A classic result by Cook, Gerards, Schrijver, and Tardos provides an upper bound of n∆ on the proximity of optimal solutions of an Integer Linear Programming problem and its standard linear relaxation. In this bound, n is the number of variables and ∆ denotes the maximum of the absolute values of the subdeterminants of the … Read more
We revisit and strengthen splitting methods for solving doubly nonnegative, DNN, relaxations of the quadratic assignment problem, QAP. We use a modified restricted contractive splitting method, rPRSM, approach. Our strengthened bounds and new dual multiplier estimates improve on the bounds and convergence results in the literature. Citation Department of Combinatorics & Optimization, University of Waterloo, … Read more
We study Kusuoka representations of law invariant coherent risk measures on the space of bounded random variables. We refine this representation by giving that any law invariant coherent risk measure can be written as an integral of the Average Value-at-Risk measures on $[0,1]$, which gives a numerically constructive way to approximate any law invariant coherent … Read more
The crew scheduling and routing problem (CSRP) consists of determining the best route and schedule for a single crew to repair damaged nodes in a network affected by extreme events. The problem also involves the design of paths to connect a depot to demand nodes that become accessible only after the damaged nodes in these … Read more
In this paper we discuss construction of the dual of a periodical formulation of infinite horizon linear stochastic programs with a discount factor. The dual problem is used for computing a deterministic upper bound for the optimal value of the considered multistage stochastic program. Numerical experiments demonstrate behavior of that upper bound especially when the … Read more
We study convex relaxations of nonconvex quadratic programs. We identify a family of so-called feasibility preserving convex relaxations, which includes the well-known copositive and doubly nonnegative relaxations, with the property that the convex relaxation is feasible if and only if the nonconvex quadratic program is feasible. We observe that each convex relaxation in this family … Read more
By rerouting and retiming trains in real-time, the propagation of reactionary delay in complex station areas can be reduced. In this study, we propose a new optimisation model and solution algorithm that can be used to determine the best combination of route and schedule changes to make. Whilst several models have been proposed to tackle … Read more
Mixed-integer programming (MIP) problem is arguably among the hardest classes of optimization problems. This paper describes how we solved 21 previously unsolved MIP instances from the MIPLIB benchmark sets. To achieve these results we used an enhanced version of ParaSCIP, setting a new record for the largest scale MIP computation: up to 80,000 cores in … Read more
We study a model for adversarial classification based on distributionally robust chance constraints. We show that under Wasserstein ambiguity, the model aims to minimize the conditional value-at-risk of the distance to misclassification, and we explore links to adversarial classification models proposed earlier and to maximum-margin classifiers. We also provide a reformulation of the distributionally robust … Read more
In this paper, we introduce a new class of decision rules, referred to as Constant Depth Decision Rules (CDDRs), for multistage optimization under linear constraints with uncertainty-affected right-hand sides. We consider two uncertainty classes: discrete uncertainties which can take at each stage at most a fixed number d of different values, and polytopic uncertainties which, … Read more