Search results for: NP - hard problem.

Authors: Agnieszka Misztal

Abstract:

The popularity of quality management system models continues to grow despite the transitional crisis in 2008. Their development is associated with demands of the new requirements for entrepreneurs, such as risk analysis projects and more emphasis on supervision of outsourced processes. In parallel, it is appropriate to focus attention on the selection of companies aspiring to a quality management system. This is particularly important in the automotive supplier industry, where requirements transferred to the levels in the supply chain should be clear, transparent and fairly satisfied. The author has carried out a series of researches aimed at finding the factors that allow for the effective implementation of the quality management system in automotive companies. The research was focused on four groups of companies: 1) manufacturing (parts and assemblies for the purpose of sale or for vehicle manufacturers), 2) service (repair and maintenance of the car) 3) services for the transport of goods or people, 4) commercial (auto parts and vehicles). The identified determinants were divided into two types of criteria: internal and external, as well as hard and soft. The article presents the hard – technical factors that an automotive company must meet in order to achieve the goal of the quality management system implementation.

Keywords: Automotive industry, quality management system.

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Authors: Vahid Mohammadi Saffarzadeh, Pourya Jafarzadeh, Masoud Mazloom

Abstract:

This paper presents a hybrid approach for solving nqueen problem by combination of PSO and SA. PSO is a population based heuristic method that sometimes traps in local maximum. To solve this problem we can use SA. Although SA suffer from many iterations and long time convergence for solving some problems, By good adjusting initial parameters such as temperature and the length of temperature stages SA guarantees convergence. In this article we use discrete PSO (due to nature of n-queen problem) to achieve a good local maximum. Then we use SA to escape from local maximum. The experimental results show that our hybrid method in comparison of SA method converges to result faster, especially for high dimensions n-queen problems.

Keywords: PSO, SA, N-queen, CSP

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Authors: Pankaj Dutta, Debjani Chakraborty

Abstract:

This paper investigates the effect of product substitution in the single-period 'newsboy-type' problem in a fuzzy environment. It is supposed that the single-period problem operates under uncertainty in customer demand, which is described by imprecise terms and modelled by fuzzy sets. To perform this analysis, we consider the fuzzy model for two-item with upward substitution. This upward substitutability is reasonable when the products can be stored according to certain attribute levels such as quality, brand or package size. We show that the explicit consideration of this substitution opportunity increase the average expected profit. Computational study is performed to observe the benefits of product's substitution.

Keywords: Fuzzy demand, Newsboy, Single-period problem, Substitution.

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Authors: Rajeev, N. K. Raigar

Abstract:

In this study, one dimensional phase change problem (a Stefan problem) is considered and a numerical solution of this problem is discussed. First, we use similarity transformation to convert the governing equations into ordinary differential equations with its boundary conditions. The solutions of ordinary differential equation with the associated boundary conditions and interface condition (Stefan condition) are obtained by using a numerical approach based on operational matrix of differentiation of shifted second kind Chebyshev wavelets. The obtained results are compared with existing exact solution which is sufficiently accurate.

Keywords: Operational matrix of differentiation, Similarity transformation, Shifted second kind Chebyshev wavelets, Stefan problem.

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Authors: Bita Tadayon, Nasser Salmasi

Abstract:

This research deals with a flexible flowshop scheduling problem with arrival and delivery of jobs in groups and processing them individually. Due to the special characteristics of each job, only a subset of machines in each stage is eligible to process that job. The objective function deals with minimization of sum of the completion time of groups on one hand and minimization of sum of the differences between completion time of jobs and delivery time of the group containing that job (waiting period) on the other hand. The problem can be stated as FFc / rj , Mj / irreg which has many applications in production and service industries. A mathematical model is proposed, the problem is proved to be NPcomplete, and an effective heuristic method is presented to schedule the jobs efficiently. This algorithm can then be used within the body of any metaheuristic algorithm for solving the problem.

Keywords: flexible flowshop scheduling, group processing, machine eligibility constraint, mathematical modeling.

