Fleet planning under demand uncertainty: a reinforcement learning approach

This work proposes a model-free reinforcement learning approach to learn a long-term fleet planning problem subjected to air-travel demand uncertainty. The aim is to develop a dynamic fleet policy that adapts over time by intermediate assessments of the states. A Deep Q-network is trained to estimate the optimal fleet decisions based on the airline and … Read more

A Unifying Framework for Sparsity Constrained Optimization

In this paper, we consider the optimization problem of minimizing a continuously differentiable function subject to both convex constraints and sparsity constraints. By exploiting a mixed-integer reformulation from the literature, we define a necessary optimality condition based on a tailored neighborhood that allows to take into account potential changes of the support set. We then … Read more

Integer Programming Methods for Solving Binary Interdiction Games

This paper studies a general class of interdiction problems in which the solution space of both the leader and follower are characterized by two discrete sets denoted the leader’s strategy set and the follower’s structure set. In this setting, the interaction between any strategy-structure pair is assumed to be binary, in the sense that the … Read more

Factorization of completely positive matrices using iterative projected gradient steps

We aim to factorize a completely positive matrix by using an optimization approach which consists in the minimization of a nonconvex smooth function over a convex and compact set. To solve this problem we propose a projected gradient algorithm with parameters that take into account the effects of relaxation and inertia. Both projection and gradient … Read more

On the generalized $\varthetahBcnumber and related problems for highly symmetric graphs

This paper is an in-depth analysis of the generalized $\vartheta$-number of a graph. The generalized $\vartheta$-number, $\vartheta_k(G)$, serves as a bound for both the $k$-multichromatic number of a graph and the maximum $k$-colorable subgraph problem. We present various properties of $\vartheta_k(G)$, such as that the series $(\vartheta_k(G))_k$ is increasing and bounded above by the order … Read more

Branch-and-bound Algorithm for Optimal Sparse Canonical Correlation Analysis

Canonical correlation analysis (CCA) is a family of multivariate statistical methods for extracting mutual information contained in multiple datasets. To improve the interpretability of CCA, here we focus on the mixed-integer optimization (MIO) approach to sparse estimation. This approach was first proposed for sparse linear regression in the 1970s, but it has recently received renewed … Read more

Limit sets in global multiobjective optimization

Inspired by the recently introduced branch-and-bound method for continuous multiobjective optimization problems from G. Eichfelder, P. Kirst, L. Meng, O. Stein, A general branch-and-bound framework for continuous global multiobjective optimization, Journal of Global Optimization, 80 (2021) 195-227, we study for a general class of branch-and-bound methods in which sense the generated terminal enclosure and the … Read more

SOS-SDP: an Exact Solver for Minimum Sum-of-Squares Clustering

The minimum sum-of-squares clustering problem (MSSC) consists in partitioning n observations into k clusters in order to minimize the sum of squared distances from the points to the centroid of their cluster. In this paper, we propose an exact algorithm for the MSSC problem based on the branch-and-bound technique. The lower bound is computed by … Read more

NOMAD version 4: Nonlinear optimization with the MADS algorithm

NOMAD is software for optimizing blackbox problems. In continuous development since 2001, it constantly evolved with the integration of new algorithmic features published in scientific publications. These features are motivated by real applications encountered by industrial partners. The latest major release of NOMAD, version 3, dates from 2008. Minor releases are produced as new features … Read more

Solving the Traveling Salesman Problem with release dates via branch-and-cut

In this paper we study the Traveling Salesman Problem with release dates (TSP-rd) and completion time minimization. The TSP-rd considers a single vehicle and a set of customers that must be served exactly once with goods that arrive to the depot over time, during the planning horizon. The time at which each requested good arrives … Read more