Bounds and Heuristic Algorithms for the Bin Packing Problem with Minimum Color Fragmentation

In this paper, we consider a recently introduced packing problem in which a given set of weighted items with colors has to be packed into a set of identical bins, while respecting capacity constraints and minimizing the total number of times that colors appear in the bins. We review exact methods from the literature and … Read more

The min-Knapsack Problem with Compactness Constraints and Applications in Statistics

In the min-Knapsack problem, one is given a set of items, each having a certain cost and weight. The objective is to select a subset with minimum cost, such that the sum of the weights is not smaller than a given constant. In this paper we introduce an extension of the min-Knapsack problem with additional … Read more

Exact Approaches for Convex Adjustable Robust Optimization

Adjustable Robust Optimization (ARO) is a paradigm for facing uncertainty in a decision problem, in case some recourse actions are allowed after the actual value of all input parameters is revealed. While several approaches have been introduced for the linear case, little is known regarding exact methods for the convex case. In this work, we … Read more

Models and Algorithms for the Weighted Safe Set Problem

Given a connected graph G = (V, E), a Safe Set S is a subset of the vertex set V such that the cardinality of each connected component in the subgraph induced by V \ S does not exceed the cardinality of any neighbor connected component in the subgraph induced by S. When the vertices … Read more

Adjustable robust optimization with discrete uncertainty

In this paper, we study Adjustable Robust Optimization (ARO) problems with discrete uncertainty. Under a very general modeling framework, we show that such two-stage robust problems can be exactly reformulated as ARO problems with objective uncertainty only. This reformulation is valid with and without the fixed recourse assumption and is not limited to continuous wait-and-see … Read more

Adjustable robust optimization with objective uncertainty

In this work, we study optimization problems where some cost parameters are not known at decision time and the decision flow is modeled as a two-stage process within a robust optimization setting. We address general problems in which all constraints (including those linking the first and the second stages) are defined by convex functions and … Read more

A solution algorithm for chance-constrained problems with integer second-stage recourse decisions

We study a class of chance-constrained two-stage stochastic optimization problems where the second-stage recourse decisions belong to mixed-integer convex sets. Due to the nonconvexity of the second-stage feasible sets, standard decomposition approaches cannot be applied. We develop a provably convergent branch-and-cut scheme that iteratively generates valid inequalities for the convex hull of the second-stage feasible … Read more

K-Adaptability in stochastic optimization

We consider stochastic problems in which both the objective function and the feasible set are affected by uncertainty. We address these problems using a K-adaptability approach, in which K solutions for the underlying problem are computed before the uncertainty dissolves and afterwards the best of them can be chosen for the realised scenario. This paradigm … Read more

A Branch-and-Price Algorithm for the Minimum Sum Coloring Problem

A proper coloring of a given graph is an assignment of colors (integer numbers) to its vertices such that two adjacent vertices receives di different colors. This paper studies the Minimum Sum Coloring Problem (MSCP), which asks for fi nding a proper coloring while minimizing the sum of the colors assigned to the vertices. This paper presents … Read more

Casting light on the hidden bilevel combinatorial structure of the k-Vertex Separator problem

Given an undirected graph, we study the capacitated vertex separator problem which asks to find a subset of vertices of minimum cardinality, the removal of which induces a graph having a bounded number of pairwise disconnected shores (subsets of vertices) of limited cardinality. The problem is of great importance in the analysis and protection of … Read more