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Authors: S. V. Kasmir Raja, P. Herbert Raj

Abstract:

The overlay approach has been widely used by many service providers for Traffic Engineering (TE) in large Internet backbones. In the overlay approach, logical connections are set up between edge nodes to form a full mesh virtual network on top of the physical topology. IP routing is then run over the virtual network. Traffic engineering objectives are achieved through carefully routing logical connections over the physical links. Although the overlay approach has been implemented in many operational networks, it has a number of well-known scaling issues. This paper proposes a new approach to achieve traffic engineering without full-mesh overlaying with the help of integrated approach and equal subset split method. Traffic engineering needs to determine the optimal routing of traffic over the existing network infrastructure by efficiently allocating resource in order to optimize traffic performance on an IP network. Even though constraint-based routing [1] of Multi-Protocol Label Switching (MPLS) is developed to address this need, since it is not widely tested or debugged, Internet Service Providers (ISPs) resort to TE methods under Open Shortest Path First (OSPF), which is the most commonly used intra-domain routing protocol. Determining OSPF link weights for optimal network performance is an NP-hard problem. As it is not possible to solve this problem, we present a subset split method to improve the efficiency and performance by minimizing the maximum link utilization in the network via a small number of link weight modifications. The results of this method are compared against results of MPLS architecture [9] and other heuristic methods.

Keywords: Constraint based routing, Link Utilization, Subsetsplit method and Traffic Engineering.

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Authors: Razib M. Othman, Safaai Deris, Rosli M. Illias

Abstract:

Annotation of a protein sequence is pivotal for the understanding of its function. Accuracy of manual annotation provided by curators is still questionable by having lesser evidence strength and yet a hard task and time consuming. A number of computational methods including tools have been developed to tackle this challenging task. However, they require high-cost hardware, are difficult to be setup by the bioscientists, or depend on time intensive and blind sequence similarity search like Basic Local Alignment Search Tool. This paper introduces a new method of assigning highly correlated Gene Ontology terms of annotated protein sequences to partially annotated or newly discovered protein sequences. This method is fully based on Gene Ontology data and annotations. Two problems had been identified to achieve this method. The first problem relates to splitting the single monolithic Gene Ontology RDF/XML file into a set of smaller files that can be easy to assess and process. Thus, these files can be enriched with protein sequences and Inferred from Electronic Annotation evidence associations. The second problem involves searching for a set of semantically similar Gene Ontology terms to a given query. The details of macro and micro problems involved and their solutions including objective of this study are described. This paper also describes the protein sequence annotation and the Gene Ontology. The methodology of this study and Gene Ontology based protein sequence annotation tool namely extended UTMGO is presented. Furthermore, its basic version which is a Gene Ontology browser that is based on semantic similarity search is also introduced.

Keywords: automatic clustering, bioinformatics tool, gene ontology, protein sequence annotation, semantic similarity search

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Authors: Joselito Medina Marin, Norberto Hernández Romero, Juan Carlos Seck Tuoh Mora, Erick S. Martinez Gomez

Abstract:

The Flow Shop Scheduling Problem (FSSP) is a typical problem that is faced by production planning managers in Flexible Manufacturing Systems (FMS). This problem consists in finding the optimal scheduling to carry out a set of jobs, which are processed in a set of machines or shared resources. Moreover, all the jobs are processed in the same machine sequence. As in all the scheduling problems, the makespan can be obtained by drawing the Gantt chart according to the operations order, among other alternatives. On this way, an FMS presenting the FSSP can be modeled by Petri nets (PNs), which are a powerful tool that has been used to model and analyze discrete event systems. Then, the makespan can be obtained by simulating the PN through the token game animation and incidence matrix. In this work, we present an adaptive PN to obtain the makespan of FSSP by applying PN analytical tools.

Keywords: Flow-shop scheduling problem, makespan, Petri nets, state equation.

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Authors: Kamil Aida-zade, C. Ardil

Abstract:

In this paper, some problem formulations of dynamic object parameters recovery described by non-autonomous system of ordinary differential equations with multipoint unshared edge conditions are investigated. Depending on the number of additional conditions the problem is reduced to an algebraic equations system or to a problem of quadratic programming. With this purpose the paper offers a new scheme of the edge conditions transfer method called by conditions shift. The method permits to get rid from differential links and multipoint unshared initially-edge conditions. The advantage of the proposed approach is concluded by capabilities of reduction of a parametric identification problem to essential simple problems of the solution of an algebraic system or quadratic programming.

Keywords: dynamic objects, ordinary differential equations, multipoint unshared edge conditions, quadratic programming, conditions shift

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Authors: K. -H. Yang

Abstract:

Supplier selection problem is one of the important issues of supply chain problems. Two categories of methodologies include qualitative and quantitative approaches which can be applied to supplier selection problems. However, due to the complexities of the problem and lacking of reliable and quantitative data, qualitative approaches are more than quantitative approaches. This study considers operational cost and supplier’s reliability factor and solves the problem by using a quantitative approach. A mixed integer programming model is the primary analytic tool. Analyses of different scenarios with variable cost and reliability structures show that the effectiveness of this approach to the supplier selection problem.

