Search results for: Coherent covering location problem

Authors: M. H. Hussain, I. Musirin, A. F. Abidin, S. R. A. Rahim

Abstract:

This paper presents the implementation of Artificial Bees Colony (ABC) algorithm in solving Directional OverCurrent Relays (DOCRs) coordination problem for near-end faults occurring in fixed network topology. The coordination optimization of DOCRs is formulated as linear programming (LP) problem. The objective function is introduced to minimize the operating time of the associated relay which depends on the time multiplier setting. The proposed technique is to taken as a technique for comparison purpose in order to highlight its superiority. The proposed algorithms have been tested successfully on 8 bus test system. The simulation results demonstrated that the ABC algorithm which has been proved to have good search ability is capable in dealing with constraint optimization problems.

Keywords: Artificial bees colony, directional overcurrent relay coordination problem, relay settings, time multiplier setting.

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Authors: H. El Ayech, A. Trabelsi

Abstract:

In this article we are going to discuss the improvement of the multi classes- classification problem using multi layer Perceptron. The considered approach consists in breaking down the n-class problem into two-classes- subproblems. The training of each two-class subproblem is made independently; as for the phase of test, we are going to confront a vector that we want to classify to all two classes- models, the elected class will be the strongest one that won-t lose any competition with the other classes. Rates of recognition gotten with the multi class-s approach by two-class-s decomposition are clearly better that those gotten by the simple multi class-s approach.

Keywords: Artificial neural network, letter-recognition, Multi class Classification, Multi Layer Perceptron.

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Authors: I. A. Farhat

Abstract:

The The dynamic economic dispatch (DED) problem is one of the complex constrained optimization problems that have nonlinear, con-convex and non-smooth objective functions. The purpose of the DED is to determine the optimal economic operation of the committed units while meeting the load demand. Associated to this constrained problem there exist highly nonlinear and non-convex practical constraints to be satisfied. Therefore, classical and derivative-based methods are likely not to converge to an optimal or near optimal solution to such a dynamic and large-scale problem. In this paper, an Artificial Immune System technique (AIS) is implemented and applied to solve the DED problem considering the transmission power losses and the valve-point effects in addition to the other operational constraints. To demonstrate the effectiveness of the proposed technique, two case studies are considered. The results obtained using the AIS are compared to those obtained by other methods reported in the literature and found better.

Keywords: Artificial Immune System (AIS), Dynamic Economic Dispatch (DED).

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Authors: Hossain Aziz, Rinku Mukherjee

Abstract:

A potential flow model is used to study the unsteady flow past two airfoils in configuration, each of which is suddenly set into motion. The airfoil bound vortices are modeled using lumped vortex elements and the wake behind the airfoil is modeled by discrete vortices. This consists of solving a steady state flow problem at each time-step where unsteadiness is incorporated through the “zero normal flow on a solid surface" boundary condition at every time instant. Additionally, along with the “zero normal flow on a solid surface" boundary condition Kelvin-s condition is used to compute the strength of the latest wake vortex shed from the trailing edge of the airfoil. Location of the wake vortices is updated at each time-step to get the wake shape at each time instant. Results are presented to show the effect of airfoil-airfoil interaction and airfoil-wake interaction on the aerodynamic characteristics of each airfoil.

Keywords: Aerodynamics, Airfoils, Configuration, Unsteady.

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Authors: Badr M. Alshammari, T. Guesmi

Abstract:

This study presents a modified version of the artificial bee colony (ABC) algorithm by including a local search technique for solving the non-convex economic power dispatch problem. The local search step is incorporated at the end of each iteration. Total system losses, valve-point loading effects and prohibited operating zones have been incorporated in the problem formulation. Thus, the problem becomes highly nonlinear and with discontinuous objective function. The proposed technique is validated using an IEEE benchmark system with ten thermal units. Simulation results demonstrate that the proposed optimization algorithm has better convergence characteristics in comparison with the original ABC algorithm.

Keywords: Economic power dispatch, artificial bee colony, valve-point loading effects, prohibited operating zones.

