Authors:Josiane da Costa Vieira Rezende; Marcone Jamilson Freitas Souza; Vitor Nazário Coelho; Alexandre Xavier Martins Pages: 7 - 14 Abstract: Publication date: April 2018 Source:Electronic Notes in Discrete Mathematics, Volume 66 Author(s): Josiane da Costa Vieira Rezende, Marcone Jamilson Freitas Souza, Vitor Nazário Coelho, Alexandre Xavier Martins This work presents a hybrid multi-start algorithm for solving generic binary linear programs. This algorithm, called HMS, is based on a Multi-Start Metaheuristic and combines exact and heuristic strategies to address the problem. The initial solutions are generated by a strategy that applies linear programming and constraint propagation for defining an optimized set of fixed variables. In order to refine them, a local search, guided by a Variable Neighborhood Descent heuristic, is called, which, in turn, uses Local Branching cuts. The algorithm was tested in a set of binary LPs from the MIPLIB 2010 library and the results pointed out its competitive performance, resulting in a promising matheuristic.

Authors:Christian Blum Pages: 15 - 22 Abstract: Publication date: April 2018 Source:Electronic Notes in Discrete Mathematics, Volume 66 Author(s): Christian Blum The minimum common string partition problem is a challenging NP-hard optimization problem from the bioinformatics field. In this work we, first, present a modification which allows to apply the current state-of-the-art technique from the literature to much larger problem instances. Second, also based on the introduced modification, we develop a reduced variable neighborhood search algorithm for tackling large-scale problem instances. The skaking step of this algorithm destroys the incumbent solution partially, in a randomized way, and generates a complete solution on the basis of the partial solution by means of integer linear programming techniques. The proposed algorithm is compared to the state-of-the-art technique from the literature. The results show that the proposed algorithm consistently outperforms the state-of-the-art algorithm in the context of problem instances based on large alphabet sizes.

Authors:Thiago Gouveia da Silva; Gilberto F. de Sousa Filho; Igor A.M. Barbosa; Nenad Mladenovic; Lucidio A.F. Cabral; Luiz Satoru Ochi; Daniel Aloise Pages: 23 - 30 Abstract: Publication date: April 2018 Source:Electronic Notes in Discrete Mathematics, Volume 66 Author(s): Thiago Gouveia da Silva, Gilberto F. de Sousa Filho, Igor A.M. Barbosa, Nenad Mladenovic, Lucidio A.F. Cabral, Luiz Satoru Ochi, Daniel Aloise Let G = ( V , E , L ) be an edge-labeled graph. Let V be the set of vertices of G, E the set of edges, L the set of labels (colors) such that each edge e ∈ E has an associated label L ( e ) . The goal of the minimum labeling global cut problem (MLGCP) is to find a subset L ′ ⊆ L of labels such that G ′ = ( V , E ′ , L \ L ′ ) is not connected and L ′ is minimized. In this work, we generate random instances for the MLGCP to perform empirical tests. Also propose a set of heuristics using concepts of Genetic Algorithm and metaheuristic VNS, including some of their procedures, like two local search moves, and an auxiliary data structure to speed up the local search. Computational experiments show that the metaheuristic VNS outperforms other methods with respect to solution quality.

Authors:Dalessandro Soares Vianna; Camila Vidaurre Soares; Edwin B. Mitacc Meza; Iara Tammela; Rodolfo Cardoso Pages: 31 - 38 Abstract: Publication date: April 2018 Source:Electronic Notes in Discrete Mathematics, Volume 66 Author(s): Dalessandro Soares Vianna, Camila Vidaurre Soares, Edwin B. Mitacc Meza, Iara Tammela, Rodolfo Cardoso The Brazilian carnival samba schools' parade is one of the biggest popular shows in the planet, currently considered a Brazilian mark. Yearly, each carnival association makes a new carnival, building complex structures of floats and costumes in a short period. Although, the costume production scheduling is still performed manually. The purpose of this work is to propose different heuristic solutions for the addressed problem, based on the metaheuristics VNS, GRASP and Simulated Annealing and in hybrid versions of these metaheuristics. In addition to these heuristics, another innovative contribution is a mixed linear integer programming model proposed for the problem. Computational experiments highlight the efficiency of hybrid VNS heuristics, with emphasis on the VNS-GRASP that combines the strategy of multiple restarts of GRASP with the flexibility of VNS search.

