Abstract: Publication date: July 2017 Source:Electronic Notes in Discrete Mathematics, Volume 60 Author(s): Akito Oshima, Rikio Ichishima, Francesc A. Muntaner-Batle In this paper, we introduce two kinds of new parameters for studying graceful properties of graphs. We also establish the relation among these parameters. Moreover, we provide the relation between super edge-magic labelings and graceful labelings of trees.

Abstract: Publication date: July 2017 Source:Electronic Notes in Discrete Mathematics, Volume 60 Author(s): R.C. Bunge, S.I. El-Zanati, J. Mudrock, C. Vanden Eynden, W. Wannasit It is known that for a given (simple) graph G with n edges, there exits a cyclic G-decomposition of K 2 n + 1 if and only if G admits a ρ-labeling. It is also known that if G is bipartite and it admits an ordered ρ-labeling, then there exists a cyclic G-decomposition of K 2 n x + 1 for every positive integer x. We extend these concepts to labelings of multigraphs through what we call λ-fold ρ-labelings and ordered λ-fold ρ-labelings. Let K m λ denote the λ-fold complete graph of order m. We sho that if a subgraph G of K 2 n / λ + 1 λ has size n, there exits a cyclic G-decomposition of K 2 n / λ + 1 λ if and only if G admits a λ-fold ρ-labeling. If in addition G is bipartite and it admits an ordered λ-fold ρ-labeling, then there exists a cyclic G-decomposition of K 2 n x / λ + 1 λ for every positive integer x. We discuss some classes of graphs and multigraphs that admit such labelings.

Abstract: Publication date: July 2017 Source:Electronic Notes in Discrete Mathematics, Volume 60 Author(s): Martin Bača, Stanislav Jendrol' In this paper we give a survey on several types of colourings of elements of graphs by different types of labellings.

Abstract: Publication date: July 2017 Source:Electronic Notes in Discrete Mathematics, Volume 60 Author(s): Mariusz Meszka, Alexander Rosa We extend the well-known notion of a ρ-labelling for ordinary graphs to 3-uniform hypergraphs, and discuss its connection to decompositions of the complete 3-uniform hypergraph.

Abstract: Publication date: July 2017 Source:Electronic Notes in Discrete Mathematics, Volume 60 Author(s): Mark Korenblit The paper investigates relationship between algebraic expressions and labeled graphs. We consider directed grid graphs having m rows and n columns. Our intent is to simplify the expressions of these graphs. With that end in view, we describe two algorithms which generate expressions of polynomial sizes for directed grid graphs.

Abstract: Publication date: July 2017 Source:Electronic Notes in Discrete Mathematics, Volume 60 Author(s): Toru Hasunuma In this paper, we newly introduce the class of universalized Sierpiński graphs ϒ(G, n) which includes generalized Sierpiński graphs S(n, G) and extended Sierpiński graphs S ++(n, k). We then present constructions of universalized Sierpiński graphs based on labeling manipulations which are useful to investigate ϒ(G, n) without depending on the exact n-tuple notation of a vertex in ϒ(G, n). We also present structural properties of universalized Sierpiński graphs such as connectivity, various colorings, hamiltonicity, factorizations, and edge-disjoint factors.

Abstract: Publication date: July 2017 Source:Electronic Notes in Discrete Mathematics, Volume 60 Author(s): Susana-Clara López Gallian's survey shows that there is a big variety of labelings of graphs. By means of (di)graphs products we can establish strong relations among some of them. Moreover, due to the freedom of one of the factors, we can also obtain enumerative results that provide lower bounds on the number of nonisomorphic labelings of a particular type. In this paper, we will focus in three of the (di)graphs products that have been used in these duties: the ⊗ h -product of digraphs, the weak tensor product of graphs and the weak ⊗ h -product of graphs.

Abstract: Publication date: July 2017 Source:Electronic Notes in Discrete Mathematics, Volume 60 Author(s): Zsolt Tuza We propose the study of many new variants of two-person graph labeling games. Hardly anything has been done in this wide open field so far.

