Decision trees have been a very popular class of predictive models for decades due to their interpretability and good performance on categorical features. However, they are not always robust and tend to overfit the data. Additionally, if allowed to grow large, they lose interpretability. In this paper, we present a novel mixed integer programming formulation … Read more
We consider the problem of characterizing the convex hull of the graph of a bilinear function $f$ on the $n$-dimensional unit cube $[0,1]^n$. Extended formulations for this convex hull are obtained by taking subsets of the facets of the Boolean Quadric Polytope (BQP). Extending existing results, we propose the systematic study of properties of $f$ … Read more
The lexicographic order can be used to force a collection of decision vectors to be all different, i.e., to take on different values in some coordinates. We consider the set of fixed-size matrices with bounded integer entries and rows in lexicographic order. We present a dynamic program to optimize a linear function over this set, … Read more
This article describes new features and enhanced algorithms made available in version 5.0 of the SCIP Optimization Suite. In its central component, the constraint integer programming solver SCIP, remarkable performance improvements have been achieved for solving mixed-integer linear and nonlinear programs. On MIPs, SCIP 5.0 is about 41 % faster than SCIP 4.0 and over … Read more
The residential load scheduling problem is concerned with finding an optimal schedule for the operation of residential loads so as to minimize the total cost of energy while aiming to respect a prescribed limit on the power level of the residence. We propose a mixed integer linear programming formulation of this problem that accounts for … Read more
Demand-response aggregators are faced with the challenge of how to best manage numerous and heterogeneous Distributed Energy Resources (DERs). This paper proposes a decentralized methodology for optimal coordination of DERs. The proposed approach is based on Dantzig-Wolfe decomposition and column generation, thus allowing to integrate any type of resource whose operation can be formulated within … Read more
We develop a mixed-integer optimal control model with partial differential equation (PDE) constraints for gas transport networks, designed for controlling extreme state transitions, such as flow reversals. Our model shows how to combine binary compressor controls with PDE flow models. We model the flow of gas using a variant of the Euler equations, which we … Read more
The analysis of infeasibility plays an important role in solving satisfiability problems (SAT) and mixed integer programs (MIPs). In mixed integer programming, this procedure is called conflict analysis. So far, modern MIP solvers use conflict analysis only for propagation and improving the dual bound, i.e., fathoming nodes that cannot contain feasible solutions. In this short … Read more
We consider a bound for the maximum-entropy sampling problem (MESP) that is based on solving a max-det problem over a relaxation of the Boolean Quadric Polytope (BQP). This approach to MESP was first suggested by Christoph Helmberg over 15 years ago, but has apparently never been further elaborated or computationally investigated. We find that the … Read more
We study a deterministic technique to check the existence of feasible points for mixed-integer nonlinear optimization problems which satisfy a structural requirement that we call granularity. We show that solving certain purely continuous optimization problems and rounding their optimal points leads to feasible points of the original mixed-integer problem, as long as the latter is … Read more