Authors:Iago A. Carvalho; Thiago F. Noronha; Chistophe Duhamel; Luiz F.M. Vieira Pages: 39 - 46 Abstract: Publication date: April 2018 Source:Electronic Notes in Discrete Mathematics, Volume 66 Author(s): Iago A. Carvalho, Thiago F. Noronha, Chistophe Duhamel, Luiz F.M. Vieira The min-max regret Shortest Path Tree problem (RSPT) is a NP-Hard Robust Optimization counterpart of the Shortest Path Tree problem, where arcs costs are modeled as intervals of possible values. This problem arises from the uncertainty in link quality the routing protocols for IPv6 Low Wireless Personal Area Networks have to handle. In this paper, we propose a Variable Neighborhood Descent (VND) heuristic based on a Mixed Integer Linear Programming formulation. An exact algorithm based on the same formulation is used to assess the quality of this heuristic. Computational experiments show that VND has an average optimality gap of 0.91%, being smaller that with the best heuristic in literature for RSPT.

Authors:B.F. Rosa; M.J.F. Souza; S.R. de Souza Pages: 47 - 54 Abstract: Publication date: April 2018 Source:Electronic Notes in Discrete Mathematics, Volume 66 Author(s): B.F. Rosa, M.J.F. Souza, S.R. de Souza This work implements and compares four algorithms based on Variable Neighborhood Search (VNS), named RVNS, GVNS f , GVNS r and GVNS rf , for solving the Single Machine Scheduling Problem with Earliness and Tardiness Penalties (SM-SPETP). Computational experiments showed that the algorithm GVNS f obtained better-quality solutions compared with the other algorithms, including an algorithm found in the literature. The algorithms GVNS r and GVNS rf obtained solutions close to the GVNS f , and outperformed the algorithm of the literature, both with respect to the quality of the solutions and the computational times.

Authors:Olfa Harrabi; Jouhaina Chaouachi Siala; Hend Bouziri Pages: 55 - 62 Abstract: Publication date: April 2018 Source:Electronic Notes in Discrete Mathematics, Volume 66 Author(s): Olfa Harrabi, Jouhaina Chaouachi Siala, Hend Bouziri The minimum sum coloring of graphs is a variant of the classical graph coloring problem which is known to be NP-hard. The problem consists on minimizing the sum colorings of different graph vertices. In this paper, we propose a new bi-objective model for the underlying problem. We also propose for the resolution a hybrid schema which combines a bi-objective genetic algorithm with an Iterated Variable Neighborhood Search. The proposed approach relies on the use of different dedicated evolutionary operators mainly crossover and mutation. We also note two important features of the Variable Neighborhood Search: the use of destroy/repair method for shaking step and a multi-neighborhood search. Combined methods led us to preliminary promising results.

Authors:Micheli Knechtel; Philippe Michelon; Serigne Gueye; Luis Satoru Ochi Pages: 63 - 70 Abstract: Publication date: April 2018 Source:Electronic Notes in Discrete Mathematics, Volume 66 Author(s): Micheli Knechtel, Philippe Michelon, Serigne Gueye, Luis Satoru Ochi Block-modeling is a framework to describe a social network as a small structure. We propose here a Neighborhood Exploration Approach with Multi-start for tackling the Extend Generalized Block-modeling. The Extend Generalized Blockmodeling is the first and most complete model approach: it allows to analyze networks without any a priory knowledge about them. The other models require at least to know the size of the partition (i.e. the number of sub-sets that the partition will contain) and a pre-definition of the ideal models.

Authors:Pablo Luiz Araújo Munhoz; Pedro Henrique González; Uéverton dos Santos Souza; Luiz Satoru Ochi; Philippe Michelon; Lúcia Maria de A. Drummond Pages: 71 - 78 Abstract: Publication date: April 2018 Source:Electronic Notes in Discrete Mathematics, Volume 66 Author(s): Pablo Luiz Araújo Munhoz, Pedro Henrique González, Uéverton dos Santos Souza, Luiz Satoru Ochi, Philippe Michelon, Lúcia Maria de A. Drummond A usual way to collect data in a Wireless Sensor Network (WSN) is by the support of a special agent, called data mule, that moves among sensor nodes and performs all communication between them. This article dealt with the Data Mule Scheduling Problem (DMSP), where in addition to the data mule routing, it is necessary to plan the speed that this data mule will use and also to schedule the attendance of the sensors in this route. Mixed integer linear programming and heuristics based on the GRASP and GVNS metaheuristics were proposed. Besides that, a set of instances were generated in order to evaluate and validate the methods.