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Authors: B. Mukanova, N. Glazyrina, S. Glazyrin

Abstract:

The formulated problem of optimization of the technological process of water treatment for thermal power plants is considered in this article. The problem is of multiparametric nature. To optimize the process, namely, reduce the amount of waste water, a new technology was developed to reuse such water. A mathematical model of the technology of wastewater reuse was developed. Optimization parameters were determined. The model consists of a material balance equation, an equation describing the kinetics of ion exchange for the non-equilibrium case and an equation for the ion exchange isotherm. The material balance equation includes a nonlinear term that depends on the kinetics of ion exchange. A direct problem of calculating the impurity concentration at the outlet of the water treatment plant was numerically solved. The direct problem was approximated by an implicit point-to-point computation difference scheme. The inverse problem was formulated as relates to determination of the parameters of the mathematical model of the water treatment plant operating in non-equilibrium conditions. The formulated inverse problem was solved. Following the results of calculation the time of start of the filter regeneration process was determined, as well as the period of regeneration process and the amount of regeneration and wash water. Multi-parameter optimization of water treatment process for thermal power plants allowed decreasing the amount of wastewater by 15%.

Keywords: Direct problem, multiparametric optimization, optimization parameters, water treatment.

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Authors: R.Mohamad Idris, A.Khairuddin, M.W.Mustafa

Abstract:

In this paper, a novel method using Bees Algorithm is proposed to determine the optimal allocation of FACTS devices for maximizing the Available Transfer Capability (ATC) of power transactions between source and sink areas in the deregulated power system. The algorithm simultaneously searches the FACTS location, FACTS parameters and FACTS types. Two types of FACTS are simulated in this study namely Thyristor Controlled Series Compensator (TCSC) and Static Var Compensator (SVC). A Repeated Power Flow with FACTS devices including ATC is used to evaluate the feasible ATC value within real and reactive power generation limits, line thermal limits, voltage limits and FACTS operation limits. An IEEE30 bus system is used to demonstrate the effectiveness of the algorithm as an optimization tool to enhance ATC. A Genetic Algorithm technique is used for validation purposes. The results clearly indicate that the introduction of FACTS devices in a right combination of location and parameters could enhance ATC and Bees Algorithm can be efficiently used for this kind of nonlinear integer optimization.

Keywords: ATC, Bees Algorithm, TCSC, SVC

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Authors: Fotis N. Koumboulis, Michael G. Skarpetis, Maria P. Tzamtzi

Abstract:

The problem of robust disturbance rejection (RDR) using a proportional state feedback controller is studied for the case of Left Invertible MIMO generalized state space linear systems with nonlinear uncertain structure. Sufficient conditions for the problem to have a solution are established. The set of all proportional feedback controllers solving the problem subject to these conditions is analytically determined.

Keywords: System theory, uncertain systems, robust control, singular systems.

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Authors: Jieun Kim, Haejin Cho, Yongtae Park, Yoonjo Kim, Jeonghwan Jeon

Abstract:

As creative economy is important theme for national policy, many countries have been raising investments through national R&D programs. Since not all of programs are aligned with the ultimate vision and R&D investment is one of the most decisive elements, the strategic fit of national R&D programs should be evaluated for effective resource allocation. This study aims at identifying the factors of strategic fit of national R&D program on the creative economy policy. For this purpose, the balanced scorecard (BSC) model for R&D is utilized to translate national strategic objectives into a set of coherent performance factors.

Keywords: Balanced scorecard, Creative economy, National R&D program, Strategic fit.

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Authors: I. A. Farhat

Abstract:

The dynamic economic dispatch (DED) problem is one of the complex constrained optimization problems that have nonlinear, con-convex and non-smooth objective functions. The purpose of the DED is to determine the optimal economic operation of the committed units while meeting the load demand.  Associated to this constrained problem there exist highly nonlinear and non-convex practical constraints to be satisfied. Therefore, classical and derivative-based methods are likely not to converge to an optimal or near optimal solution to such a dynamic and large-scale problem. In this paper, an Artificial Immune System technique (AIS) is implemented and applied to solve the DED problem considering the transmission power losses and the valve-point effects in addition to the other operational constraints. To demonstrate the effectiveness of the proposed technique, two case studies are considered. The results obtained using the AIS are compared to those obtained by other methods reported in the literature and found better.

Keywords: Artificial Immune System (AIS), Dynamic Economic Dispatch (DED).