Abstract: Publication date: July 2017 Source:Electronic Notes in Discrete Mathematics, Volume 60 Author(s): Dalibor Fronček, Petr Kovář, Tereza Kovářová, Bohumil Krajc, Michal Kravčenko, Aaron Shepanik, Adam Silber Let G = ( V , E ) be a simple graph of order n. A bijection f : V → { 1 , 2 , … , n } is a handicap labeling of G if there exists an integer ℓ such that ∑ u ∈ N ( v ) f ( u ) = ℓ + f ( v ) for all v ∈ V , where N(v) is the set of all vertices adjacent to v. Any graph which admits a handicap labeling is a handicap graph. We present an overview of results, which completely answer the question of existence of regular handicap graphs of even order.

Abstract: Publication date: July 2017 Source:Electronic Notes in Discrete Mathematics, Volume 60 Author(s): S.A. Katre, Laleh Yahyaei, S. Arumugam Let G = ( V , E ) be a graph. An injection f : V → { 2 , 3 , 4 , … , } is called a coprime labeling of G if for any two vertices u , v ∈ V , u and v are adjacent if and only if f(u) and f(v) are coprime. We prove that every graph admits a coprime labeling. A prime number p is said to be used by the coprime labeling f if p divides f(v) for some v ∈ V . Let μ ( G , f ) be the number of primes used by the labeling f. Then min { μ ( G , f ) : f is a coprime labeling of G } is called the coprime index of G and is denoted by μ ( G ) . We prove that for any graph G with Δ ( G ) < n − 1 , μ ( G ) = θ 1 ( G ‾ ) where θ 1 ( G ‾ ) is the edge-clique covering number of G ‾ . We also determine the value of μ ( G ) for several classes of graphs.

Abstract: Publication date: July 2017 Source:Electronic Notes in Discrete Mathematics, Volume 60 Author(s): Mirka Miller, Joe Ryan, Zdeněk Ryjáček A sum graph G is a graph with a mapping of the vertex set of G onto a set of positive integers S in such a way that two vertices of G are adjacent if and only if the sum of their labels is an element of S. In an exclusive sum graph the integers of S that are the sum of two other integers of S form a set of integers that label a collection of isolated vertices associated with the graph G. A graph bears a k-exclusive sum labelling (abbreviated k-ESL), if the set of isolated vertices is of cardinality k. In this paper, observing that the property of having a k-ESL is hereditary, we provide a characterisation of graphs that have a k-exclusive sum labelling, for any k ≥ 1 , in terms of describing a universal graph for the property.

Abstract: Publication date: June 2017 Source:Electronic Notes in Discrete Mathematics, Volume 59 Author(s): Samy Abbes We study the notion of uniform measure on the space of infinite executions of a 1-safe Petri net. Here, executions of 1-safe Petri nets are understood up to commutation of concurrent transitions, which introduces a challenge compared to usual transition systems. We obtain that the random generation of infinite executions reduces to the simulation of a finite state Markov chain. Algorithmic issues are discussed.

Abstract: Publication date: June 2017 Source:Electronic Notes in Discrete Mathematics, Volume 59 Author(s): Martin Loebl, Pavel Rytíř We show that the weight enumerator of any binary linear code is equal to the permanent of a 3-dimensional hypermatrix (3-matrix). We also show that each permanent is a determinant of a 3-matrix. As an application we write the dimer partition function of a finite 3-dimensional cubic lattice as the determinant of the vertex-adjacency 3-matrix of a 2-dimensional simplicial complex which preserves the natural embedding of the cubic lattice. Keywords: Ising problem, dimer problem, partition function, perfect matching, Kasteleyn matrix, linear binary code, permanent, 3-dimensional cubic lattice, triangular configuration, 2-dimensional simplicial complex.