Authors:H. Costa; L.R. Galvão; L.H.C. Merschmann; M.J.F. Souza Pages: 79 - 86 Abstract: Publication date: April 2018 Source:Electronic Notes in Discrete Mathematics, Volume 66 Author(s): H. Costa, L.R. Galvão, L.H.C. Merschmann, M.J.F. Souza Feature selection, usually adopted as a preprocessing step for data mining, is used to select a subset of predictive features aiming to improve the performance of a predictive model. Despite of the benefits of feature selection for classification task, to the best of our knowledge, there is no work in the literature that addresses feature selection in conjunction with global hierarchical classifiers. Thus, in this paper, we fill this gap proposing a feature selection method based on Variable Neighborhood Search (VNS) metaheuristic for the hierarchical classification context. Computational experiments were carried out on five bioinformatics datasets to evaluate the effect of the proposed algorithm on classification performance when using a global hierarchical classifier. As result, we have obtained a classifier performance improvement for three datasets and a competitive result for a fourth dataset, which indicates the suitability of the proposed method for the hierarchical classification scenario.

Authors:E.C. de Siqueira; M.J.F. Souza; S.R. de Souza Pages: 87 - 94 Abstract: Publication date: April 2018 Source:Electronic Notes in Discrete Mathematics, Volume 66 Author(s): E.C. de Siqueira, M.J.F. Souza, S.R. de Souza This paper addresses the Hybrid Flow Shop Problem (HFSP) through the Multi-objective Variable Neighborhood Search metaheuristic (MOVNS). In this problem, we have a set of jobs that must be performed on a set of stages. At each stage, we have a set of unrelated parallel machines. Some jobs may skip stages. In this paper we considere two evaluation criteria under simultaneous analysis: the minimization of the makespan and the minimization of the weighted sum of tardiness. Instances of the HFSP from literature are solved by four versions of the MOVNS algorithm. The results are evaluated using the Hypervolume, Epsilon, Spacing and Sphere counting metrics.

Authors:Júlia Cária de Freitas; Puca Huachi Vaz Penna Pages: 95 - 102 Abstract: Publication date: April 2018 Source:Electronic Notes in Discrete Mathematics, Volume 66 Author(s): Júlia Cária de Freitas, Puca Huachi Vaz Penna Unmanned aerial vehicles (UAV), or drones, have the potential to reduce cost and time in last mile deliveries. This paper presents the scenario which a drone works in collaboration with a delivery truck to distribute parcels. This Traveling Salesman Problem (TSP) variant has some particularities that make the originals constraints insufficient. In more detail must be considered the flying time-limit of the drone that inhibits them from visiting all customers and the parcel must not exceed the payload of the drone. To solve the problem, the initial solution is created from the optimal TSP solution obtained by the Concorde solver. Next, an implementation of the Randomized Variable Neighborhood Descent (RVND) heuristic is used as a local search to obtain the problem solution. To test the proposed heuristic, 11 instances based on the well-known TSP benchmark set were created. Computational experiments show the use of drones for last mile delivery can reduce the total delivery time up to almost 20%. Moreover providing a faster delivery this system has a positive environmental impact as it reduces the truck travel distance.

Authors:Alexandre Frias Faria; Sérgio Ricardo de Souza; Carlos Alexandre Silva Pages: 103 - 110 Abstract: Publication date: April 2018 Source:Electronic Notes in Discrete Mathematics, Volume 66 Author(s): Alexandre Frias Faria, Sérgio Ricardo de Souza, Carlos Alexandre Silva This paper presents an algorithm for the optimization version of the Multi-Way Number Partitioning Problem (MWNPP). This problem consists in distributing the elements of a given sequence into k disjoint subsets so that the sums of each subset elements fit in the shortest interval. The metaheuristic Variable Neighborhood Descent (VND), a deterministic variant of Variable Neighborhood Search (VNS), adapted for solving the MWNPP, has a good performance over instances less than six subsets. It is carried out a comparative study with two algorithms, Karmarkar-Karp Heuristic and Longest Processing Time, using randomly generated instances and objective functions values. The statistical tests show that results of the VND proposed are significantly better than literature constructive methods and its improvements.

Authors:Felipe O. Mota; Elizabeth F. Wanner; Eduardo J.S. Luz; Gladston J.P. Moreira Pages: 111 - 118 Abstract: Publication date: April 2018 Source:Electronic Notes in Discrete Mathematics, Volume 66 Author(s): Felipe O. Mota, Elizabeth F. Wanner, Eduardo J.S. Luz, Gladston J.P. Moreira This paper presents a hybrid PSO algorithm with a VND-based operator for handling equality constraint problems in continuous optimization. The VND operator can be defined both as a local search and a kind of elitism operator for equality constraint problems playing the role of “fixing” the best estimates of the feasible set. Experiments performed on benchmark problems suggest that the VND operator can enhance both the convergence speed and the accuracy of the final result.

