Mixed Integer Programming via…
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 consider {\em Mixed Linear Regression (MLR)}, where training data have been generated from a mixture of distinct linear models (or clusters) and we seek to identify the corresponding coefficient vectors. We introduce a {\em Mixed Integer…
Quantum computing is emerging as a new computing resource that could be superior to conventional computing for certain classes of optimization problems. However, in principle, most existing approaches to quantum optimization are intended to…
Deriving a good variable selection strategy in branch-and-bound is essential for the efficiency of modern mixed-integer programming (MIP) solvers. With MIP branching data collected during the previous solution process, learning to branch…
Efficient algorithms and solvers are required to provide optimal or near-optimal solutions quickly and enable organizations to react promptly to dynamic situations such as supply chain disruptions or changing customer demands.…
Large Neighbourhood Search (LNS) is a powerful heuristic framework for solving Mixed-Integer Programming (MIP) problems. However, designing effective variable selection strategies in LNS remains challenging, especially for diverse sets of…
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…
Mixed integer convex and nonlinear programs, MICP and MINLP, are expressive but require long solving times. Recent work that combines data-driven methods on solver heuristics has shown potential to overcome this issue allowing for…
We give an explicit geometric way to build mixed-integer programming (MIP) formulations for unions of polyhedra. The construction is simply described in terms of spanning hyperplanes in an r-dimensional linear space. The resulting MIP…
Integer programming (IP), as the name suggests is an integer-variable-based approach commonly used to formulate real-world optimization problems with constraints. Currently, quantum algorithms reformulate the IP into an unconstrained form…
In the last twenty-five years (1990-2014), algorithmic advances in integer optimization combined with hardware improvements have resulted in an astonishing 200 billion factor speedup in solving Mixed Integer Optimization (MIO) problems. We…
Cutting planes are crucial for the performance of branch-and-cut algorithms for solving mixed-integer programming (MIP) problems, and linear row aggregation has been successfully applied to better leverage the potential of several major…
Cutting planes for mixed-integer linear programs (MILPs) are typically computed in rounds by iteratively solving optimization problems, the so-called separation. Instead, we reframe the problem of finding good cutting planes as a continuous…
Integer programming (IP) is a general optimization framework widely applicable to a variety of unstructured and structured problems arising in, e.g., scheduling, production planning, and graph optimization. As IP models many provably hard…
Today's fast linear algebra and numerical optimization tools have pushed the frontier of model predictive control (MPC) forward, to the efficient control of highly nonlinear and hybrid systems. The field of hybrid MPC has demonstrated that…
In line with the growing trend of using machine learning to help solve combinatorial optimisation problems, one promising idea is to improve node selection within a mixed integer programming (MIP) branch-and-bound tree by using a learned…
Besides training, mathematical optimization is also used in deep learning to model and solve formulations over trained neural networks for purposes such as verification, compression, and optimization with learned constraints. However,…
Maritime Inventory Routing Problem (MIRP) plays a crucial role in the integration of global maritime commerce levels. However, there are still no well-established methodologies capable of efficiently solving large MIRP instances or their…
Planning in hybrid systems with both discrete and continuous control variables is important for dealing with real-world applications such as extra-planetary exploration and multi-vehicle transportation systems. Meanwhile, generating…
This paper presents a hybrid CPU-GPU framework for solving combinatorial scheduling problems formulated as Integer Linear Programming (ILP). While scheduling underpins many optimization tasks in computing systems, solving these problems…