Abstract: Publication date: June 2017 Source:Electronic Notes in Discrete Mathematics, Volume 59 Author(s): Malvina G. Vamvakari Consider a sequence of independent q-Bernoulli trials with odds of success geometrically decreasing with rate q, 0 < q < 1 . In this work, we introduce the process generated by making a step to the right when the outcome of the ith q-Bernoulli trial is “success” and a step to the left otherwise, for i = 1 , 2 , … , n . Furhtermore, the ith q-Bernoulli trial, happens during the ith part of a suitable defined partition of the time period ( 0 , t ] , i = 1 , 2 , … , n . The position X n , q ( t ) at time t of this process defines a q-random walk. Also, asymptotically, as n → ∞ , by a q-analogue of the De Moivre-Laplace theorem, we approximate this q-random walk by a q-Brownian motion. This q-Brownian motion is the continuous analogue of the q-random walk process and is distributed according to a linear transformed standardized Stieltjes-Wigert distribution.

Abstract: Publication date: June 2017 Source:Electronic Notes in Discrete Mathematics, Volume 59 Author(s): Stephen DeSalvo We demonstrate an approach for exact sampling of certain discrete combinatorial distributions, which is a hybrid of exact Boltzmann sampling and the recursive method, using probabilistic divide-and-conquer (PDC). The approach specializes to exact Boltzmann sampling in the trivial setting, and specializes to PDC deterministic second half in the first non-trivial application. A large class of examples is given for which this method broadly applies, and several examples are worked out explicitly.

Abstract: Publication date: June 2017 Source:Electronic Notes in Discrete Mathematics, Volume 59 Author(s): Enrico Formenti, Paolo Massazza The behaviour of a bad Tetris player suggests a class of polyominoes that we call prefix-closed. Such a class contains all polyominoes P such that for any integer i > 0 the first i columns of P form a polyomino. We provide a simple discrete dynamical system that allows us to define an algorithm for generating all prefix-closed polyominoes of size n in constant amortized time using O ( n ) space.

Abstract: Publication date: June 2017 Source:Electronic Notes in Discrete Mathematics, Volume 59 Author(s): Jeremie Lumbroso, Marni Mishna, Yann Ponty A two-dimensional lattice walk model is said to be reluctant if its defining step set has a strong drift away from the negative half-planes. We consider the uniform random generation of reluctant walks of length n in the positive quadrant, noting that a naive rejection from unconstrained walks has exponential time complexity. A baseline algorithm using the recursive method requires Θ ( n 4 ) time and memory. We consider an alternative strategy which draws unidimensional walks from a well-chosen half-plane model, as identified by Johnson, Mishna and Yeats. The resulting generator is provably efficient, and typically outperforms the baseline algorithm. A general analysis of its complexity requires further developments to characterize the subexponential growth factors of reluctant walks, and motivates the design of efficient algorithms for the generation of 1D walks taking irrational step sets.

Abstract: Publication date: June 2017 Source:Electronic Notes in Discrete Mathematics, Volume 59 Author(s): Riccardo Biagioli, Frédéric Jouhet, Philippe Nadeau We give exact formulas for the bivariate generating series of 321-avoiding affine permutations with respect to rank and Coxeter length. We use two different combinatorial approaches, both based on the theory of heaps of pieces.

Abstract: Publication date: June 2017 Source:Electronic Notes in Discrete Mathematics, Volume 59 Author(s): Cyril Banderier, Michael Wallner In queuing theory, it is usual to have some models with a “reset” of the queue. In terms of lattice paths, it is like having the possibility of jumping from any altitude to zero. These objects have the interesting feature that they do not have the same intuitive probabilistic behavior like classical Dyck paths (the typical properties of which are strongly related to Brownian motion theory), and this article quantifies some relations between these two types of paths. We give a bijection with some other lattice paths and a link with a continuous fraction expansion, and prove several formulae for related combinatorial structures conjectured in the On-line Encyclopedia of Integer Sequences. Thanks to the kernel method and via analytic combinatorics, we derive the enumeration and limit laws of these “lattice paths with catastrophes”, for any finite set of jumps.

