Combinatorial Problems

This paper presents the SR-GCWS-CS probabilistic algorithm that combines Monte Carlo simulation with splitting techniques and the Clarke and Wright savings heuristic to find competitive quasi-optimal solutions to the Capacitated Vehicle Routing Problem (CVRP) in reasonable response times. The algorithm, which does not require complex fine-tuning processes, can be used as an alternative to other metaheuristics—such as Simulated Annealing, Tabu Search, Genetic Algorithms, Ant Colony Optimization or GRASP, which ...

Answer Set Programming is a very convenient framework to represent various problems issued from Artificial Intelligence (nonmonotonic reasoning, planning, diagnosis...). Furthermore, it can be used to neatly encode combinatorial problems. In all cases, the solutions are obtained as sets of literals: the Answer Sets. Ant Colony Optimization is a general metaheuristics that has been already successfully used to solve hard combinatorial problems (traveling salesman problem, graph coloring, quadratic assignment...). It is based on the collective behavior of artificial ants exploring a graph and exchanging pieces of information by means of pheromone traces. The purpose of this work is to show how Ant Colony Optimization can be used to compute an answer set of a logic program.

Recently, it has been recognizedthat phase transitions play an important role in the proba- bilistic analysis of combinatorial optimization problems. However, there are in fact many other relations that leadto close ties between computer science andstatistical physics. This review aims at presenting the tools andconcepts d esignedby physicists to d eal with optimization or decision problems in a language accessible

J. Carlos Alves, J. Canas Ferreira, C. Albuquerque, Jose F. Oliveira, J. Soeiro Ferreira, J. Silva Matos, FAFNER-Accelerating Nesting Problems with FPGAs, Proceedings of the Seventh Annual IEEE Symposium on Field-Programmable Custom Computing Machines, ...

This paper provides an approach to perform initial sizing optimisation of anisotropic composite panels with T-shaped stiffeners. The method divides the optimisation problem into two steps. At the first step, composite optimisation is performed using mathematical programming, where the skin and the stiffeners are modelled using lamination parameters accounting for their anisotropy. Skin and stiffener laminates are assumed to be

For a graph G=(V, E) its line graph L(G) has the node set E and two nodes of L(G) are adjacent if the corresponding edges of G have a common endpoint. The problem of finding G for a given L was already optimally solved by Lehot[7] and Roussopoulos[11]. Here we present a new dynamic solution to this problem, where we can add or delete a node v in L(G) in time proportional to the size of its adjacency list.

Metaheuristic search techniques strongly employ randomized decisions while searching for solutions to structural optimization problems. These techniques play an increasingly important role for practically solving hard combinatorial problems from various domains. Over the past few years there has been considerable success in developing metaheuristic search algorithms as well as randomized systematic search methods for obtaining solutions to discrete programming problems. This paper examines minimum weight design of pinjointed geodesic steel domes using seven metaheuristic search techniques; namely, simulated annealing, genetic algorithms, evolution strategies, particle swarm optimizer, tabu search, ant colony optimization and harmony search methods. The optimum design problem of geodesic steel domes is formulated according to design limitations stipulated by ASD-AISC (Allowable Stress Design Code of American Institute of Steel Institution). The minimum design loads and combined load ...

The flowshop scheduling problem (FSP) has been widely studied in the literature and many techniques for its solution have been proposed. Some authors have concluded that genetic algorithms are not suitable for this hard, combinatorial problem unless hybridization is used. This work proposes new genetic algorithms for solving the permutation FSP that prove to be competitive when compared to many other well known algorithms. The optimization criterion considered is the minimization of the total completion time or makespan (CmaxCmax). We show a robust genetic algorithm and a fast hybrid implementation. These algorithms use new genetic operators, advanced techniques like hybridization with local search and an efficient population initialization as well as a new generational scheme. A complete evaluation of the different parameters and operators of the algorithms by means of a Design of Experiments approach is also given. The algorithm's effectiveness is compared against 11 other methods, including genetic algorithms, tabu search, simulated annealing and other advanced and recent techniques. For the evaluations we use Taillard's well known standard benchmark. The results show that the proposed algorithms are very effective and at the same time are easy to implement.