Keywords: Mixed integer programming, quantitative approach, supplier’s reliability, supplier selection.

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Authors: Hari Babu Kotte, Radhika Ambatipudi, Dr. Kent Bertilsson

Abstract:

The experimental and theoretical results of a ZVS (Zero Voltage Switching) isolated flyback DC-DC converter using multilayered coreless PCB step down 2:1 transformer are presented. The performance characteristics of the transformer are shown which are useful for the parameters extraction. The measured energy efficiency of the transformer is found to be more than 94% with the sinusoidal input voltage excitation. The designed flyback converter has been tested successfully upto the output power level of 10W, with a switching frequency in the range of 2.7MHz-4.3MHz. The input voltage of the converter is varied from 25V-40V DC. Frequency modulation technique is employed by maintaining constant off time to regulate the output voltage of the converter. The energy efficiency of the isolated flyback converter circuit under ZVS condition in the MHz frequency region is found to be approximately in the range of 72-84%. This paper gives the comparative results in terms of the energy efficiency of the hard switched and soft switched flyback converter in the MHz frequency region.

Keywords: Coreless PCB step down transformer, DC-DCconverter, Flyback, Hard Switched Converter, MHz frequencyregion, Multilayered PCB transformer, Zero Voltage Switching

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Authors: S. Kavitha, Nirmala P. Ratchagar

Abstract:

This paper presents the novel deterministic dynamic programming approach for solving optimization problem with quadratic objective function with linear equality and inequality constraints. The proposed method employs backward recursion in which computations proceeds from last stage to first stage in a multi-stage decision problem. A generalized recursive equation which gives the exact solution of an optimization problem is derived in this paper. The method is purely analytical and avoids the usage of initial solution. The feasibility of the proposed method is demonstrated with a practical example. The numerical results show that the proposed method provides global optimum solution with negligible computation time.

Keywords: Backward recursion, Dynamic programming, Multi-stage decision problem, Quadratic objective function.

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Authors: Flur R. Ismagilov, Vyacheslav E. Vavilov, Denis V. Gusakov

Abstract:

This paper is devoted to solve the problem of increasing the electrification of aircraft engines by installing a synchronous generator at high pressure shaft. Technical solution of this problem by various research centers is discussed. A design solution of the problem was proposed. To evaluate the effectiveness of the proposed cooling system, thermal analysis was carried out in ANSYS software.

Keywords: Flur R. Ismagilov, Vyacheslav E. Vavilov, Denis V. Gusakov

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Authors: Frank Emmert-Streib, Matthias Dehmer

Abstract:

Inferring the network structure from time series data is a hard problem, especially if the time series is short and noisy. DNA microarray is a technology allowing to monitor the mRNA concentration of thousands of genes simultaneously that produces data of these characteristics. In this study we try to investigate the influence of the experimental design on the quality of the result. More precisely, we investigate the influence of two different types of random single gene perturbations on the inference of genetic networks from time series data. To obtain an objective quality measure for this influence we simulate gene expression values with a biologically plausible model of a known network structure. Within this framework we study the influence of single gene knock-outs in opposite to linearly controlled expression for single genes on the quality of the infered network structure.

Keywords: Dynamic Bayesian networks, microarray data, structure learning, Markov chain Monte Carlo.

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Authors: Y. Abdelrazig

Abstract:

Evolutionary optimization methods such as genetic algorithms have been used extensively for the construction site layout problem. More recently, ant colony optimization algorithms, which are evolutionary methods based on the foraging behavior of ants, have been successfully applied to benchmark combinatorial optimization problems. This paper proposes a formulation of the site layout problem in terms of a sequencing problem that is suitable for solution using an ant colony optimization algorithm. In the construction industry, site layout is a very important planning problem. The objective of site layout is to position temporary facilities both geographically and at the correct time such that the construction work can be performed satisfactorily with minimal costs and improved safety and working environment. During the last decade, evolutionary methods such as genetic algorithms have been used extensively for the construction site layout problem. This paper proposes an ant colony optimization model for construction site layout. A simple case study for a highway project is utilized to illustrate the application of the model.