Abstract: Publication date: June 2017 Source:Electronic Notes in Discrete Mathematics, Volume 59 Author(s): Adrien Boussicault, Veronica Guerrini This paper introduces a further combinatorial interpretation in terms of permutations of the well-known Catalan number sequence. The permutations we treat have been called cap permutations because of their look, and their family does not coincide with any permutation class defined by the avoidance of a pattern of length 3. Rather, they come from labeling parallelogram polyominoes in a way that resembles some operations defined on tree-like tableaux. Our main contribution is to provide a growth for such family of permutations that is ruled by an ECO operator and allows us to write a new, and non-trivial, succession rule for Catalan numbers. Then, we move on to characterize cap permutations: first, it is studied a simple subfamily of cap permutations that possesses nice properties, and then we extend them to the bigger family of all cap permutations.

Abstract: Publication date: June 2017 Source:Electronic Notes in Discrete Mathematics, Volume 59 Author(s): Alexandre Blondin Massé, Éric Marcotte In 2009, Brlek, Koskas and Provençal proposed a data structure allowing self-intersection detection of discrete paths in linear time and space in the worst case. However, their ideas do not apply in a straightforward manner to arbitrary lattices. We propose an extension of their results to lattices of Z 2 whose adjacency relation is between points at distance one with respect to the uniform norm.

Abstract: Publication date: June 2017 Source:Electronic Notes in Discrete Mathematics, Volume 59 Author(s): Adrien Boussicault, Patxi Laborde-Zubieta A periodic parallelogram polyomino is a parallelogram polyomino in which we glue the first and the last column. In this work we extend a bijection between ordered trees and parallelogram polyominoes in order to compute the generating function of periodic parallelogram polyominoes with respect to the height, the width and the intrinsic thickness, a new statistic unrelated to the existing statistics on parallelogram polyominoes. Moreover we define a rotation over periodic parallelogram polyominoes, which induces a partitioning in equivalent classes called strips. We also compute the generating function of strips using the theory of Pólya.

Abstract: Publication date: June 2017 Source:Electronic Notes in Discrete Mathematics, Volume 59 Author(s): Olivier Bodini, Antoine Genitrini, Nicolas Rolin We introduce a new technique to specify increasing labeled structures. For such objects, the boxed product as introduced by Greene is sufficient to efficiently specify the class, however for particular classes the size of the specification is very large. In particular, in the case of partially ordered sets, the calculus of the total orders compatibles with the poset (called linear extensions) can be tedious. We here developed an idea due to Stanley that uses a geometrical interpretation to calculate the linear extensions of a given poset. We will present a way to extend this idea to the symbolic method, and illustrate it with the example of specific increasing trees with exactly one repeated label, and show how to uniformly generate such structures.

Abstract: Publication date: April 2017 Source:Electronic Notes in Discrete Mathematics, Volume 58 Author(s): Samuel Souza Brito, Haroldo Gambini Santos Chvàtal-Gomory cuts are well-known cutting planes for Integer Programming problems. As shown in previous works, the inclusion of these cuts allows to significantly reducing the integrality gap. This work presents a Local Search heuristic approach based on Variable Neighborhood Search to discover violated Chvàtal-Gomory inequalities. Since this problem is known to be NP-hard, this approach was designed to generate violated inequalities in restricted amounts of time. Constraints are grouped in several sets, considering the amount of common variables. These sets are processed in parallel in order to obtain the best multipliers and produce violated cuts. We report some preliminary results obtained for MIPLIB 3.0 and 2003 instance sets, comparing our approach with an integer programming based separation method. Our algorithm was able to separate many violated inequalities, reducing the duality gap. Furthermore, it uses an extended numerical precision implementation, since it is not specifically bound to simplex based solvers.

