This paper studies the problems of partitioning the vertices of a graph G = (V,E) into (or covering with) a minimum number of low-diameter clusters from the lenses of approximation algorithms and integer programming. Here, the low-diameter criterion is formalized by an s-club, which is a subset of vertices whose induced subgraph has diameter at … Read more
Sandwiching algorithms, also known as Benson-type algorithms, approximate the nondominated set of convex bounded multiobjective optimization problems by constructing and iteratively improving polyhedral inner and outer approximations. Using a set-valued metric, an estimate of the approximation quality is determined as the distance between the inner and outer approximation. The convergence of the algorithm is evaluated … Read more
In practical applications, one often has not only one, but several objectives that need to be optimized simultaneously. What is more, modeling such real world problems usually involves using both, continuous and integer variables. This then results in multi-objective mixed-integer optimization problems, which are in focus of this paper. We present an approximation concept, called … Read more
In this work we investigate the min-max-min robust optimization problem and the k-adaptability robust optimization problem for binary problems with uncertain costs. The idea of the first approach is to calculate a set of k feasible solutions which are worst-case optimal if in each possible scenario the best of the k solutions is implemented. It … Read more
We consider two-stage robust linear programs with uncertain righthand side. We develop a General Polyhedral Approximation (GPA), in which the uncertainty set $\mathcal{U}$ is substituted by a finite set of polytopes derived from the vertex set of an arbitrary polytope that dominates $\mathcal{U}$. The union of the polytopes need not contain $\mathcal{U}$. We analyse and … Read more
We study the D-optimal Data Fusion (DDF) problem, which aims to select new data points, given an existing Fisher information matrix, so as to maximize the logarithm of the determinant of the overall Fisher information matrix. We show that the DDF problem is NP-hard and has no constant-factor polynomial-time approximation algorithm unless P = NP. … Read more
We investigate the optimal piecewise linear interpolation of the bivariate product xy over rectangular domains. More precisely, our aim is to minimize the number of simplices in the triangulation underlying the interpolation, while respecting a prescribed approximation error. First, we show how to construct optimal triangulations consisting of up to five simplices. Using these as … Read more
We study a two-stage, finite-scenarios stochastic version of the set multicover problem, where there is uncertainty about a demand for each element to be covered and the penalty cost is imposed linearly on the shortfall in each demand. This problem is NP-hard and has an application in shift scheduling in crowdsourced delivery services. For this … Read more
We study a competitive facility location problem (CFLP), where two firms sequentially open new facilities within their budgets, in order to maximize their market shares of demand that follows a probabilistic choice model. This process is a Stackelberg game and admits a bilevel mixed-integer nonlinear program (MINLP) formulation. We derive an equivalent, single-level MINLP reformulation … Read more
In this paper, we study assortment planning under the marginal distribution model (MDM), a semiparametric choice model that only requires information about the marginal noise in the utilities of alternatives and does not assume independence of the noise terms. It is already known in the literature that the multinomial logit (MNL) model belongs to the … Read more