Annals of Operations Research

Maturana, Sergio; Ríos-Mercado, Roger Z.; Vera, Jorge

doi: 10.1007/s10479-019-03510-wpmid: N/A

Borghini, Fabrizio; Méndez-Díaz, Isabel; Zabala, Paula

doi: 10.1007/s10479-018-2977-xpmid: N/A

This paper addresses the edge coloring by total labeling graph problem. This is a labeling of the vertices and edges of a graph such that the weights (colors) of the edges, defined by the sum of its label and the labels of its two endpoints, determine a proper edge coloring of the graph. We propose two integer programming formulations and derive valid inequalities which are added as cutting planes on a Branch-and-Cut framework. In order to improve the efficiency of the algorithm, we also develop initial and primal heuristics. The algorithm is tested on random instances and the computational results show that it is very effective in comparison with CPLEX. It is displayed that it reduces both the CPU time (for solved instances) and the final percentage gap (for unsolved instances), and that it is capable of solving instances that are out of the reach of CPLEX.

da Silva, André Renato Villela; Ochi, Luiz Satoru; Barros, Bruno José da Silva; Pinheiro, Rian Gabriel S.

doi: 10.1007/s10479-018-2796-0pmid: N/A

This paper deals with the Flooding Problem on graphs. This problem consists in finding the shortest sequence of flooding moves that turns a colored graph into a monochromatic one. The problem has applications in some areas as disease propagation, for example. Three metaheuristics versions are proposed and compared with the literature results. A new integer programming formulation is also proposed and tested with the only formulation known. The obtained results indicate that both the proposed formulation and the Evolutionary Algorithm are, respectively, the best exact and heuristic approaches for the problem.

Durán, Guillermo; Safe, Martín; Warnes, Xavier

doi: 10.1007/s10479-017-2712-zpmid: N/A

Given a simple graph G, a set C⊆V(G)\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$C \subseteq V(G)$$\end{document} is a neighborhood cover set if every edge and vertex of G belongs to some G[v] with v∈C\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$v \in C$$\end{document}, where G[v] denotes the subgraph of G induced by the closed neighborhood of the vertex v. Two elements of E(G)∪V(G)\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$E(G) \cup V(G)$$\end{document} are neighborhood-independent if there is no vertex v∈V(G)\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$v\in V(G)$$\end{document} such that both elements are in G[v]. A set S⊆V(G)∪E(G)\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$S\subseteq V(G)\cup E(G)$$\end{document} is neighborhood-independent if every pair of elements of S is neighborhood-independent. Let ρn(G)\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\rho _{\mathrm {n}}(G)$$\end{document} be the size of a minimum neighborhood cover set and αn(G)\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\alpha _{\mathrm {n}}(G)$$\end{document} of a maximum neighborhood-independent set. Lehel and Tuza defined neighborhood-perfect graphs G as those where the equality ρn(G′)=αn(G′)\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\rho _{\mathrm {n}}(G^\prime ) = \alpha _{\mathrm {n}}(G^\prime )$$\end{document} holds for every induced subgraph G′\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$G^\prime $$\end{document} of G. In this work we prove forbidden induced subgraph characterizations of the class of neighborhood-perfect graphs, restricted to two superclasses of cographs: P4\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$P_4$$\end{document}-tidy graphs and tree-cographs. We give as well linear-time algorithms for solving the recognition problem of neighborhood-perfect graphs and the problem of finding a minimum neighborhood cover set and a maximum neighborhood-independent set in these same classes. Finally we prove that although for complements of trees finding these optimal sets can be achieved in linear-time, for complements of bipartite graphs it is NP\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\mathrm {NP}$$\end{document}-hard.

Moreno, Sebastián; Pereira, Jordi; Yushimito, Wilfredo

doi: 10.1007/s10479-017-2742-6pmid: N/A

The objective of territorial design for a distribution company is the definition of geographic areas that group customers. These geographic areas, usually called districts or territories, should comply with operational rules while maximizing potential sales and minimizing incurred costs. Consequently, territorial design can be seen as a clustering problem in which clients are geographically grouped according to certain criteria which usually vary according to specific objectives and requirements (e.g. costs, delivery times, workload, number of clients, etc.). In this work, we provide a novel hybrid approach for territorial design by means of combining a K-means-based approach for clustering construction with an optimization framework. The K-means approach incorporates the novelty of using tour length approximation techniques to satisfy the conditions of a pork and poultry distributor based in the region of Valparaíso in Chile. The resulting method proves to be robust in the experiments performed, and the Valparaíso case study shows significant savings when compared to the original solution used by the company.