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Authors: Mohsen Ziaee

Abstract:

In this paper, a mixed integer linear programming (MILP) model is presented to solve the flexible job shop scheduling problem (FJSP). This problem is one of the hardest combinatorial problems. The objective considered is the minimization of the makespan. The computational results of the proposed MILP model were compared with those of the best known mathematical model in the literature in terms of the computational time. The results show that our model has better performance with respect to all the considered performance measures including relative percentage deviation (RPD) value, number of constraints, and total number of variables. By this improved mathematical model, larger FJS problems can be optimally solved in reasonable time, and therefore, the model would be a better tool for the performance evaluation of the approximation algorithms developed for the problem.

Keywords: Scheduling, flexible job shop, makespan, mixed integer linear programming.

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Authors: Fadia M. A. Ghali

Abstract:

The problem of wastewater treatment in Egypt is a two-fold problem; the first part concerning the existing rural areas, the second one dealing with new industrial/domestic areas. In Egypt several agricultural projects have been initiated by the government and the private sector as well, in order to change its infrastructure. As a reliable energy source, photovoltaic pumping systems have contributed to supply water for local rural communities worldwide; they can also be implemented to solve the problem “wastewater environment pollution". The solution of this problem can be categorised as recycle process. In addition, because of regional conditions past technologies are being reexamined to select a smallscale treatment system requiring low construction and maintenance costs. This paper gives the design guidelines of a Photovoltaic Small- Scale Wastewater Treatment Plant (PVSSWTP) based on technologies that can be transferred.

Keywords: Renewable energy sources, Photovoltaic, small-scale projects, wastewater treatment.

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Authors: San Nah Sze, Wei King Tiong

Abstract:

The multiple traveling salesman problem (mTSP) can be used to model many practical problems. The mTSP is more complicated than the traveling salesman problem (TSP) because it requires determining which cities to assign to each salesman, as well as the optimal ordering of the cities within each salesman's tour. Previous studies proposed that Genetic Algorithm (GA), Integer Programming (IP) and several neural network (NN) approaches could be used to solve mTSP. This paper compared the results for mTSP, solved with Genetic Algorithm (GA) and Nearest Neighbor Algorithm (NNA). The number of cities is clustered into a few groups using k-means clustering technique. The number of groups depends on the number of salesman. Then, each group is solved with NNA and GA as an independent TSP. It is found that k-means clustering and NNA are superior to GA in terms of performance (evaluated by fitness function) and computing time.

Keywords: Multiple Traveling Salesman Problem, GeneticAlgorithm, Nearest Neighbor Algorithm, k-Means Clustering.

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Authors: T. Hussain, M. W. Siddiqi, A. Iqbal

Abstract:

The study is aimed to test causal relationship between growth and unemployment, using time series data for Pakistan from 1972 to 2006. Growth is considered to be a pathway to decrease the level of unemployment. Unemployment is a social and political issue. It is a phenomenon where human resources are wasted leading to deacceleration in growth. Johanson Cointegration shows that there is long run relationship between growth and unemployment. For short run dynamics and causality, the study utilizes Vector Error Correction Model (VECM). The results of VECM indicate that there is short and long run causal relation between growth and unemployment including capital, labor and human capital as explanatory variables.

Keywords: Economic Growth, Unemployment, Cointegrationand Causality.

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Authors: Vijaya K. Srivastava, Davide Spinello

Abstract:

This paper presents established 3ⁿ enumeration procedure for mixed integer optimization problems for solving multi-objective reliability and redundancy allocation problem subject to design constraints. The formulated problem is to find the optimum level of unit reliability and the number of units for each subsystem. A number of illustrative examples are provided and compared to indicate the application of the superiority of the proposed method.

Keywords: Integer programming, mixed integer programming, multi-objective optimization, reliability redundancy allocation.

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Authors: Hossein Ali Akbarpour, Fatemeh Dadkhah

Abstract:

This paper considers a multi criteria cell formation problem in Cellular Manufacturing System (CMS). Minimizing the number of voids and exceptional elements in cells simultaneously are two proposed objective functions. This problem is an Np-hard problem according to the literature, and therefore, we can-t find the optimal solution by an exact method. In this paper we developed two ant algorithms, Ant Colony Optimization (ACO) and Max-Min Ant System (MMAS), based on Data Envelopment Analysis (DEA). Both of them try to find the efficient solutions based on efficiency concept in DEA. Each artificial ant is considered as a Decision Making Unit (DMU). For each DMU we considered two inputs, the values of objective functions, and one output, the value of one for all of them. In order to evaluate performance of proposed methods we provided an experimental design with some empirical problem in three different sizes, small, medium and large. We defined three different criteria that show which algorithm has the best performance.