Authors:Jerzy Duda; Adam Stawowy Pages: 119 - 126 Abstract: Publication date: April 2018 Source:Electronic Notes in Discrete Mathematics, Volume 66 Author(s): Jerzy Duda, Adam Stawowy The paper presents a novel variable neighborhood search (VNS) algorithm combined with a linear programming solver (LPS) to solve multi-item multi-family capacitated lot-sizing problem with setup times independent of the family sequence. The model has a direct application to real production planning in foundry industry, where the goal is to create the batches of manufactured castings and the sequence of the melted metal loads to prevent delays in delivery of goods to customers. We developed a simple and fast VNS based algorithm with problem-specific operators that are responsible for the neighborhood generating. For large instances of the problem the proposed algorithm is able to provide better results than CPLEX solver.

Authors:Leandro Resende Mundim; Thiago Alves de Queiroz Pages: 127 - 134 Abstract: Publication date: April 2018 Source:Electronic Notes in Discrete Mathematics, Volume 66 Author(s): Leandro Resende Mundim, Thiago Alves de Queiroz We developed a variable neighborhood search heuristic and a mixed integer programming model for the identical parallel machine scheduling problem with sequence dependent setup time. For this problem, we consider minimizing two objectives, which are the makespan and the flow time. The heuristic proposed has a constructive procedure to build initial solutions, five neighborhood structures, and a local search based on the variable neighborhood descent. Computational experiments indicate that the heuristic is very fast and can return better solutions than the model since it found 90% of the best solutions. It also outperformed all solutions computed with the longest processing time and the shortest processing time rules, both commonly adopted for scheduling problems.

Authors:Guilherme Dhein; Alberto Francisco Kummer Neto; Olinto César Bassi de Araújo Pages: 135 - 142 Abstract: Publication date: April 2018 Source:Electronic Notes in Discrete Mathematics, Volume 66 Author(s): Guilherme Dhein, Alberto Francisco Kummer Neto, Olinto César Bassi de Araújo We consider a variant of the classical Multiple Traveling Salesmen Problem in which the distance between any two vehicles is never greater than a fixed distance D. This new feature allows salesmen to help each other timely if an emergency happens, with an estimated backup response time related to D. To achieve this goal, a spatial and temporal synchronization is required, and it incorporates routes interdependence difficulties to be overcomed. A Genetic Algorithm and a Local Search Genetic Algorithm that embodies a Variable Neighborhood Descent procedure are proposed to solve this problem. Computational results are reported on modified benchmark instances taken from TSPLIB in order to exhibit prospects of the proposed algorithms. Through an analysis of results, the highly effective performance of our proposed Local Search Genetic Algorithm is shown in comparison to the classical Genetic Algorithm.

Authors:Ali Baniamerian; Mahdi Bashiri; Fahime Zabihi Pages: 143 - 150 Abstract: Publication date: April 2018 Source:Electronic Notes in Discrete Mathematics, Volume 66 Author(s): Ali Baniamerian, Mahdi Bashiri, Fahime Zabihi This paper addresses a novel hybrid metaheuristic combining the Genetic algorithm (GA) and Modified Variable Neighborhood Search (MVNS) for the vehicle routing problem with cross-docking. In this paper, we propose four shaking and two neighbourhood structures in a modified version of the VNS. The basic VNS is an efficient and successful method to solve combinatorial optimization problems, but sometimes applying it in problems with large solution space is time consuming, so to avoid expending too much computational time, a multi-part solution representation with a new searching approach is proposed and some modifications are applied to the VNS and hybridized with the GA. To show the effectiveness of the proposed hybridized approach, a comparative study is performed for existing vehicle routing problem with cross docking test problems.

Authors:Jean Torres; Emerson Silva; Edna A. Hoshino Pages: 151 - 158 Abstract: Publication date: April 2018 Source:Electronic Notes in Discrete Mathematics, Volume 66 Author(s): Jean Torres, Emerson Silva, Edna A. Hoshino The Distinguishing Substring Selection Problem aims to find a target string close to all strings in a given set of good strings and far enough of strings in another set of bad strings. This problem has applications in bioinformatics and it is related to the closest substring problem and other string selection problems. In this work, we investigate two heuristics for the problem based on rounding procedures and variable neighborhood search approaches. Both heuristics consider the solution of the linear relaxation of an integer programming formulation for the problem as an initial solution. We conducted computational experiments in three groups of instances. The rounding procedure provides good solutions and the VNS improves these results using different rounding procedures as neighborhood structures. To the best of our knowledge, this is the first paper that provides computational results for the problem.

Authors:J.C.T. Campos; A.X. Martins; M.J.F. Souza Pages: 159 - 166 Abstract: Publication date: April 2018 Source:Electronic Notes in Discrete Mathematics, Volume 66 Author(s): J.C.T. Campos, A.X. Martins, M.J.F. Souza This work addresses the multi-level capacitated minimum spanning tree (MLCMST) problem. It consists of finding a minimal cost spanning tree such that the flow to be transferred from a central node (root) to the other nodes is bounded by the edge capacities. In this paper, a hybrid algorithm, combining the Variable Neighborhood Search (VNS) metaheuristic and one mathematical programming formulation of the literature, is used for solving it. The formulation is used to give an initial solution to VNS. Five neighborhoods are used for exploring the solution space. Results show that the VNS is able to improve the initial solutions and to obtain small gap solutions for all instance sets.

