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About 10,000 papers for “mixed-integer linear programming”

$MC^2$ Mixed Integer and Linear Programming

Polson, Nick, Sokolov, Vadim · ArXiv.org · 2025

In this paper, we design $MC^2$ algorithms for Mixed Integer and Linear Programming. By expressing a constrained optimisation as one of simulation from a Boltzmann distribution, we reformulate integer and linear programming as Monte Carlo optimisation problems. The key insight is that solving these optimisation problems requires the ability to simulate from truncated distributions, namely multivariate exponentials and Gaussians. Efficient simulation can be achieved using the algorithms of Kent and Davis. We demonstrate our methodology on portfolio optimisation and the classical farmer problem from stochastic programming. Finally, we conclude with directions for future research.

Cited by 0Open access

Noncommercial Software for Mixed-Integer Linear Programming

J. T. Linderoth , et al. · 2005

We present an overview of noncommercial software tools for the solution of mixed-integer linear programs (MILPs). We first review solution methodologies for MILPs and then present an overview of the available software, including detailed descriptions of eight software packages available under open-source or other noncommercial licenses. Each package is categorized as a black-box solver, a callable library, a solver framework, or some combination of these. The distinguishing features of all eight packages are described. The paper concludes with case studies that illustrate the use of two of the solver frameworks to develop custom solvers for specific problem classes and with benchmarking of the six black-box solvers.

Cited by 0

Maximum consensus with mixed integer linear programming

Yang Heng Kee · Adelaide Research & Scholarship (AR&S) (University of Adelaide) · 2016

Maximum consensus is fundamentally important in computer vision as a criterion for robust estimation, where the goal is to estimate the parameters of a model of best fit. It is computationally demanding to solve such problems exactly. Instead, conventional methods employ randomised sample-and-test techniques to approximate a solution, which fail to guarantee the optimality of the result. This thesis makes several contributions towards solving the maximum consensus problem exactly in the context of Mixed Integer Linear Programming. In particular, two preprocessing techniques aimed at improving the speed and efficiency of exact methods are proposed.

Cited by 0Open access

$MC^2$ Mixed Integer and Linear Programming

Polson, Nick, Sokolov, Vadim · arXiv (Cornell University) · 2025

In this paper, we design $MC^2$ algorithms for Mixed Integer and Linear Programming. By expressing a constrained optimisation as one of simulation from a Boltzmann distribution, we reformulate integer and linear programming as Monte Carlo optimisation problems. The key insight is that solving these optimisation problems requires the ability to simulate from truncated distributions, namely multivariate exponentials and Gaussians. Efficient simulation can be achieved using the algorithms of Kent and Davis. We demonstrate our methodology on portfolio optimisation and the classical farmer problem from stochastic programming. Finally, we conclude with directions for future research.

Cited by 0Open access

Parallel Solvers for Mixed Integer Linear Programming

Ted K. Ralphs, Yuji Shinano, Timo Berthold et al. · 2016

In this article, we introduce parallel mixed integer linear programming (MILP) solvers. MILP solving algorithms have been improved tremendously in the last two decades. Currently, commercial MILP solvers are known as a strong optimization tool. Parallel MILP solver development has started in 1990s. However, since the improvements of solving algorithms have much impact to solve MILP problems than application of parallel computing, there were not many visible successes. With the spread of multi-core CPUs, current state-of-the-art MILP solvers have parallel implementations and researches to apply parallelism in the solving algorithm also getting popular. We summarize current existing parallel MILP solver architectures.

Cited by 8

Polyhedral Approaches to Mixed Integer Linear Programming

Conforti, Michele, Cornuejols, Gerard, Zambelli, Giacomo · KiltHub Repository · 2018

This survey presents tools from polyhedral theory that are used in integer programming. It applies them to the study of valid inequalities for mixed integer linear sets, such as Gomory's mixed integer cuts.

Cited by 0Open access

Optimization algorithm study : mixed integer linear programming

Tittawat Fongchantuk · 2018

In the present, many petrochemical and petroleum products (engine fuel, solvent, plastic and synthetic rubber. etc.) are important. They are transported by ship, pipe line or train every day. So, minimizing transportation cost and time or maximizing profit is an important key of every company. In this optimization process, the optimal supply chain must be well developed in mathematical programming with the objective function of minimum cost or maximum profit and be solved by using optimization solvers. Objective functions and their constraints are solved by suitable types of optimization solvers: Linear programming (LP) and mixed integer linear programming (MILP). MILP is one of the most widely used optimization technique for designing supply chain, and developed by using linear programming and branch-and-bound technique. In this research, MILP algorithm is studied and developed on FORTRAN 4.0 to study MILP procedure, and then it is applied with case study of biofuel production supply chain. Finally, the results are validated with solver in Microsoft Excel. The result shows that the MILP algorithm can show many solutions with one optimum point for multiple optimum problems for benefit of alternative solutions, while only one solution is obtained from solver in Microsoft Excel. Moreover, the optimal SCNPV from the algorithm is close to one from Microsoft Excel. It shows that the MILP algorithm is high efficient for accuracy solution and benefit for alternative of suitable solutions in optimizing supply chain problems.

Cited by 0Open access

Generative Branching for Mixed-Integer Linear Programming

Ruobing Wang, Xin Li, Yangchuan Wang et al. · Proceedings of the AAAI Conference on Artificial Intelligence · 2026

Branch-and-bound (B&B) is a fundamental algorithmic framework for solving Mixed-Integer Linear Programming (MILP) problems, where branching decisions critically affect solver efficiency. Recent learning-based methods apply imitation learning to select branching variables, but their deterministic predictions limit exploration and generalization. In this paper, we propose a novel framework that formulates branching variable selection as a conditional generative process, exploring deep-level decision features. Our approach leverages diffusion models to enable diverse and exploratory branching score generation, while consistency modeling distills this process into efficient one-step inference conditioned on the B&B state. This mode allows our method to achieve both high-quality and fast branching decisions, significantly improving the overall performance of branch-and-bound solvers. Extensive experiments on challenging cross-scale and cross-category benchmarks demonstrate that our framework consistently outperforms state-of-the-art imitation learning baselines, delivering substantial improvements in solution quality, computational efficiency, and inference speed.

Cited by 0Open access