Keywords: Ant algorithm, Cellular manufacturing system, Data envelopment analysis, Efficiency

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Authors: Fengxia Zheng

Abstract:

By using two new fixed point theorems for mixed monotone operators, the positive solution of nonlinear fractional differential equation boundary value problem is studied. Its existence and uniqueness is proved, and an iterative scheme is constructed to approximate it.

Keywords: Fractional differential equation, boundary value problem, positive solution, existence and uniqueness, fixed point theorem, mixed monotone operator.

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Authors: Rosshairy Abd Rahman, Chooi-Leng Ang, Razamin Ramli

Abstract:

Feed is one of the factors which play an important role in determining a successful development of an aquaculture industry. It is always critical to produce the best aquaculture diet at a minimum cost in order to trim down the operational cost and gain more profit. However, the feed mix problem becomes increasingly difficult since many issues need to be considered simultaneously. Thus, the purpose of this paper is to review the current techniques used by nutritionist and researchers to tackle the issues. Additionally, this paper introduce an enhance algorithm which is deemed suitable to deal with all the issues arise. The proposed technique refers to Hybrid Genetic Algorithm which is expected to obtain the minimum cost diet for farmed animal, while satisfying nutritional requirements. Hybrid GA technique with artificial bee algorithm is expected to reduce the penalty function and provide a better solution for the feed mix problem.

Keywords: Artificial bee algorithm, feed mix problem, hybrid genetic algorithm.

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Authors: Daniel Kostrzewa, Henryk Josiński

Abstract:

The expanded Invasive Weed Optimization algorithm (exIWO) is an optimization metaheuristic modelled on the original IWO version created by the researchers from the University of Tehran. The authors of the present paper have extended the exIWO algorithm introducing a set of both deterministic and non-deterministic strategies of individuals’ selection. The goal of the project was to evaluate the exIWO by testing its usefulness for solving some test instances of the traveling salesman problem (TSP) taken from the TSPLIB collection which allows comparing the experimental results with optimal values.

Keywords: Expanded Invasive Weed Optimization algorithm (exIWO), Traveling Salesman Problem (TSP), heuristic approach, inversion operator.

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Authors: Y. K. Lin, H. T. Hsieh, F. Y. Hsieh

Abstract:

Total weighted tardiness is a measure of customer satisfaction. Minimizing it represents satisfying the general requirement of on-time delivery. In this research, we consider an ant colony optimization (ACO) algorithm to solve the problem of scheduling unrelated parallel machines to minimize total weighted tardiness. The problem is NP-hard in the strong sense. Computational results show that the proposed ACO algorithm is giving promising results compared to other existing algorithms.

Keywords: ant colony optimization, total weighted tardiness, unrelated parallel machines.

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Authors: Yang Zhou, Kangfeng Zheng, Wei Ni, Ren Ping Liu

Abstract:

Software-defined networking (SDN) provides a solution for scalable network framework with decoupled control and data plane. However, this architecture also induces a particular distributed denial-of-service (DDoS) attack that can affect or even overwhelm the SDN network. DDoS attack detection problem has to date been mostly researched as entropy comparison problem. However, this problem lacks the utilization of SDN, and the results are not accurate. In this paper, we propose a DDoS attack detection method, which interprets DDoS detection as a signature matching problem and is formulated as Earth Mover’s Distance (EMD) model. Considering the feasibility and accuracy, we further propose to define the cost function of EMD to be a generalized Kullback-Leibler divergence. Simulation results show that our proposed method can detect DDoS attacks by comparing EMD values with the ones computed in the case without attacks. Moreover, our method can significantly increase the true positive rate of detection.

Keywords: DDoS detection, EMD, relative entropy, SDN.