Authors:Sinaide Nunes Bezerra; Sérgio Ricardo de Souza; Marcone Jamilson Freitas Souza Pages: 167 - 174 Abstract: Publication date: April 2018 Source:Electronic Notes in Discrete Mathematics, Volume 66 Author(s): Sinaide Nunes Bezerra, Sérgio Ricardo de Souza, Marcone Jamilson Freitas Souza This paper presents an algorithm based on the General Variable Neighborhood Search (GVNS) metaheuristic for solving the Multi-Depot Vehicle Routing Problem (MDVRP). The MDVRP consists in designing a set of vehicle routes serving all customers, such that the maximum number of vehicle per depot and vehicle-capacity are respected, and the total cost of transportation is minimized. The proposed algorithm uses Randomized Variable Neighborhood Descent (RVND) as local search method and it is tested in classical instances of the problem. The obtained results are presented and discussed in this paper.

Authors:Anderson Zudio; Daniel Henrique da Silva Costa; Bruno Porto Masquio; Igor M. Coelho; Paulo Eustáquio Duarte Pinto Pages: 175 - 182 Abstract: Publication date: April 2018 Source:Electronic Notes in Discrete Mathematics, Volume 66 Author(s): Anderson Zudio, Daniel Henrique da Silva Costa, Bruno Porto Masquio, Igor M. Coelho, Paulo Eustáquio Duarte Pinto The classic bin packing problem consists of packing a set of boxes with fixed orientation into the minimum number of bins. In this work we present a variable neighborhood descent (VND) inspired algorithm which improves the state-of-art biased random-key genetic algorithm (BRKGA), proposed in [6], for the three-dimensional bin packing problem. The constructive greedy heuristic method to pack the boxes uses an integer sequence to establish the order of boxes to be packed. The presented BRKGA/VND variant fills the initial and mutant population based on sorted box sequences. The devised hybrid method shows significantly superior average fitness through the generations, therefore, solutions with high quality are found faster. The novel approach is tested with a standard set of 320 instances. The computational experiment demonstrate that BRKGA/VND produces equal or better results compared to other state-of-art algorithms proposed in the literature. The empirical data shows that BRKGA/VND hybrid variant systematically produces high quality solutions at fewer iterations compared to the results attained by BRKGA.

Authors:Rodolfo Pereira Araujo; Eyder Rios; Igor Machado Coelho; Leandro A.J. Marzulo; Maria Clicia Castro Pages: 183 - 190 Abstract: Publication date: April 2018 Source:Electronic Notes in Discrete Mathematics, Volume 66 Author(s): Rodolfo Pereira Araujo, Eyder Rios, Igor Machado Coelho, Leandro A.J. Marzulo, Maria Clicia Castro The Traveling Thief Problem (TTP) is a multi-component combinatorial optimization problem that combines two well-known problems in the literature: the Traveling Salesman Problem (TSP) and the Knapsack Problem (KP). This paper proposes a novel list-constrained local search process inspired in Variable Neighborhood Descent (VND) for multiple neighborhood structures, combined with a metaheuristic Greedy Randomized Adaptive Search Procedure (GRASP). The local search implementation was made in a Graphics Processing Unit (GPU) architecture in order to explore the massive number of computing cores to simultaneously explore neighbor solutions, while the GRASP was implemented exploring the natural parallelism of a multi-core CPU. The computational results were compared to state-of-the-art results in literature and indicate promising research directions for the design of novel search algorithms in high performance architectures.

Authors:Rodney O.M. Diana; Sérgio R. de Souza; Moacir F.F. Filho Pages: 191 - 198 Abstract: Publication date: April 2018 Source:Electronic Notes in Discrete Mathematics, Volume 66 Author(s): Rodney O.M. Diana, Sérgio R. de Souza, Moacir F.F. Filho This paper addresses the total weighted tardiness minimization problem on unrelated parallel machines with sequence dependent setup times and job ready times. The problem consists in scheduling a set of jobs reducing the penalty costs caused by the delays in the job due dates. This is a NP-Hard problem and has been extensively studied in recent literature. In order to solve this, an ILS-VND hybrid metaheuristic is proposed, where a local search heuristic Variable Neighborhood Descent (VND) is integrated with Iterated Local Search (ILS) metaheuristic with multiple restarts. The results is compared with two state-of-art metaheuristics proposed in the literature. The statistical analysis indicates that for the most scenarios the proposed method outperforms the references metaheuristics.

