Drone delivery is drawing increasing attention in last-mile delivery. Effective solution methods to solve decision-making problems arising in drone delivery allow to run and assess drone delivery systems. In this paper, we focus on delivery systems with a single traditional vehicle and multiple drones working in tandem to fulfill customer requests. We address the Traveling … Read more
This work introduces the StoMADS-PB algorithm for constrained stochastic blackbox optimization, which is an extension of the mesh adaptive direct-search (MADS) method originally developed for deterministic blackbox optimization under general constraints. The values of the objective and constraint functions are provided by a noisy blackbox, i.e., they can only be computed with random noise whose … Read more
The running time for solving a mixed-integer linear optimization problem (MIP) strongly depends on the number of its integral variables. Bader et al. [Math. Progr. 169 (2018) 565–584] equivalently reformulate an integer program into an MIP that contains a reduced number of integrality constraints, when compared to the original model. Generalizing the concept of totally … Read more
In this paper we present the nonconvex exterior-point optimization solver (NExOS)—a novel first-order algorithm tailored to constrained nonconvex learning problems. We consider the problem of minimizing a convex function over nonconvex constraints, where the projection onto the constraint set is single-valued around local minima. A wide range of nonconvex learning problems have this structure including … Read more
This work proposes a partial optimization metaheuristic under special intensification conditions (POPMUSIC) for the classical capacitated vehicle routing problem (CVRP). The proposed approach uses a branch-cut-and-price algorithm as a powerful heuristic to solve subproblems whose dimensions are typically between 25 and 200 customers. The whole algorithm can be seen as the application of local search … Read more
We study non-convex optimization problems over simplices. We show that for a large class of objective functions, the convex approximation obtained from the Reformulation-Linearization Technique (RLT) admits optimal solutions that exhibit a sparsity pattern. This characteristic of the optimal solutions allows us to conclude that (i) a linear matrix inequality constraint, which is often added … Read more
We study the problem of finding an optimal assortment of products maximizing the expected revenue, in which customer preferences are modeled using a Nested Logit choice model. This problem is known to be polynomially solvable in a specific case and NP-hard otherwise, with only approximation algorithms existing in the literature. For the NP-hard cases, we … Read more
Inverse optimization is the problem of determining the values of missing input parameters that are closest to given estimates and that will make a given solution optimal. This study is concerned with the relationship of a particular inverse mixed integer linear optimization problem (MILPs) to both the original problem and the separation problem associated with … Read more
Despite the success of branch-and-cut methods for solving mixed integer bilevel linear optimization problems (MIBLPs) in practice, there are still gaps in both the theory and practice surrounding these methods. In the first part of this paper, we lay out a basic theory of valid inequalities and cutting-plane methods for MIBLPs that parallels the existing … Read more
Less-than-Truckload (LTL) carriers transport freight shipments from origins to destinations by consolidating freight using a network of terminals. As daily freight quantities are uncertain, carriers dynamically adjust planned freight routes on the day of operations. We introduce the Dynamic Freight Routing Problem (DFRP) and model this problem as a Markov Decision Process (MDP). To overcome … Read more