We study the Knapsack Problem with Conflict Graph (KPCG), a generalization of the Knapsack Problem in which a conflict graph specifies pairs of items (vertices of the graph) which cannot be simultaneously selected in a solution. The KPCG asks for determining a maximum-profit subset of items of total weight no larger than the knapsack capacity … Read more
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
As we approach the physical limits predicted by Moore’s law, a variety of specialized hardware is emerging to tackle specialized tasks in different domains. Within combinatorial optimization, adiabatic quantum computers, CMOS annealers, and optical parametric oscillators are few of the emerging specialized hardware technology aimed at solving optimization problems. In terms of mathematical framework, the … Read more
Beginning in the 1960s, techniques from operations research began to be used to generate political districting plans. A classical example is the integer programming model of Hess et al. (Operations Research 13(6):998–1006, 1965). Due to the model’s compactness-seeking objective, it tends to generate contiguous or nearly-contiguous districts, although none of the model’s constraints explicitly impose … Read more
We consider non-convex mixed-integer quadratic programs in which all variables are explicitly bounded. Many exact methods for such problems use additional variables, representing products of pairs of original variables. We study the convex hull of feasible solutions in this extended space. Some other approaches use bit representation to convert bounded integer variables into binary variables. … Read more
In this paper we go one step further in the automatic generation of FPTASes for multi-stage stochastic dynamic programs with scalar state and action spaces, in where the cost-to-go functions have a monotone structure in the state variable. While there exist a few frameworks for automatic generation of FPTASes, so far none of them is … Read more
We consider the problem of optimizing a linear function over a lattice polytope P contained in [0,k]^n and defined via m linear inequalities. We design a simplex algorithm that, given an initial vertex, reaches an optimal vertex by tracing a path along the edges of P of length at most O(n^6 k log k). The … Read more
We discuss a new facility layout problem, the so-called Directed Circular Facility Layout Problem (DCFLP). The DCFLP aims to find an optimal arrangement of machines on a circular material handling system such that the total weighted sum of the center-to-center distances between all pairs of machines measured in clockwise direction is minimized. Several real-world applications, … Read more
Split delivery routing problems are concerned with serving the demand of a set of customers with a fleet of capacitated vehicles at minimum cost, where a customer can be served by more than one vehicle if beneficial. They generalize traditional variants of routing problems and have applications in commercial as well as humanitarian logistics. Previously, … Read more
Polynomial optimization problems over binary variables can be expressed as integer programs using a linearization with extra monomials in addition to those arising in the given polynomial. We characterize when such a linearization yields an integral relaxation polytope, generalizing work by Del Pia and Khajavirad (SIAM Journal on Optimization, 2018) and Buchheim, Crama and Rodríguez-Heck … Read more