Authors:Diógenes V.M. Ferreira; Vitor N. Coelho Pages: 199 - 206 Abstract: Publication date: April 2018 Source:Electronic Notes in Discrete Mathematics, Volume 66 Author(s): Diógenes V.M. Ferreira, Vitor N. Coelho Control lops are nowadays everywhere, from tiny devices to robust industrial applications. However, even when only few parameters are being dealt, manually fine-tuning has been shown to be a meticulous task for achieving designers' desired performance. Fine-tuning a controller parameters is an arduous job that requests expertise of the domain. On the other hand, metaheuristics have been barely applied for accomplishing this task. In particular, due to different behaviors that a control loop can have, a multi-objective analysis shows up as essential. In this work, we apply a Multi-Objective Variable Neighborhood Search based algorithm for assisting the design of a Buck Converter, integrating the optimization process with an evaluation mechanism integrated with a circuit simulation software. The obtained Pareto Front presented various response behaviors, optimizing different desired characteristics. We suggest that the proposed framework is a promising tool for assisting decision makers to design more efficient and dynamic systems.

Authors:Huggo Silva Ferreira; Eduardo Theodoro Bogue; Thiago F. Noronha; Slim Belhaiza; Christian Prins Pages: 207 - 214 Abstract: Publication date: April 2018 Source:Electronic Notes in Discrete Mathematics, Volume 66 Author(s): Huggo Silva Ferreira, Eduardo Theodoro Bogue, Thiago F. Noronha, Slim Belhaiza, Christian Prins The Vehicle Routing Problem (VRP) with Multiple Time Windows is a generalization of VRP, where the customers have one or more time windows in which they can be visited. The best heuristic in the literature is a Hybrid Variable Neighborhood Tabu Search (HVNTS) that mostly deals with infeasible solutions, because it is assumed that one may not reach some regions of the search space without passing through infeasible solutions. In this short paper, we propose a simpler Variable Neighborhood Search heuristic where all the computational effort is spent on searching for feasible solutions. Computational experiments showed that the proposed heuristic is competitive with the best heuristic in the literature.

Authors:Mateus N. Coelho; Vitor N. Coelho; Igor M. Coelho; Bruno N. Coelho; Marcone J.F. Souza Pages: 215 - 222 Abstract: Publication date: April 2018 Source:Electronic Notes in Discrete Mathematics, Volume 66 Author(s): Mateus N. Coelho, Vitor N. Coelho, Igor M. Coelho, Bruno N. Coelho, Marcone J.F. Souza This paper focus on the learning of music time series. In this context, from compressed digital audio files, we sought to verify how a song can be learned, both in terms of amplitude and frequency. Given the enormous amount of data contained in those time series, the use of classical learning methods becomes limited. Typical compressed acquisitions in MP3 files usually contains 44100 samples per second. In this context, the use of metaheuristic algorithms for this learning task, in a big-data environment, is justified, and the use of deep learning techniques sounds necessary. In this paper, a Hybrid Forecasting Model, calibrated with the Reduced Variable Neighborhood Search, with parallel processing using Graphical Processing Units, is used as a deep learning tool. Case studies composed of simple musical compositions are used for verifying the potential of the method for such application. We suggest that the techniques investigated here can also be used for the learning, classification and computational music composition.

Authors:Matheus Guedes Vilas Boas; Haroldo Gambini Santos; Luiz Henrique de Campos Merschmann Pages: 223 - 230 Abstract: Publication date: April 2018 Source:Electronic Notes in Discrete Mathematics, Volume 66 Author(s): Matheus Guedes Vilas Boas, Haroldo Gambini Santos, Luiz Henrique de Campos Merschmann In this paper we propose a hybrid approach for the Feature Based Parameter Tuning Problem (FBPTP) of Mixed-Integer Programming (MIP) solvers. These solvers are complex programs composed of many procedures whose execution is embedded in the Branch-and-Bound framework and their execution can be configured by setting different parameters. The diversity of models that can be formulated as MIP problems can be exploited to devise better parameter settings for groups of problems, considering lessons learned from previous experiments. Decision trees can be used to define the best parameter settings for different problem types. However the construction of optimal decision trees is a NP-Hard problem. Thus, we propose an Integer Programming Model to construct optimal decision trees for FBPTP. A Variable Neighborhood Search heuristic is employed to accelerate the production of high quality solutions. Encouraging computational results were obtained for the open source MIP solver COIN-OR CBC: executions in the test sets considering decisions based on our decision trees built using training sets prove the effectiveness of the proposed method compared to default settings, an improvement of 7% in solver's performance was obtained both in execution times as well in the number of solved instances.

