Related papers: $MC^2$ Mixed Integer and Linear Programming
This paper deals with exploiting symmetry for solving linear and integer programming problems. Basic properties of linear representations of finite groups can be used to reduce symmetric linear programming to solving linear programs of…
For multiparametric mixed-integer convex programming problems such as those encountered in hybrid model predictive control, we propose an algorithm for generating a feasible partition of a subset of the parameter space. The result is a…
Probably one of the most striking examples of the close connections between global optimization processes and statistical physics is the simulated annealing method, inspired by the famous Monte Carlo algorithm devised by Metropolis et al.…
We develop an optimization framework for identifying ideal Mixed Binary Linear Programs (MBLP) which is linear when using known input data and nonconvex quadratic over parametric input data. These techniques are applied to various…
Recent studies stressed the fact that covariance matrices computed from empirical financial time series appear to contain a high amount of noise. This makes the classical Markowitz Mean-Variance Optimization model unable to correctly…
It has been found that stochastic algorithms often find good solutions much more rapidly than inherently-batch approaches. Indeed, a very useful rule of thumb is that often, when solving a machine learning problem, an iterative technique…
In this study, we introduce an innovative deep learning framework that employs a transformer model to address the challenges of mixed-integer programs, specifically focusing on the Capacitated Lot Sizing Problem (CLSP). Our approach, to our…
We propose a new approach to utilize quantum computers for binary linear programming (BLP), which can be extended to general integer linear programs (ILP). Quantum optimization algorithms, hybrid or quantum-only, are currently general…
This applied research article explores the application of Mixed-Integer Linear Programming (MILP) to address line-balancing challenges in the garment industry, focusing on optimizing production processes under multiple constraints. By…
In this article we consider computing expectations w.r.t.~probability laws associated to a certain class of stochastic systems. In order to achieve such a task, one must not only resort to numerical approximation of the expectation, but…
Mixed-integer linear programming (MILP) is widely employed for modeling combinatorial optimization problems. In practice, similar MILP instances with only coefficient variations are routinely solved, and machine learning (ML) algorithms are…
Can Monte Carlo (MC) solvers be directly used in gradient-based methods for PDE-constrained optimization problems? In these problems, a gradient of the loss function is typically presented as a product of two PDE solutions, one for the…
We review the basic outline of the highly successful diffusion Monte Carlo technique commonly used in contexts ranging from electronic structure calculations to rare event simulation and data assimilation, and propose a new class of…
In this article, we discuss an exact algorithm for solving mixed integer concave minimization problems. A piecewise inner-approximation of the concave function is achieved using an auxiliary linear program that leads to a bilevel program,…
Reducing the cognitive complexity of a piece of code to a given threshold is not trivial. Recently, we modeled software cognitive complexity reduction as an optimization problem and we proposed an approach to assist developers on this task.…
Classical algorithms in numerical analysis for numerical integration (quadrature/cubature) follow the principle of approximate and integrate: the integrand is approximated by a simple function (e.g. a polynomial), which is then integrated…
We extend the Longstaff-Schwartz algorithm for approximately solving optimal stopping problems on high-dimensional state spaces. We reformulate the optimal stopping problem for Markov processes in discrete time as a generalized statistical…
When dealing with difficult inverse problems such as inverse rendering, using Monte Carlo estimated gradients to optimise parameters can slow down convergence due to variance. Averaging many gradient samples in each iteration reduces this…
Bayesian models have become very popular over the last years in several fields such as signal processing, statistics, and machine learning. Bayesian inference requires the approximation of complicated integrals involving posterior…
We propose a clustering-based iterative algorithm to solve certain optimization problems in machine learning, where we start the algorithm by aggregating the original data, solving the problem on aggregated data, and then in subsequent…