In this paper, we show how to efficiently schedule the Brazilian OR conference using a matheuristic approach. The event has traditionally around 300 presentations across a period of 3 to 4 days, and building a schedule for the technical sessions is an arduous task. The proposed algorithm integrates the concepts of iterated local search and … Read more
Optimization problems with discrete decisions are nonconvex and thus lack strong duality, which limits the usefulness of tools such as shadow prices. It was shown in Burer (2009) that mixed-binary quadratic programs can be written as completely positive programs, which are convex. We apply this perspective by writing unit commitment in power systems as a … Read more
The exponential function and its logarithmic counterpart are essential corner stones of nonlinear mathematical modeling. In this paper we treat their conic extensions, the exponential cone and the relative entropy cone, in primal, dual and polar form, and show that finding the nearest mapping of a point onto these convex sets all reduce to a … Read more
Decision making problems are typically concerned with maximizing efficiency. In contrast, we address problems where there are multiple stakeholders and a centralized decision maker who is obliged to decide in a fair manner. Different decisions give different utility to each stakeholder. In cases where these decisions are made repeatedly, we provide efficient mathematical programming formulations … Read more
In the daily dispatching of urban deliveries, a delivery manager has to consider workload balance among the couriers to maintain workforce morale. We consider two types of workload: incentive workload, which relates to the delivery quantity and affects a courier’s income, and effort workload, which relates to the delivery time and affects a courier’s health. … Read more
We study solution sensitivity for nonlinear programs (NLPs) whose structure is induced by a graph $\mathcal{G}=(\mathcal{V},\mathcal{E})$. These graph-structured NLPs arise in many applications such as dynamic optimization, stochastic optimization, optimization with partial differential equations, and network optimization. We show that the sensitivity of the primal-dual solution at node $i\in \mathcal{V}$ against a data perturbation at … Read more
In bilevel optimization, hierarchical optimization problems are considered in which two players – the leader and the follower – act and react in a non-cooperative and sequential manner. In many real-world applications, the leader may face a follower whose reaction deviates from the one expected by the leader due to some kind of bounded rationality. … Read more
We explore generalizations of some integrated learning and optimization frameworks for data-driven contextual stochastic optimization that can adapt to heteroscedasticity. We identify conditions on the stochastic program, data generation process, and the prediction setup under which these generalizations possess asymptotic and finite sample guarantees for a class of stochastic programs, including two-stage stochastic mixed-integer programs … Read more
Robust optimization (RO) is one of the key paradigms for solving optimization problems affected by uncertainty. Two principal approaches for RO, the robust counterpart method and the adversarial approach, potentially lead to excessively large optimization problems. For that reason, first order approaches, based on online-convex-optimization, have been proposed (Ben-Tal et al. (2015), Kilinc-Karzan and Ho-Nguyen … Read more
The usual integer programming formulation for the maximum clique problem has several undesirable properties, including a weak LP relaxation, a quadratic number of constraints and nonzeros when applied to sparse graphs, and poor guarantees on the number of branch-and-bound nodes needed to solve it. With this as motivation, we propose new mixed integer programs (MIPs) … Read more