Authors:Cristina Martínez; Alberto Besana Pages: 3 - 9 Abstract: Publication date: March 2018 Source:Electronic Notes in Discrete Mathematics, Volume 65 Author(s): Cristina Martínez, Alberto Besana We study q–designs over finite fields and their connection to network coding. We prove that invariant subgrassmanians in the Grassmannian G k , n ( F q ) parametrizing k–planes in the vector space F q n by the action of any triangle group hold a t–design.

Authors:Ludwig Kampel; Bernhard Garn; Dimitris E. Simos Pages: 11 - 16 Abstract: Publication date: March 2018 Source:Electronic Notes in Discrete Mathematics, Volume 65 Author(s): Ludwig Kampel, Bernhard Garn, Dimitris E. Simos In this paper, we provide yet another construction on how to map problems pertaining covering arrays to specialized set cover problems. With this mapping it is possible to compute optimal covering arrays via minimal solutions of the generated set cover problem.

Authors:Daniel Panario; Brett Stevens; Georgios Tzanakis Pages: 17 - 22 Abstract: Publication date: March 2018 Source:Electronic Notes in Discrete Mathematics, Volume 65 Author(s): Daniel Panario, Brett Stevens, Georgios Tzanakis We study the number of rows that agree with a given t-tuple in arrays constructed using linear feedback shift registers and primitive polynomials over finite fields.

Authors:Michael Braun; Alfred Wassermann Pages: 23 - 29 Abstract: Publication date: March 2018 Source:Electronic Notes in Discrete Mathematics, Volume 65 Author(s): Michael Braun, Alfred Wassermann We report the computer construction of 1316 mutually disjoint 2-(13, 3, 1)2 subspace designs. By combining disjoint designs and using supplementary subspace designs we conclude that subspace designs exist for 1 ≤ λ ≤ 2047 .

Authors:Iliya Bluskov Pages: 31 - 36 Abstract: Publication date: March 2018 Source:Electronic Notes in Discrete Mathematics, Volume 65 Author(s): Iliya Bluskov The constant A ( n , d , w ) is the maximum number of words in an ( n , d , w ) binary code, that is, a code of minimal distance d, with words of length n and weight w. We improve the best known lower bounds on A ( n , d , w ) for three sets of parameters by using optimization; in particular, we show that A ( 29 , 8 , 5 ) ≥ 36 , A ( 30 , 8 , 5 ) ≥ 41 , and A ( 32 , 8 , 5 ) = 44 by explicitly giving the respective codes. The (32, 8, 5) code is optimal and leads to eight more new optimal codes. We show this by improving the known result on the problem of finding the packing number P ( v , 5 , 2 ) for v ≡ 12 (mod 20).

Abstract: Publication date: June 2018 Source:Electronic Notes in Discrete Mathematics, Volume 67 Author(s): Mihai Rebenciuc, Simona Mihaela Bibic Structural health monitoring (SHM) evaluation consists to determining the modes (resonances) of vibration characteristic of the structure and each of them is represented by its modal parameters which can be obtained experimentally and can be analyzed by different procedures. In this regard, the present paper constitutes the first part of an extended paper and aims to inventory some methods of classical and non-classical mathematics with the specific computing scheme.

Abstract: Publication date: June 2018 Source:Electronic Notes in Discrete Mathematics, Volume 67 Author(s): Aynur Şahin, Metin Başarır In this paper, we modify the iteration process of Agarwal et al. (J. Nonlinear Convex Anal. 8(1) (2007), 61–79) to three multi-valued mappings and prove the strong and △-convergence theorems of this iteration in a hyperbolic space. Our theorems extend and improve some recent results announced in the current literature.

Abstract: Publication date: June 2018 Source:Electronic Notes in Discrete Mathematics, Volume 67 Author(s): Mihai Dupac The importance of numerical methods in science and engineering [Chapra, S.C., and R.P. Canale, “Numerical Methods for Engineers,” McGraw-Hill, 6th Ed., 2010] was long recognised and considered a fundamental factor in improving productivity and reducing production costs. The ability to model flexible systems and describe their trajectories [Gasparetto A., Boscariol P., Lanzutti A., Vidoni R., Trajectory planning in Robotics, Mathematics in Computer Science 6 (2012), pp. 269–279] involves usually the study of nonlinear coupled partial differential equations. Since their exact solutions are not normally feasible in practice, computational methods [V. Kumar, M. Zefran, J.P. Ostrowski, Motion Planning and Control of Robots, Handbook of Industrial Robotics, 2nd Edition, J. Wiley and Sons (2007), pp. 295–315] can be considered.

Abstract: Publication date: June 2018 Source:Electronic Notes in Discrete Mathematics, Volume 67 Author(s): Huda Aldweby, Maslina Darus In this article, a q-integral operator which is analogue to the well known Bernardi integral operator is investigated. Integral preserving property for a subclass of analytic functions defined by this q-operator is proved. Moreover, special new q-integral operators are obtained as consequences.