Abstract: Publication date: April 2017 Source:Electronic Notes in Discrete Mathematics, Volume 58 Author(s): Thays A. Oliveira, Vitor N. Coelho, Helena Ramalhinho, Marcone J.F. Souza, Bruno N. Coelho, Daniel C. Rezende, Igor M. Coelho This paper focuses on Book Marketing Campaigns, where the benefit of offering each book is calculated based on a bipartite graph (biclique). A quasi Biclique problem is assessed for obtaining the probabilities of success of a given client buy a given book, considering it had received another book as free offer. The remaining optimization decision problem can be solved following the Targeted Offers Problem in Direct Marketing Campaigns. The main objective is to maximize the feedback of customers purchases, offering books to the set of customers with the highest probability of buying others ones from its biclique and, at the same time, minimizing campaign operational costs. Given the combinatorial nature of the problem and the large volume of data, which can involve real cases with up to one million customers, metaheuristics procedures have been used as an efficient way for solving it. Here, a hybrid trajectory search based algorithm, namely GGVNS, which combines the Greedy Randomized Adaptive Search Procedures and General Variable Neighborhood Search, is used. The strategy for generating the quasi Biclique problem is described and a new instance generator for the TOPDMC is introduced. Computational results regarding the GGVNS algorithm shows it is able to find useful and profitable sets of clients.

Abstract: Publication date: April 2017 Source:Electronic Notes in Discrete Mathematics, Volume 58 Author(s): Olivera Janković, Zorica Stanimirović This paper deals with the uncapacitated r-allocation p-hub maximal covering problem (UrApHMCP) with binary coverage criterion. This problem consists of choosing p hub locations from a set of nodes so as to maximize the total demand covered while satisfying the r-allocation strategy. The applied binary coverage criterion ensures that the distance between any origin–destination pair through located hubs should be shorter than a predetermined distance. An integer linear programming model for the considered problem is introduced. As a solution method to UrApHMCP, a General Variable Neighborhood Search (GVNS) heuristic is proposed. A greedy procedure is used to construct an initial solution to GVNS. Neighborhood structures explored within the GVNS are defined by operators that change a set of chosen hubs and node to hub assignments. Variable Neighborhood Descent with sequential search strategy is used as an improvement procedure. The results of computational experiments on standard p-hub benchmark instances show the efficiency and effectiveness of the proposed GVNS when solving the considered problem.

Abstract: Publication date: April 2017 Source:Electronic Notes in Discrete Mathematics, Volume 58 Author(s): Y. Kochetov, A. Kondakov We study a new variant of the bin packing problem. Given a set of items, each item has a set of colors. Each bin has a color capacity, the total number of colors for a bin is the union of colors for its items and can not exceed the bin capacity. We want to pack all items into the minimal number of bins. For this NP-hard problem we apply the column generation technique based on the VNS matheuristic for the pricing problem. To get optimal or near optimal solutions we apply VNS matheuristic again using optimal solution for the large scale linear programming relaxation. Computational experiments are reported for the randomly generated test instances with large bin capacity and number of items up to 250.

Abstract: Publication date: April 2017 Source:Electronic Notes in Discrete Mathematics, Volume 58 Author(s): Nikolaos Antoniadis, Angelo Sifaleras In this paper, we study various parallelization schemes for the Variable Neighborhood Search (VNS) metaheuristic on a CPU-GPU system via OpenMP and OpenACC. A hybrid parallel VNS method is applied to recent benchmark problem instances for the multi-product dynamic lot sizing problem with product returns and recovery, which appears in reverse logistics and is known to be NP-hard. We report our findings regarding these parallelization approaches and present promising computational results.

Abstract: Publication date: April 2017 Source:Electronic Notes in Discrete Mathematics, Volume 58 Author(s): Vívian L. Aguiar Santos, José Elias C. Arroyo In this paper, we study an unrelated parallel machine scheduling problem in which the jobs cause deterioration of the machines. This deterioration decreases the performance of the machines, and therefore, the processing times of the jobs are increased over time. The problem is to find the processing sequence of jobs on each machine in order to reduce the deterioration of the machines and consequently minimize the makespan. This problem is NP-hard when the number of machines is greater or equal than two, and hence we propose a heuristic based on the Iterated Greedy meta-heuristic coupled with a variant of the Variable Neighborhood Descent method that uses a random ordering of neighborhoods in local search phase. The performance of our heuristic, named IG-RVND, is compared with the state-of-the-art meta-heuristic proposed in the literature for the problem under study. The results show that the our heuristic outperform the existing algorithm by a significant margin.