Cea, Sebastián; Durán, Guillermo; Guajardo, Mario; Sauré, Denis; Siebert, Joaquín; Zamorano, Gonzalo

doi: 10.1007/s10479-019-03261-8pmid: N/A

This paper analyzes the procedure used by FIFA up until 2018 to rank national football teams and define by random draw the groups for the initial phase of the World Cup finals. A predictive model is calibrated to form a reference ranking to evaluate the performance of a series of simple changes to that procedure. These proposed modifications are guided by a qualitative and statistical analysis of the FIFA ranking. We then analyze the use of this ranking to determine the groups for the World Cup finals. After enumerating a series of deficiencies in the group assignments for the 2014 World Cup, a mixed integer linear programming model is developed and used to balance the difficulty levels of the groups.

de Andrade, Rafael Castro; Saraiva, Rommel Dias

doi: 10.1007/s10479-017-2743-5pmid: N/A

Let D=(V,A)\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$D=(V,A)$$\end{document} be a digraph with a set of vertices V, and a set of arcs A, with cij∈R\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$c_{ij} \in {\mathbb {R}}$$\end{document} representing the cost of each arc (i,j)∈A\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$(i,j) \in A$$\end{document}. The problem of finding the shortest-path avoiding negative cycles (SPNC) is NP-hard and consists in determining, if it exists, a path of minimum cost between two distinguished vertices s∈V\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$s \in V$$\end{document}, and t∈V\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$t \in V$$\end{document}. We propose three exact solution approaches for SPNC, including a compact primal-dual model, a combinatorial branch-and-bound algorithm, and a cutting-plane method. Extensive computational experiments performed on both benchmark and randomly generated instances indicate that our approaches either outperform or are competitive with existing mixed-integer programming models for the SPNC while providing optimal solutions for challenging instances in small execution times.

Guignard, Monique

doi: 10.1007/s10479-018-3092-8pmid: N/A

The Reformulation Linearization Technique (RLT) of Sherali and Adams (Manag Sci 32(10):1274–1290, 1986; SIAM J Discrete Math 3(3):411–430, 1990), when applied to a pure 0–1 quadratic optimization problem with linear constraints (P), constructs a hierarchy of LP (i.e., continuous and linear) models of increasing sizes. These provide monotonically improving continuous bounds on the optimal value of (P) as the level, i.e., the stage in the process, increases. When the level reaches the dimension of the original solution space, the last model provides an LP bound equal to the IP optimum. In practice, unfortunately, the problem size increases so rapidly that for large instances, even computing bounds for RLT models of level k (called RLTk) for small k may be challenging. Their size and their complexity increase drastically with k. To our knowledge, only results for bounds of levels 1, 2, and 3 have been reported in the literature. We are proposing, for certain quadratic problem types, a way of producing stronger bounds than continuous RLT1 bounds in a fraction of the time it would take to compute continuous RLT2 bounds. The approach consists in applying a specific decomposable Lagrangean relaxation to a specially constructed RLT1-type linear 0–1 model. If the overall Lagrangean problem does not have the integrality property, and if it can be solved as a 0–1 rather than a continuous problem, one may be able to obtain 0–1 RLT1 bounds of roughly the same quality as standard continuous RLT2 bounds, but in a fraction of the time and with much smaller storage requirements. If one actually decomposes the Lagrangean relaxation model, this two-step procedure, reformulation plus decomposed Lagrangean relaxation, will produce linear 0–1 Lagrangean subproblems with a dimension no larger than that of the original model. We first present numerical results for the Crossdock Door Assignment Problem, a special case of the Generalized Quadratic Assignment Problem. These show that just solving one Lagrangean relaxation problem in 0–1 variables produces a bound close to or better than the standard continuous RLT2 bound (when available) but much faster, especially for larger instances, even if one does not actually decompose the Lagrangean problem. We then present numerical results for the 0–1 quadratic knapsack problem, for which no RLT2 bounds are available to our knowledge, but we show that solving an initial Lagrangean relaxation of a specific 0–1 RLT1 decomposable model drastically improves the quality of the bounds. In both cases, solving the fully decomposed rather than the decomposable Lagrangean problem to optimality will make it feasible to compute such bounds for instances much too large for computing the standard continuous RLT2 bounds.

Campêlo, Manoel; Figueiredo, Tatiane; Silva, Ana

doi: 10.1007/s10479-018-2759-5pmid: N/A

Based on the sociometric analysis of social networks, we introduce the sociotechnical teams formation problem (STFP). Given a group of individuals with different skill-sets and a social network that captures the mutual affinity between them, the problem consists in finding a set of pairwise disjoint teams, as harmonious as possible, with a minimum specified number of individuals per team per skill. We prove that STFP is NP\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\mathcal {NP}$$\end{document}-hard and propose an integer linear programming formulation. We show several classes of facet-inducing inequalities for the corresponding polytope. Computational experiments performed on a set of 120 test instances attest the efficiency of a solution method based on the formulation strengthened by valid inequalities and on a simulated annealing algorithm used to provide good initial feasible solutions.

Melo, Wendel; Fampa, Marcia; Raupp, Fernanda

doi: 10.1007/s10479-018-2872-5pmid: N/A

We present an overview of the main algorithms in the literature for convex mixed integer nonlinear programming and discuss aspects of their implementation in a new open source computational package called Muriqui Optimizer. We provide extensive computational results comparing the implementations of all approaches considered on a set of 343 benchmark test problems. Finally, we present to the technical and scientific community the new software Muriqui Optimizer.