En el ámbito de la lógica matemática existe un problema sobre la relación lógica entre dos versiones débiles del Axioma de elección (AE) que no se ha podido resolver desde el año 2000 (aproximadamente). Tales versiones están relacionadas con ultrafiltros no principales y con Propiedades Ramsey (Bernstein, Polarizada, Subretículo, Ramsey, Ordinales flotantes, etc). La primera versión débil del AE es la siguiente (A): “Existen ultrafiltros no principales sobre el conjunto de los números naturales (ℕ)”. Y la segunda versión débil del AE es la siguiente (B): “Existen ultraflitros sobre ℕ”. Se sabe que A implica B, pero se desconoce si B implica A. Di Prisco y Henle conjeturan en los artículos ([1], [2]) que esto no ocurre, es decir, conjeturan que B no implica A, en otras palabras, conjeturan que  A es más fuerte estrictamente que B, que A es independiente de B, pero esto no se ha podido demostrar todavía aunque se ha intentado hacer desde hace aproximadamente 21 años. Una descripción detallada de este problema abierto puede encontrarse en esta ponencia (dictada en el marco del Día Mundial de la Lógica 14-01-2022) y en  el artículo [3].

[1] C. Di Prisco y H. Henle. “Doughnuts, Floating Ordinals, Square Brackets, and Ultraflitters”. Journal of Symbolic Logic 65 (2000) 462-473. [2] C. Di Prisco y H. Henle. “Partitions of the reals and choice”. En “Models, algebras and proofs”. X. Caicedo y C.M. Montenegro. Eds. Lecture Notes in Pure and Appl. Math, 203, Marcel Dekker, 1999. [3] F. Galindo. “Tópicos de ultrafiltros”. Divulgaciones Matemáticas. Vol. 21, No 1-2, 2020.

Instituciones organizadoras del evento: Centro de Estudios Filosóficos de la  Pontificia Universidad Católica del Perú (PUCP), Universidad Nacional Autónoma de México (UNAM), Universidad Autónoma de la Ciudad de México (UACM), Universidad Autónoma de Madrid (UAM), Pontificia Universidad Católica de Argentina (UCA).

The study of partition properties of the set of real num- bers in several of its dierent presentations has been a very active field of research with interesting and sometimes surprising results. These partition properties are of the following form: if the set of real num- bers (or a related space) is partitioned into a finite collection of pieces, there is a "large" collection of reals contained in one of the pieces. Dif- ferent notions of largeness have been considered, and they give rise to properties of varied combinatorial character. The interplay be- tween metamathematical questions and combinatorial problems has been present throughout the development of the theory. Most of these properties are, in their full generality, inconsistent with the axiom of choice, but versions of them where only partitions into simple pieces are considered, for example, Borel pieces, can be proved to be true. Nevertheless, the unrestricted versions are consistent with weak forms of the ax...

We study convex relaxations of the image labeling problem on a continuous domain with regularizers based on metric interaction potentials. The generic framework ensures existence of minimizers and covers a wide range of relaxations of the originally combinatorial problem. We focus on two specific relaxations that differ in flexibility and simplicity -- one can be used to tightly relax any metric interaction potential, while the other one only covers Euclidean metrics but requires less computational effort. For solving the nonsmooth discretized problem, we propose a globally convergent Douglas-Rachford scheme, and show that a sequence of dual iterates can be recovered in order to provide a posteriori optimality bounds. In a quantitative comparison to two other first-order methods, the approach shows competitive performance on synthetical and real-world images. By combining the method with an improved binarization technique for nonstandard potentials, we were able to routinely recover discrete solutions within 1%--5% of the global optimum for the combinatorial image labeling problem.

The polyhedral approach is one of the most powerful techniques available for solvinghard combinatorial optimization problems. The main idea behind the technique is toconsider the linear relaxation of the integer combinatorial optimization problem, and tryto iteratively strengthen the linear formulation by adding violated strong valid inequalities,i.e., inequalities that are violated by the current fractional solution but satisfiedby all feasible solutions,

Combinatorial optimization problems arise in several areas ranging from management to mathematics and graph theory. Most combinatorial optimization problems are compu- tationally hard due to the restriction that a subset of the variables have to take integral values. During the last two decades there has been a remarkable development in polyhedral techniques leading to an increase in the size of