Runtime analyses of randomized search heuristics for combinatorial optimization problems often depend on the size of the largest weight. We consider replacing the given set of weights with smaller weights such that the behavior of the randomized search heuristic does not change. Upper bounds on the size of the new, equivalent weights allow us to obtain upper bounds on the expected runtime of su...

Computational molecular biology has emerged as one of the most exciting interdisciplinary fields. It has currently benefited from concepts and theoretical results obtained by different scientific research communities, including genetics, biochemistry, and computer science. In the past few years it has been shown that a large number of molecular biology problems can be formulated as combinatoria...

In this paper an application of constraint logic programming (CLP) to the resolution of nesting problems is presented. Nesting problems are a special case of the cutting and packing problems, in which the pieces generally have non-convex shapes. Due to their combinatorial optimization nature, nesting problems have traditionally been tackled by heuristics and in the recent past by meta-heuristic...

The Multiscale method is a class of algorithmic techniques for solving efficiently and effectively large-scale computational and optimization problems. This method was originally invented for solving elliptic partial differential equations and up to now it represents the most effective class of numerical algorithms for them. During the last two decades, there were many successful attempts to ad...

Many important applications in the real world that can be modelled as combinatorial optimization problems are actually dynamic in nature. However, research on dynamic optimization focuses on continuous optimization problems, and rarely targets combinatorial problems. Moreover, dynamic combinatorial problems, when addressed, are typically tackled within an application context. In this thesis, dy...

In the probabilistic two-dimensional Bin Packing problem (2D-PBPP), one is asked to pack a random number of rectangular items, without overlap and any rotation, into the minimum number of identical square bins. In this paper we consider the re-optimization procedure used for solving probabilistic combinatorial optimization problems and an approximation of this strategy: the redistribution strat...

The Traveling Salesman Problem (TSP) is a well-known NPhard combinatorial optimization problem, for which a large variety of evolutionary algorithms are known. However, these heuristics fail to find solutions for large instances due to time and memory constraints. Here, we discuss a set of edge fixing heuristics to transform large TSP problems into smaller problems, which can be solved easily w...

We perform a statistical analysis of the structure of the search space of some planar, euclidian instances of the traveling salesman problem. We want to depict this structure from the point of view of iterated local search algorithms. The objective is two-fold: understanding the experimentally known good performance of metaheuristics on the TSP and other combinatorial optimization problems; des...

Exact algorithms allow one to find optimal solutions to NP-hard combinatorial optimization (CO) problems. Many research papers report on solving large instances of some NPhard problems (see, e.g., [25, 27]). The running time of exact algorithms is often very high for large instances (many hours or even days), and very large instances remain beyond the capabilities of exact algorithms. Even for ...

Many combinatorial optimization problems can be phrased in the language of constraint satisfaction problems. We introduce a graph neural network architecture for solving such The is generic; it works all binary Training unsupervised, and sufficient to train on relatively small instances; resulting networks perform well much larger instances (at least 10-times larger). experimentally evaluate ou...