This tutorial provides an introduction to the use of decision diagrams for solving discrete optimization problems. A decision diagram is a graphical representation of the solution space, representing decisions sequentially as paths from a root node to a target node. By merging isomorphic subgraphs (or equivalent subproblems), decision diagrams can compactly represent an exponential solution … Read more
The most successful approaches for the TSP use the integer programming model proposed in 1954 by Dantzig, Fulkerson, and Johnson (DFJ). Although this model has exponentially many subtour elimination constraints (SECs), it has been observed that relatively few of them are needed to prove optimality in practice. This leads us to wonder: What is the … Read more
The maximum-entropy sampling problem (MESP) aims to select the most informative principal submatrix of a prespecified size from a given covariance matrix. This paper proposes an augmented factorization bound for MESP based on concave relaxation. By leveraging majorization and Schur-concavity theory, we demonstrate that this new bound dominates the classic factorization bound of Nikolov (2015) and a recent … Read more
This paper is devoted to the Truck-to-dock Door Assignment Problem. Two integer programming formulations introduced after 2009 are examined. Our review of the literature takes note of the criticisms and limitations addressed to the seminal work of 2009. Although the published adjustments that followed present strong argument and technical background, we have identified several errors, … Read more
We introduce the prime programming problem as a subclass of integer programming. These optimization models impose the restriction of feasible solutions being prime numbers. Then, we demonstrate how several classical problems in number theory can be formulated as prime programs. To solve such problems with a commercial optimization solver, we extend the branch-and-bound procedure of … Read more
We present randomized reconstruction approaches for optimal solutions to mixed-integer elliptic PDE control systems. Approximation properties and relations to sum-up rounding are derived using the cut norm. This enables us to dispose of space-filling curves required for sum-up rounding. Rates of almost sure convergence in the cut norm and the SUR norm in control space … Read more
We are excited to present the early release of Part I of our book “Optimizing with Column Generation: advanced Branch-Cut-and-Price Algorithms”. While the book’s ultimate goal, as suggested by its subtitle, is to describe cutting-edge techniques in these algorithms, this objective is primarily addressed in the forthcoming Part II. However, we feel that the completed … Read more
The single-source capacitated facility location problem with customer preferences (SSCFLPCP) is known to be strongly NP-hard. Computational tests imply that state-of-the-art solvers struggle with computing exact solutions. In this paper, we contribute two novel preprocessing methods which reduce the size of the considered integer programming formulation, and introduce sets of valid inequalities which decrease the … Read more
Motivated by our collaboration with a residency program at an academic health system, we propose new integer programming (IP) approaches for the resident-to-rotation assignment problem (RRAP). Given sets of residents, resident classes, and departments, as well as a block structure for each class, staffing needs, rotation requirements for each class, program rules, and resident vacation … Read more
In this paper, we address an extension of the classical two-dimensional bin packing (2BPP) that considers the spread of customer orders (2BPP-OS). The 2BPP-OS addresses a set of rectangular items, required from different customer orders, to be cut from a set of rectangular bins. All the items of a customer order are dispatched together to … Read more