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Authors: Mohammad Saeri, Noor Rizkiyah, Kambang Vetrani Asie, Titin Apung Atikah

Abstract:

The study aims to assess efficient specific-location soybean farming technology assembly by assisting the farmers in applying the suggested technology. Superimposed trial was conducted to know NPK fertilizer effect toward soybean growth and yield and soybean improved variety test for the dissemination of improved variety. The assessment was conducted at the farmers group of Sumber Rejeki, Kepulungan Village, Gempol Sub-district, Pasuruan Regency as the soybean central at Pasuruan area. The number of farmers involved in the study was 38 people with 25 ha soybean area. This study was held from July to October 2012.  The recommended technology package agreed at the socialization time and used in this research were: using Argomulyo variety seeds of 40 kg/ha, planting by drilling, planting by distance of 40x10 cm, deciding the seeds amount of 2-3 seeds per hole, and giving fertilization based on recommendation of East Java AIAT of 50 kg Urea, 100 kg SP-36 and 50 kg KCl.  Farmers around the research location were used as control group. Assessment on soybean farming system was considered effective because it could increase the production up to 38%. The farming analysis showed that the result collaborator farmers gained were positively higher than non-collaborator farmers with RC ratio of 2.03 and 1.54, respectively. Argomulyo variety has the prospect to be developed due to the high yield of about 2 tons/ha and the larger seeds. The NPK fertilization test at the soybean plants showed that the fertilization had minor effect on the yield.

Keywords: Farming system, soybean, variety, location specific farming.

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Authors: Nileshkumar Vaishnav, Aditya Tatu

Abstract:

An algebraic framework for processing graph signals axiomatically designates the graph adjacency matrix as the shift operator. In this setup, we often encounter a problem wherein we know the filtered output and the filter coefficients, and need to find out the input graph signal. Solution to this problem using direct approach requires O(N3) operations, where N is the number of vertices in graph. In this paper, we adapt the spectral graph partitioning method for partitioning of graphs and use it to reduce the computational cost of the filtering problem. We use the example of denoising of the temperature data to illustrate the efficacy of the approach.

Keywords: Graph signal processing, graph partitioning, inverse filtering on graphs, algebraic signal processing.

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Authors: Ferinar Moaidi, Mahdi Moaidi

Abstract:

Environmental issues and the ever-increasing in demand of electrical energy make it necessary to have distributed generation (DG) resources in the power system. In this research, in order to realize the goals of reducing losses and improving the voltage profile in a microgrid, the allocation and sizing of DGs have been used. The proposed Genetic Algorithm (GA) is described from the array of artificial intelligence methods for solving the problem. The algorithm is implemented on the IEEE 33 buses network. This study is presented in two scenarios, primarily to illustrate the effect of location and determination of DGs has been done to reduce losses and improve the voltage profile. On the other hand, decisions made with the one-level assumptions of load are not universally accepted for all levels of load. Therefore, in this study, load modelling is performed and the results are presented for multi-levels load state.

Keywords: Distributed generation, genetic algorithm, microgrid, load modelling, loss reduction, voltage improvement.

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Authors: J. R. Mudakavi, K. Puttanna

Abstract:

Chromium in the environment is considered as one of the most toxic elements probably next only to mercury and arsenic. It is acutely toxic, mutagenic and carcinogenic in the environment. Chromium contamination of soil and underground water due to industrial activities is a very serious problem in several parts of India covering Karnataka, Tamil Nadu, Andhra Pradesh etc. Functionally modified Activated Carbon Fabrics (ACF) offer targeted chromium removal from drinking water and industrial effluents. Activated carbon fabric is a light weight adsorbing material with high surface area and low resistance to fluid flow. We have investigated surface modification of ACF using various acids in the laboratory through batch as well as through continuous flow column experiments with a view to develop the optimum conditions for chromium removal. Among the various acids investigated, phosphoric acid modified ACF gave best results with a removal efficiency of 95% under optimum conditions. Optimum pH was around 2 – 4 with 2 hours contact time. Continuous column experiments with an effective bed contact time (EBCT) of 5 minutes indicated that breakthrough occurred after 300 bed volumes. Adsorption data followed a Freundlich isotherm pattern. Nickel adsorbs preferentially and sulphate reduces chromium adsorption by 50%. The ACF could be regenerated up to 52.3% using 3 M NaOH under optimal conditions. The process is simple, economical, energy efficient and applicable to industrial effluents and drinking water.

Keywords: Activated carbon fabric, adsorption, drinking water, hexavalent chromium.