Abstract: Publication date: April 2017 Source:Electronic Notes in Discrete Mathematics, Volume 58 Author(s): Sana Frifita, Malek Masmoudi, Jalel Euchi Home healthcare centers are facing increasing demands and researchers are attracted by the related routing and scheduling issue that is presented in literature as a VRP with synchronization and time windows constraints. The goal is to optimize the assignment of visits to home caregivers and the sequence of visits execution. In this paper, a General Variable Neighborhood Search is provided. Experiments conducted on benchmark instances from the literature clearly show that our method is fast and outperforms the existing approaches on half of the instances.

Abstract: Publication date: April 2017 Source:Electronic Notes in Discrete Mathematics, Volume 58 Author(s): Samia Hasni, Said Toumi, Bassem Jarboui, Anis Mjirda We address a multi-product version of the IRP, in which a supplier is responsible for the distribution of several products to a set of geographically dispersed customers using a feet of heterogeneous vehicles. We deal with a deterministic version of demand rates in which the supplier has full knowledge of future demands. To generate good solutions, we have developed an algorithm based on the Variable Neighborhood Search capable of solving this variant. Our comparative tests on a large set of artificial instances have shown that our heuristic can produce high quality solutions.

Abstract: Publication date: April 2017 Source:Electronic Notes in Discrete Mathematics, Volume 58 Author(s): V.N. Coelho, I.M. Coelho, B.N. Coelho, M.J.F. Souza, F.G. Guimarães, E.J. da S. Luz, A.C. Barbosa, M.N. Coelho, G.G. Netto, R.C. Costa, A.A. Pinto, A. de P. Figueiredo, M.E.V. Elias, D.C.O.G. Filho, T.A. Oliveira Brain activity can be seen as a time series, in particular, electroencephalogram (EEG) can measure it over a specific time period. In this regard, brain fingerprinting can be subjected to be learned by machine learning techniques. These models have been advocated as EEG-based biometric systems. In this study, we apply a recent Hybrid Focasting Model, which calibrates its if-then fuzzy rules with a hybrid GVNS metaheuristic algorithm, in order to learn those patterns. Due to the stochasticity of the VNS procedure, models with different characteristics can be generated for each individual. Some EEG recordings from 109 volunteers, measured using a 64-channels EEGs, with 160 HZ of sampling rate, are used as cases of study. Different forecasting models are calibrated with the GVNS and used for the classification purpose. New rules for classifying the individuals using forecasting models are introduced. Computational results indicate that the proposed strategy can be improved and embedded in the future biometric systems.

Abstract: Publication date: April 2017 Source:Electronic Notes in Discrete Mathematics, Volume 58 Author(s): Alba Agustin, Angel Juan, Eduardo G. Pardo In this paper we propose a Variable Neighborhood Search approach for the Crew Pairing Problem. This problem consist in assigning a crew to each of the flights of a flight scheduling, in a predefined time horizon. The main objective of the problem is to minimize the number of cabin crews needed to cover all the flights subject to a set of constraints. These constraints are real-life specifications regulated by airline rules and other operational challenges. In particular we propose a General Variable Neighborhood Search algorithm to tackle the problem and we have tested our approach over a real instance provided by an airline and over an additional set of generated instances. The obtained results have been compared with a previous multi-start approach in the state of the art and with the initial solution provided to the algorithm which, in the case of the real instance, was the solution in use by the airline.

Abstract: Publication date: April 2017 Source:Electronic Notes in Discrete Mathematics, Volume 58 Author(s): M. Bruglieri, S. Mancini, F. Pezzella, O. Pisacane, S. Suraci We propose a three-phase matheuristic, combining an exact method with a Variable Neighborhood Search local Branching (VNSB) to route a fleet of Electric Vehicles (EVs). EVs are allowed stopping at the recharging stations along their routes to (also partially) recharge their batteries. We hierarchically minimize the number of EVs used and the total time spent by the EVs, i.e., travel times, charging times and waiting times (due to the customer time windows). The first two phases are based on Mixed Integer Linear Programs to generate feasible solutions, used in a VNSB algorithm. Numerical results on benchmark instances show that the proposed approach finds good quality solutions in reasonable amount of time.

