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Machine learning has increasingly been employed to solve NP-hard combinatorial optimization problems, resulting in the emergence of neural solvers that demonstrate remarkable performance, even with minimal domain-specific knowledge. To…

We tackle the problem of graph partitioning for image segmentation using correlation clustering (CC), which we treat as an integer linear program (ILP). We reformulate optimization in the ILP so as to admit efficient optimization via…

Many tasks in our modern life, such as planning an efficient travel, image processing and optimizing integrated circuit design, are modeled as complex combinatorial optimization problems with binary variables. Such problems can be mapped to…

This work addresses inverse linear optimization where the goal is to infer the unknown cost vector of a linear program. Specifically, we consider the data-driven setting in which the available data are noisy observations of optimal…

Combinatorial optimization serves as an essential part in many modern industrial applications. A great number of the problems are offline setting due to safety and/or cost issues. While simulation-based approaches appear difficult to…

We consider the problem of jointly estimating the parameters as well as the structure of binary valued Markov Random Fields, in contrast to earlier work that focus on one of the two problems. We formulate the problem as a maximization of…

Test optimization contains test case selection and minimization, which is an important challenge in software testing and has been addressed with search-based approaches intensively in the past. Inspired by the recent advancement of using…

The vehicle routing problem is a well known class of NP-hard combinatorial optimisation problems in literature. Traditional solution methods involve either carefully designed heuristics, or time-consuming metaheuristics. Recent work in…

We introduce and study the combinatorial optimization problem with interaction costs (COPIC). COPIC is the problem of finding two combinatorial structures, one from each of two given families, such that the sum of their independent linear…

Cooperative Co-evolution, through the decomposition of the problem space, is a primary approach for solving large-scale global optimization problems. Typically, when the subspaces are disjoint, the algorithms demonstrate significantly both…

A promising approach to achieve computational supremacy over the classical von Neumann architecture explores classical and quantum hardware as Ising machines. The minimisation of the Ising Hamiltonian is known to be NP-hard problem for…

Compressing resource-intensive large language models by removing whole transformer blocks is a seemingly simple idea, but identifying which blocks to remove constitutes an exponentially difficult combinatorial problem. In this paper, we…

This paper is about how to partition decision variables while decomposing a large-scale optimization problem for the best performance of distributed solution methods. Solving a large-scale optimization problem sequen- tially can be…

Binary optimization, a representative subclass of discrete optimization, plays an important role in mathematical optimization and has various applications in computer vision and machine learning. Usually, binary optimization problems are…

We explore the potential of spatial-photonic Ising machines (SPIMs) to address computationally intensive Ising problems that employ low-rank and circulant coupling matrices. Our results indicate that the performance of SPIMs is critically…

Sparse optimization is a central problem in machine learning and computer vision. However, this problem is inherently NP-hard and thus difficult to solve in general. Combinatorial search methods find the global optimal solution but are…

Energy systems planning models identify least-cost strategies for expansion and operation of energy systems and provide decision support for investment, planning, regulation, and policy. Most are formulated as linear programming (LP) or…

Recent work on neural scaling laws demonstrates that model performance scales predictably with compute budget, model size, and dataset size. In this work, we develop scaling laws based on problem complexity. We analyze two fundamental…

This paper introduces a new method of partitioning the solution space of a multi-objective optimisation problem for parallel processing, called Efficient Projection Partitioning. This method projects solutions down into a single dimension,…

We introduce a methodology for generating benchmark problem sets for Ising machines---devices designed to solve discrete optimization problems cast as Ising models. In our approach, linear systems of equations are cast as Ising cost…