Computing the edge expansion of a graph is a famously hard combinatorial problem for which there have been many approximation studies. We present two variants of exact algorithms using semidefinite programming (SDP) to compute this constant for any graph. The first variant uses the SDP relaxation first to reduce the search space considerably. The problem … Read more
Consider the problem of maximizing a monotone-increasing submodular function defined on a set of weighted items under an unknown knapsack capacity. Assume that items are packed sequentially into the knapsack and that the capacity of the knapsack is accessed through an oracle that answers whether an item fits into the currently packed knapsack. If an … Read more
Inspired by its occurrence as a substructure in a stochastic railway timetabling model, we study in this work a special case of the bipartite boolean quadric polytope. It models conditional relations across three sets of binary variables, where selections within two implying sets imply a choice in a corresponding implied set. We call this polytope … Read more
The multi-stop station location problem (MSLP) aims to place stations such that a set of trips is feasible with respect to length bounds while minimizing cost. Each trip consists of a sequence of stops that must be visited in a given order, and a length bound that controls the maximum length that is possible without … Read more
The Multi-Vehicle Covering Tour Problem (m-CTP) involves a graph in which the set of vertices is partitioned into a depot and three distinct subsets representing customers, mandatory facilities, and optional facilities. Each customer is linked to a specific subset of optional facilities that define its coverage set. The goal is to determine a set of … Read more
Adaptive robust optimization problems have received significant attention in recent years, but remain notoriously difficult to solve when recourse decisions are discrete in nature. In this paper, we propose new reformulation techniques for adaptive robust binary optimization (ARBO) problems with objective uncertainty. Without loss of generality, we focus on ARBO problems with “selective adaptability”, a … Read more
In a recent work, Schmitt and Singh propose a new quadratic facility location model to address ecological challenges faced by policymakers in Bavaria, Germany. Building on this previous work, we significantly extend our understanding of this new problem. We develop connections to traditional combinatorial optimization models and show the problem is NP-hard. We then develop … Read more
In this paper, we investigate the integrality gap of the Asymmetric Traveling Salesman Problem (ATSP) with respect to the linear relaxation given by the Asymmetric Subtour Elimination Problem (ASEP) for instances with n nodes, where n is small. In particular, we focus on the geometric properties and symmetries of the ASEP polytope ($P^{n}_{ASEP}$) and its vertices. The … Read more
We introduce a polyhedral framework for characterizing instances of quadratic combinatorial optimization programs (QCOPs) as being linearizable, meaning that the quadratic objective can be equivalently rewritten as linear in such a manner that preserves the objective function value at all feasible solutions. In particular, we show that an instance is linearizable if and only if … Read more
This paper describes the computational challenge developed for a computational competition held in 2023 for the 20th anniversary of the Mixed Integer Programming Workshop. The topic of this competition was reoptimization, also known as warm starting, of mixed integer linear optimization problems after slight changes to the input data for a common formulation. The challenge … Read more