Abstract: Publication date: April 2017 Source:Electronic Notes in Discrete Mathematics, Volume 58 Author(s): Jerzy Duda The paper presents a genetic algorithm (GA) hybridized with variable neighborhood search (VNS) to solve multi-item capacitated lot-sizing multi-family problem with setup times. The problem has a practical application in production planning e.g., in foundry industry, so test cases for computational experiments were based on the data from the real production process in a foundry. The VNS algorithm is used after a certain number of GA generations for all individuals in the population to improve solutions. The presented method applied for large instances of the problem outperforms both a dedicated genetic algorithm and a CLPEX Solver-based rolling horizon methods known from the literature.

Abstract: Publication date: April 2017 Source:Electronic Notes in Discrete Mathematics, Volume 58 Author(s): Telmo Pinto, Cláudio Alves, José Valério de Carvalho In this paper, we explore a capacitated vehicle routing problem with loading constraints and mixed linehauls and backhauls. The problem belongs to the subclass of pickup and delivery problems. To solve this problem, we describe a set of variable neighborhood search approaches whose shaking and local search phases rely on different neighborhood structures. Some of these structures were specially developed for this problem. All the strategies were implemented and exhaustively tested. The results of this computational study are discussed at the end of this paper.

Abstract: Publication date: April 2017 Source:Electronic Notes in Discrete Mathematics, Volume 58 Author(s): Rahma Borchani, Abdelkerim Elloumi, Malek Masmoudi University course timetabling problem refers to schedule a set of lectures, tutorials and practical works to a limited number of teachers, classrooms and time slots over a planning horizon while satisfying a set of hard and soft constraints. In this paper, we investigate Variable Neighborhood Descent approach to tackle a specific course timetabling problem related to the case of the Faculty of Economics and Management Sciences of Sfax in Tunisia. The objective is to minimize the total number of holes and the number of isolated lessons for all student groups. We have developed eleven specific neighborhood structures: six of these are designed for correcting the holes, while the other five are designed for adjusting the isolated lessons. Computations are made on real instances and numerical results show that our approach outperforms the existing solution with the elimination of 52.47 % of holes and isolated sessions on average.

Abstract: Publication date: April 2017 Source:Electronic Notes in Discrete Mathematics, Volume 58 Author(s): Israel López-Plata, Christopher Expósito-Izquierdo, Belén Melián-Batista, José Marcos Moreno-Vega This work addresses the problem of operational management of the internal delivery vehicles on the yard of a maritime container terminal using a Variable Neighbourhood Search algorithm. An empirical analysis is performed to find the Variable Neighbourhood Search variant that provides the best result for the proposed problem. This analysis tests 144 different variants on a wide range of realistic scenarios.

Abstract: Publication date: April 2017 Source:Electronic Notes in Discrete Mathematics, Volume 58 Author(s): Ana Anokić, Zorica Stanimirović, Tatjana Davidović, Đorđe Stakić Low price of raw materials in sugar industry and characteristics of production method lead to the specific transport organization problem. A new variant of Vehicle Scheduling Problem (VSP) that arises from transportation of sugar beet is considered. The problem is formulated as a Mixed Integer Quadratically Constraint Programming (MIQCP) model, which reflects the objective and specific constrains from practice. Computational experiments are conducted on real-life instances obtained from a sugar company in Serbia and the set of generated instances of larger dimensions. The proposed MIQCP model is used within the framework of Extended Lingo 15 solver, providing optimal solutions on small-size instances only. In order to find solutions on larger problem instances, a metaheuristic method based on Variable Neighborhood Search (VNS) is designed. Obtained computational results show that the proposed VNS quickly reaches all known optimal solutions on small-size instances. On larger problem instances, for which Lingo 15 solver could not find even a feasible solution, VNS provides best solutions in relatively short running times.