Keywords: Construction site layout, optimization, ant colony.

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Authors: B. Geethanjali, K. Adalarasu, R. Rajsekaran

Abstract:

Music has a great effect on human body and mind; it can have a positive effect on hormone system. Objective of this study is to analysis the effect of music (carnatic, hard rock and jazz) on brain activity during mental work load using electroencephalography (EEG). Eight healthy subjects without special musical education participated in the study. EEG signals were acquired at frontal (Fz), parietal (Pz) and central (Cz) lobes of brain while listening to music at three experimental condition (rest, music without mental task and music with mental task). Spectral powers features were extracted at alpha, theta and beta brain rhythms. While listening to jazz music, the alpha and theta powers were significantly (p < 0.05) high for rest as compared to music with and without mental task in Cz. While listening to Carnatic music, the beta power was significantly (p < 0.05) high for with mental task as compared to rest and music without mental task at Cz and Fz location. This finding corroborates that attention based activities are enhanced while listening to jazz and carnatic as compare to Hard rock during mental task.

Keywords: Music, Brain Function, Electroencephalography (EEG), Mental Task, Features extraction parameters

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Authors: A. Shirzadeh Chaleshtari, Sh. Shadrokh

Abstract:

Renewable and non-renewable resource constraints have been vast studied in theoretical fields of project scheduling problems. However, although cumulative resources are widespread in practical cases, the literature on project scheduling problems subject to these resources is scant. So in order to study this type of resources more, in this paper we use the framework of a resource constrained project scheduling problem (RCPSP) with finish-start precedence relations between activities and subject to the cumulative resources in addition to the renewable resources. We develop a branch and bound algorithm for this problem customizing precedence tree algorithm of RCPSP. We perform extensive experimental analysis on the algorithm to check its effectiveness and performance for solving different instances of the problem in question.

Keywords: Resource constrained project scheduling problem, cumulative resources, branch and bound algorithm, precedence tree.

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Authors: Bin Cai, Shilong Wang, Haibo Hu

Abstract:

The job shop scheduling problem (JSSP) is well known as one of the most difficult combinatorial optimization problems. This paper presents a hybrid genetic algorithm for the JSSP with the objective of minimizing makespan. The efficiency of the genetic algorithm is enhanced by integrating it with a local search method. The chromosome representation of the problem is based on operations. Schedules are constructed using a procedure that generates full active schedules. In each generation, a local search heuristic based on Nowicki and Smutnicki-s neighborhood is applied to improve the solutions. The approach is tested on a set of standard instances taken from the literature and compared with other approaches. The computation results validate the effectiveness of the proposed algorithm.

Keywords: Genetic algorithm, Job shop scheduling problem, Local search, Meta-heuristic algorithm

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Authors: Seyed Habib A. Rahmati

Abstract:

During last decades, developing multi-objective evolutionary algorithms for optimization problems has found considerable attention. Flexible job shop scheduling problem, as an important scheduling optimization problem, has found this attention too. However, most of the multi-objective algorithms that are developed for this problem use nonprofessional approaches. In another words, most of them combine their objectives and then solve multi-objective problem through single objective approaches. Of course, except some scarce researches that uses Pareto-based algorithms. Therefore, in this paper, a new Pareto-based algorithm called controlled elitism non-dominated sorting genetic algorithm (CENSGA) is proposed for the multi-objective FJSP (MOFJSP). Our considered objectives are makespan, critical machine work load, and total work load of machines. The proposed algorithm is also compared with one the best Pareto-based algorithms of the literature on some multi-objective criteria, statistically.

Keywords: Scheduling, Flexible job shop scheduling problem, controlled elitism non-dominated sorting genetic algorithm

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Authors: Amdouni Hamida, Gammoudi Mohamed Mohsen

Abstract:

In order to help the expert to validate association rules extracted from data, some quality measures are proposed in the literature. We distinguish two categories: objective and subjective measures. The first one depends on a fixed threshold and on data quality from which the rules are extracted. The second one consists on providing to the expert some tools in the objective to explore and visualize rules during the evaluation step. However, the number of extracted rules to validate remains high. Thus, the manually mining rules task is very hard. To solve this problem, we propose, in this paper, a semi-automatic method to assist the expert during the association rule's validation. Our method uses rule-based classification as follow: (i) We transform association rules into classification rules (classifiers), (ii) We use the generated classifiers for data classification. (iii) We visualize association rules with their quality classification to give an idea to the expert and to assist him during validation process.