Abstract: Publication date: June 2018 Source:Electronic Notes in Discrete Mathematics, Volume 67 Author(s): Huseyin Cakalli In this paper, we introduce and investigate the concepts of down continuity and down compactness. A real valued function f on a subset E of R, the set of real numbers is down continuous if it preserves downward half Cauchy sequences. It turns out that the set of down continuous functions is a proper subset of the set of continuous functions.

Abstract: Publication date: June 2018 Source:Electronic Notes in Discrete Mathematics, Volume 67 Author(s): Şebnem Yıldız In this paper, we have generalized a main theorem dealing with quasi-f-power increasing sequence to A , θ n k summability method by using Fourier series.

Abstract: Publication date: June 2018 Source:Electronic Notes in Discrete Mathematics, Volume 67 Author(s): Şebnem Yıldız In this paper, a known theorem dealing with N ¯ , p n k summability methods of Fourier series is generalized to A , θ n k summability method by taking normal matrices.

Abstract: Publication date: June 2018 Source:Electronic Notes in Discrete Mathematics, Volume 67 Author(s): Nicholas Korpelainen We establish the first known boundary class for the k-path partition problem and deduce that for a graph class defined by finitely many minimal forbidden induced subgraphs, the k-path partition problem remains NP-hard unless one of the forbidden induced subgraphs is a subcubic tree (a tree of maximum degree at most 3) with at most one vertex of degree 3.

Abstract: Publication date: June 2018 Source:Electronic Notes in Discrete Mathematics, Volume 67 Author(s): Richard Conniss Many, if not most, real world scheduling problems fall into the class of NP. Classical, mathematically exact methods when applied to these problems often suffer from scaling issues, that prevent the computation of a solution in reasonable time. Similarly, real world problems can often be characterised by the requirement to dynamically change any prebuilt roster in reaction to unforeseen changes to the resources available, such as short notice staff absence or a change in the requirements of the task to be fulfilled. Metaheuristic methods have been successfully used to make approximations to optimal solutions which are good enough for practical use. In this paper an example of a novel and complex employee scheduling, or rostering, problem will be discussed and a simple metaheuristic method demonstrated to solve the problem.

Abstract: Publication date: June 2018 Source:Electronic Notes in Discrete Mathematics, Volume 67 Author(s): Ovidiu Bagdasar, Eve Hedderwick, Ioan-Lucian Popa Horadam sequences are second-order linear recurrences in the complex plane which depend on two initial conditions and two recurrence coefficients which are complex numbers. Recently, numerous papers have been devoted to the periodicity of these sequences, as well as to generalizations and applications. In this paper we investigate aspects related to the sequence of rations of consecutive terms and geometric bounds of Horadam sequences. We also propose some directions for further study.

Abstract: Publication date: June 2018 Source:Electronic Notes in Discrete Mathematics, Volume 67 Author(s): Armen G. Bagdasaryan, Ovidiu Bagdasar In this paper we present theoretical and computational results regarding generalized arithmetic m-triangles. The numerical values recover well-known number sequences, indexed in the OEIS including binomial coefficients and their extensions. Some combinatorial interpretations, generating functions and also asymptotic formulae for these triangles are provided.

Abstract: Publication date: June 2018 Source:Electronic Notes in Discrete Mathematics, Volume 67 Author(s): Diana Pătraşcu Borlea The aim of this paper is to give some characterizations of the uniform polynomial dichotomy for linear discrete dynamical systems on the half-line.

Abstract: Publication date: June 2018 Source:Electronic Notes in Discrete Mathematics, Volume 67 Author(s): Mihail Megan, Traian Ceauşu, Violeta Crai (Terlea) The paper considers some concepts of trichotomy with different growth rates for evolution operators in Banach spaces. Connections between these concepts and characterizations in terms of Lyapunov-type sequences of norms are given. The main result is an equivalence between the nonuniform trichotomy and a certain type of uniform trichotomy, using sequences of norms.

Abstract: Publication date: June 2018 Source:Electronic Notes in Discrete Mathematics, Volume 67 Author(s): Larisa Elena Biriş, Traian Ceauşu, Claudia Luminiţa Mihiţ, Ioan-Lucian Popa In the present paper the concept of uniform exponential trisplitting for skew-product flows in Banach space is considered. This concept is a generalisation of the well-known concept of uniform exponential trichotomy. Connections between these concepts are presented and some illustrating examples prove that these are distinct. Also, we present necessary and sufficient conditions for the uniform exponential trisplitting concept with invariant and strongly invariant projectors. Finally, a characterisation in terms of Lyapunov sequences is given.