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
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
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
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
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
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
When constructing political districting plans, prominent criteria include population balance, contiguity, and compactness. The compactness of a districting plan, which is often judged by the “eyeball test,” has been quantified in many ways, e.g., Length-Width, Polsby-Popper, and Moment-of-Inertia. This paper considers the number of cut edges, which has recently gained traction in the redistricting literature … Read more
This work proposes to create a tool for support for cost reduction in wagon maintenance through the distribution of the annual plan in workshops. The distribution depends on the type of wagon, the scope of the maintenance service that each workshop serves, and the capacity that is supported by the workshops. This plan is a … Read more
In this paper, we study a retailer price optimization problem which includes the practical constraints: maximum number of price changes and minimum amount of price change (if a change is recommended). We provide a closed-form formula for the Euclidean projection onto the feasible set defined by these two constraints, based on which a simple gradient … Read more
A new business opportunity beckons with the emergence of prosumers. This article proposes an innovative business model to harness the potential of aggregating behind-the-meter residential storage in which the aggregator compensates participants for using their storage system on an on-demand basis. A bilevel optimization model is developed to evaluate the potential of this proposed business … Read more