Keywords: Association rules, Rule-based classification, Classification quality, Validation.

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Authors: Priyadarsini P.L.K, Hemalatha T.

Abstract:

In the Top Right Access point Minimum Length Corridor (TRA-MLC) problem [1], a rectangular boundary partitioned into rectilinear polygons is given and the problem is to find a corridor of least total length and it must include the top right corner of the outer rectangular boundary. A corridor is a tree containing a set of line segments lying along the outer rectangular boundary and/or on the boundary of the rectilinear polygons. The corridor must contain at least one point from the boundaries of the outer rectangle and also the rectilinear polygons. Gutierrez and Gonzalez [1] proved that the MLC problem, along with some of its restricted versions and variants, are NP-complete. In this paper, we give a shorter proof of NP-Completeness of TRA-MLC by findig the reduction in the following way.

Keywords: NP-complete, 2-connected planar graph, Grid embedding of a plane graph.

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Authors: Peyman Sindareh Esfahani, Jeffery Kurt Pieper

Abstract:

In this paper, the problem of robust model predictive control (MPC) for discrete-time linear systems in linear fractional transformation form with structured uncertainty and norm-bounded disturbance is investigated. The problem of minimization of the cost function for MPC design is converted to minimization of the worst case of the cost function. Then, this problem is reduced to minimization of an upper bound of the cost function subject to a terminal inequality satisfying the l₂-norm of the closed loop system. The characteristic of the linear fractional transformation system is taken into account, and by using some mathematical tools, the robust predictive controller design problem is turned into a linear matrix inequality minimization problem. Afterwards, a formulation which includes an integrator to improve the performance of the proposed robust model predictive controller in steady state condition is studied. The validity of the approaches is illustrated through a robust control benchmark problem.

Keywords: Linear fractional transformation, linear matrix inequality, robust model predictive control, state feedback control.

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Authors: D.K. Rao, M.G.M. Khan, K.G. Reddy

Abstract:

The focus of this paper is to develop a technique of solving a combined problem of determining Optimum Strata Boundaries(OSB) and Optimum Sample Size (OSS) of each stratum, when the population understudy isskewed and the study variable has a Pareto frequency distribution. The problem of determining the OSB isformulated as a Mathematical Programming Problem (MPP) which is then solved by dynamic programming technique. A numerical example is presented to illustrate the computational details of the proposed method. The proposed technique is useful to obtain OSB and OSS for a Pareto type skewed population, which minimizes the variance of the estimate of population mean.

Keywords: Stratified sampling, Optimum strata boundaries, Optimum sample size, Pareto distribution, Mathematical programming problem, Dynamic programming technique.

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Authors: P.S. Prakash, S. Selvan

Abstract:

IP networks are evolving from data communication infrastructure into many real-time applications such as video conferencing, IP telephony and require stringent Quality of Service (QoS) requirements. A rudimentary issue in QoS routing is to find a path between a source-destination pair that satisfies two or more endto- end constraints and termed to be NP hard or complete. In this context, we present an algorithm Multi Constraint Path Problem Version 3 (MCPv3), where all constraints are approximated and return a feasible path in much quicker time. We present another algorithm namely Delay Coerced Multi Constrained Routing (DCMCR) where coerce one constraint and approximate the remaining constraints. Our algorithm returns a feasible path, if exists, in polynomial time between a source-destination pair whose first weight satisfied by the first constraint and every other weight is bounded by remaining constraints by a predefined approximation factor (a). We present our experimental results with different topologies and network conditions.

Keywords: Routing, Quality-of-Service (QoS), additive constraints, shortest path, delay coercion.

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Authors: Daniel Gonzales, Zev Winkelman, Trung Tran, Ricardo Sanchez, Dulani Woods, John Hollywood

Abstract:

We have developed a distributed computing capability, Digital Forensics Compute Cluster (DFORC2) to speed up the ingestion and processing of digital evidence that is resident on computer hard drives. DFORC2 parallelizes evidence ingestion and file processing steps. It can be run on a standalone computer cluster or in the Amazon Web Services (AWS) cloud. When running in a virtualized computing environment, its cluster resources can be dynamically scaled up or down using Kubernetes. DFORC2 is an open source project that uses Autopsy, Apache Spark and Kafka, and other open source software packages. It extends the proven open source digital forensics capabilities of Autopsy to compute clusters and cloud architectures, so digital forensics tasks can be accomplished efficiently by a scalable array of cluster compute nodes. In this paper, we describe DFORC2 and compare it with a standalone version of Autopsy when both are used to process evidence from hard drives of different sizes.