Abstract: Publication date: April 2017 Source:Electronic Notes in Discrete Mathematics, Volume 58 Author(s): Shima Golmohamadi, Reza Tavakkoli-Moghaddam, Mostafa Hajiaghaei-Keshteli Nowadays finding effective solution for transportation problem is one of the main issues both in industries and academia. According to the real world, in this paper it is assumed that the products are transferred in batches in a fixed charge transportation problem. Furthermore, the fuzzy values are used according to the parameters value in the real world. In addition, six meta-heuristics are utilized in order to solve the presented model. Most of these algorithms are firstly used for a mathematical model in transportation problem literature. Because of the importance of tuning the parameters in solving the given problem, the Taguchi method is used. Finally, computational results with different problem sizes are studied and analyzed.

Abstract: Publication date: April 2017 Source:Electronic Notes in Discrete Mathematics, Volume 58 Author(s): Antonio Alonso-Ayuso, Laureano F. Escudero, F. Javier Martín-Campo, Nenad Mladenović The aircraft conflict resolution problem needs to provide response to such situation in which two or more aircraft violate the safety distances that must be kept during the flight. Then, given the aircraft trajectories, the aim consists of finding a new configuration such that every conflict situation must be avoided. To deal with conflict avoidance an aircraft may change velocity, heading angle and altitude level. Due to nonlinearities involved in the exact model and the need of an almost real-time response, a Variable Neighborhood Search approach is presented within the multiobjective environment.

Abstract: Publication date: April 2017 Source:Electronic Notes in Discrete Mathematics, Volume 58 Author(s): Jack Brimberg, Nenad Mladenović, Raca Todosijević, Dragan Urošević In this paper we review a recently proposed variant of variable neighborhood search (VNS) referred to as nested variable neighborhood search (NVNS) and propose a generalization of this approach. In addition, we develop a heuristic stemming from this general framework and apply it on the capacitated clustering problem (CCP). Based on obtained results the proposed heuristic outperforms the current state-of-the-art for the CCP.

Abstract: Publication date: April 2017 Source:Electronic Notes in Discrete Mathematics, Volume 58 Author(s): Leslie Pérez Cáceres, Thomas Stützle Methods for automatic algorithm configuration integrate some search mechanism for generating candidate algorithm configurations and mechanisms for handling the stochasticity of the algorithm configuration problem. One popular algorithm configurator is ParamILS, which searches the configuration space using an iterated local search algorithm. In our research, we explore variable neighborhood search mechanisms as an alternative for the one-exchange neighborhood that is searched in the local search phase of ParamILS. In this article, we explore a reduced variable neighborhood search for automatic configuration. Our experimental results are promising and indicate directions for extending our work.

Abstract: Publication date: April 2017 Source:Electronic Notes in Discrete Mathematics, Volume 58 Author(s): Marwa Harzi, Saoussen Krichen This paper is concerned with designing an integrated transportation solver for the Vehicle Routing Problem with Time Windows (VRPTW). The VRPTW is one of the most tackled transportation problems in real-world situations. It consists in determining the minimum cost distance routes for a number of homogeneous vehicles stationed at a depot, that have a task of delivering goods to a number of customers within a specified time windows. As the VRPTW is known to be NP-hard combinatorial problem, it is hard to be solve in a reasonable computational time. Therefore, numerous metaheuristics-based approaches have been developed for finding near-optimal solution for VRPTW. To cope with the VRPTW, a VND approach is proposed. In order to demonstrate the performance of the approach in term of solution quality, we apply it on benchmark instances. The VND provided better results, in terms of solution quality, than existing approaches results.

Abstract: Publication date: April 2017 Source:Electronic Notes in Discrete Mathematics, Volume 58 Author(s): J. Sánchez-Oro, A. Martínez-Gavara, M. Laguna, A. Duarte, R. Martí Graphs are used to represent reality in several areas of knowledge. Drawings of graphs have many applications, from project scheduling to software diagrams. The main quality desired for drawings of graphs is readability, and crossing reduction is a fundamental aesthetic criterion for a good representation of a graph. In this paper we target the edge crossing reduction in the context of incremental graph drawing, in which we want to preserve the layout of a graph over successive drawings. We propose a hybrid method based on the GRASP (Greedy Randomized Adaptive Search Procedure) and VND (Variable Neighborhood Descent) methodologies and compare it with previous methods via simulation.