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Authors: Hisham A. Elfergani, Ayad A. Abdalla, Ahmed R. Ballil

Abstract:

Acoustic Emission (AE) is one of the most effective non-destructive tests that can be used to detect the defect process as it is occurring. AE techniques can be used to monitor a wide range of structures and materials such as metals, non-metals and combinations of these when load is applied. The current work investigates the effectiveness and accuracy of TOA method in AE tests involving reinforced composite concrete-mortar structures. A series of experimental tests were performed using the Hsu-Neilson (H-N) source to study 2-D location accuracy using this method on concrete-mortar (400×400 mm) specimens. Four AE sensors (R3I – resonant frequency 30 kHz) were mounted to the mortar surface and six sources were performed at each point of preselected locations on the upper surface of the mortar. Results show that the TOA method can be used effectively to locate signals on composite concrete/mortar specimen and has high accuracy.

Keywords: Acoustic emission, time of arrival, composite materials, reinforced concrete.

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Authors: B. Mikulskienė

Abstract:

Public administration institutions in cooperation with politicians are not the sole policy decision makers in full meaning any longer. Meanwhile, a special role, namely steering the decision making process, could be delegated to them. Despite the wide scientific discussion on different aspects what has direct impact on policy creation, there is a lack of holistic practical managerial advice, which could integrate infrastructure of policy decision making with intellectual capital and with interconnection of partnership. The proposed harmonized decision making model of process, people and partnership entitled by acronym HM-3P is analyzed as a framework for implementation of public administration steering role seeking the coherent social involvement in policy decision making.

Keywords: participatory decision making, partnership, stakeholders.

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Authors: Mikel Niño, Roberto V. Zicari, Todor Ivanov, Kim Hee, Naveed Mushtaq, Marten Rosselli, Concha Sánchez-Ocaña, Karsten Tolle, José Miguel Blanco, Arantza Illarramendi, Jörg Besier, Harry Underwood

Abstract:

One of the application fields for data analysis techniques and technologies gaining momentum is the area of social good or “common good”, covering cases related to humanitarian crises, global health care, or ecology and environmental issues, among others. The promotion of data-driven projects in this field aims at increasing the efficacy and efficiency of social initiatives, improving the way these actions help humanity in general and people in need in particular. This application field, however, poses its own barriers and challenges when developing data-driven projects, lagging behind in comparison with other scenarios. These challenges derive from aspects such as the scope and scale of the social issue to solve, cultural and political barriers, the skills of main stakeholders and the technological resources available, the motivation to be engaged in such projects, or the ethical and legal issues related to sensitive data. This paper analyzes the application of data projects in the field of social good, reviewing its current state and noteworthy initiatives, and presenting a framework covering the key aspects to analyze in such projects. The goal is to provide guidelines to understand the main challenges and opportunities for this type of data project, as well as identifying the main differential issues compared to “classical” data projects in general. A case study is presented on the initial steps and stakeholder analysis of a data project for the inclusion of refugees in the city of Frankfurt, Germany, in order to empirically confront the framework with a real example.

Keywords: Data-Driven projects, humanitarian operations, personal and sensitive data, social good, stakeholders analysis.

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Authors: Bin Cai, Shilong Wang, Haibo Hu

Abstract:

The job shop scheduling problem (JSSP) is a notoriously difficult problem in combinatorial optimization. This paper presents a hybrid artificial immune system for the JSSP with the objective of minimizing makespan. The proposed approach combines the artificial immune system, which has a powerful global exploration capability, with the local search method, which can exploit the optimal antibody. The antibody coding scheme is based on the operation based representation. The decoding procedure limits the search space to the set of full active schedules. In each generation, a local search heuristic based on the neighborhood structure proposed by Nowicki and Smutnicki is applied to improve the solutions. The approach is tested on 43 benchmark problems taken from the literature and compared with other approaches. The computation results validate the effectiveness of the proposed algorithm.

Keywords: Artificial immune system, Job shop scheduling problem, Local search, Metaheuristic algorithm

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Authors: Udaya Kumar Reddy K. R, K. Viswanathan Iyer

Abstract:

Given a simple connected unweighted undirected graph G = (V (G), E(G)) with |V (G)| = n and |E(G)| = m, we present a new algorithm for the all-pairs shortest-path (APSP) problem. The running time of our algorithm is in O(n2 log n). This bound is an improvement over previous best known O(n2.376) time bound of Raimund Seidel (1995) for general graphs. The algorithm presented does not rely on fast matrix multiplication. Our algorithm with slight modifications, enables us to compute the APSP problem for unweighted directed graph in time O(n2 log n), improving a previous best known O(n2.575) time bound of Uri Zwick (2002).

Keywords: Distance in graphs, Dynamic programming, Graphalgorithms, Shortest paths.

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