Keywords: Cloud computing, cybersecurity, digital forensics, Kafka, Kubernetes, Spark.

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Authors: A. V. Varfolomeeva, N. S. Tkachenko, A. G. Tishchenko

Abstract:

In this study, we addressed the problem of weak validity, implausible results, and inaccurate reporting in psychological research on different species. The theoretical basis of the study was the systems-evolutionary approach (SEA). We assumed that the root of the problem is the values and attitudes of the researchers (in particular anthropomorphism and anthropocentrism). The first aim of the study was the formulation of a research design that avoids this problem. Based on a literature review, we concluded that such design, amongst other things, should include methodics with playful components. The second aim was to conduct a series of studies on the differences in the formation of instrumental skill in rats raised and housed in different environments. As a result, we revealed that there are contradictions between some of the statements of SEA, so that it is not possible to choose one of the alternative hypotheses. We suggested that in order to get out of this problem, it is necessary to modify these provisions by aligning them with the attitude of multicentrism.

Keywords: epistemological attitudes, experimental design, validity, psychological structure, learning

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Authors: Yongxin Yuan, Hao Liu

Abstract:

In this paper, we first give the representation of the general solution of the following least-squares problem (LSP): Given matrices X ∈ Rn×p, B ∈ Rp×p and A0 ∈ Rr×r, find a matrix A ∈ Rn×n such that XT AX − B = min, s. t. A([1, r]) = A0, where A([1, r]) is the r×r leading principal submatrix of the matrix A. We then consider a best approximation problem: given an n × n matrix A˜ with A˜([1, r]) = A0, find Aˆ ∈ SE such that A˜ − Aˆ = minA∈SE A˜ − A, where SE is the solution set of LSP. We show that the best approximation solution Aˆ is unique and derive an explicit formula for it. Keyw

Keywords: Inverse problem, Least-squares solution, model updating, Singular value decomposition (SVD), Optimal approximation.

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Authors: Ahmad Rabanimotlagh

Abstract:

In this paper an ant colony optimization algorithm is developed to solve the permutation flow shop scheduling problem. In the permutation flow shop scheduling problem which has been vastly studied in the literature, there are a set of m machines and a set of n jobs. All the jobs are processed on all the machines and the sequence of jobs being processed is the same on all the machines. Here this problem is optimized considering two criteria, makespan and total flow time. Then the results are compared with the ones obtained by previously developed algorithms. Finally it is visible that our proposed approach performs best among all other algorithms in the literature.

Keywords: Scheduling, Flow shop, Ant colony optimization, Makespan, Flow time

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Authors: A.S. Rebaï, M. Elloumi

Abstract:

The Shortest Approximate Common Superstring (SACS) problem is : Given a set of strings f={w1, w2, ... , wn}, where no wi is an approximate substring of wj, i ≠ j, find a shortest string Sa, such that, every string of f is an approximate substring of Sa. When the number of the strings n>2, the SACS problem becomes NP-complete. In this paper, we present a greedy approximation SACS algorithm. Our algorithm is a 1/2-approximation for the SACS problem. It is of complexity O(n2*(l2+log(n))) in computing time, where n is the number of the strings and l is the length of a string. Our SACS algorithm is based on computation of the Length of the Approximate Longest Overlap (LALO).

Keywords: Shortest approximate common superstring, approximation algorithms, strings overlaps, complexities.

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Authors: Sheikh Muhammad Azam, Masood-ur-Rehman, Adnan Khalid Bhatti, Nadeem Daudpota

Abstract:

Very Large and/or computationally complex optimization problems sometimes require parallel or highperformance computing for achieving a reasonable time for computation. One of the most popular and most complicate problems of this family is “Traveling Salesman Problem". In this paper we have introduced a Branch & Bound based algorithm for the solution of such complicated problems. The main focus of the algorithm is to solve the “symmetric traveling salesman problem". We reviewed some of already available algorithms and felt that there is need of new algorithm which should give optimal solution or near to the optimal solution. On the basis of the use of logarithmic sampling, it was found that the proposed algorithm produced a relatively optimal solution for the problem and results excellent performance as compared with the traditional algorithms of this series.

Keywords: Parallel execution, symmetric traveling salesman problem, branch and bound algorithm, logarithmic sampling.

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