Search results for: discrete breeding swarm

Authors: Tarek Aboueldahab, Hanan Farag

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Parallel Job Shop Scheduling Problem (JSP) is a multi-objective and multi constrains NP- optimization problem. Traditional Artificial Intelligence techniques have been widely used; however, they could be trapped into the local minimum without reaching the optimum solution, so we propose a hybrid Artificial Intelligence model (AI) with Discrete Breeding Swarm (DBS) added to traditional Artificial Intelligence to avoid this trapping. This model is applied in the cost minimization of the Car Sequencing and Operator Allocation (CSOA) problem. The practical experiment shows that our model outperforms other techniques in cost minimization.

Keywords: parallel job shop scheduling problem, artificial intelligence, discrete breeding swarm, car sequencing and operator allocation, cost minimization

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Authors: Tarek Aboueldahab, Hanan Farag

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Cost minimization of Multiple Vehicle Routing Problem becomes a critical issue in the field of transportation because it is NP-hard optimization problem and the search space is complex. Many researches use the hybridization of artificial intelligence (AI) models to solve this problem; however, it can not guarantee to reach the best solution due to the difficulty of searching the whole search space. To overcome this problem, we introduce the hybrid model of Discrete Particle Swarm Optimization (DPSO) with a passive congregation which enable searching the whole search space to compromise between both local and global search. The practical experiment shows that our model obviously outperforms other hybrid models in cost minimization.

Keywords: cost minimization, multi-vehicle routing problem, passive congregation, discrete swarm, passive congregation

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Authors: Broderick Crawford, Ricardo Soto, Natalia Berrios, Eduardo Olguin

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In this paper, we present a binary cat swarm optimization for solving the Set covering problem. The set covering problem is a well-known NP-hard problem with many practical applications, including those involving scheduling, production planning and location problems. Binary cat swarm optimization is a recent swarm metaheuristic technique based on the behavior of discrete cats. Domestic cats show the ability to hunt and are curious about moving objects. The cats have two modes of behavior: seeking mode and tracing mode. We illustrate this approach with 65 instances of the problem from the OR-Library. Moreover, we solve this problem with 40 new binarization techniques and we select the technical with the best results obtained. Finally, we make a comparison between results obtained in previous studies and the new binarization technique, that is, with roulette wheel as transfer function and V3 as discretization technique.

Keywords: binary cat swarm optimization, binarization methods, metaheuristic, set covering problem

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Authors: Takahiro Hino, Michiharu Maeda

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Particle swarm optimization (PSO) is an optimization approach that achieves the social model of bird flocking and fish schooling. PSO works in continuous space and can solve continuous optimization problem with high quality. Set-based particle swarm optimization (SPSO) functions in discrete space by using a set. SPSO can solve combinatorial optimization problem with high quality and is successful to apply to the large-scale problem. In this paper, we present an algorithm of SPSO with status memory to decide the position based on the previous position for solving traveling salesman problem (TSP). In order to show the effectiveness of our approach. We examine SPSOSM for TSP compared to the existing algorithms.

Keywords: combinatorial optimization problems, particle swarm optimization, set-based particle swarm optimization, traveling salesman problem

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Authors: Omaima N. Ahmad AL-Allaf

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Over communication networks, images can be easily copied and distributed in an illegal way. The copyright protection for authors and owners is necessary. Therefore, the digital watermarking techniques play an important role as a valid solution for authority problems. Digital image watermarking techniques are used to hide watermarks into images to achieve copyright protection and prevent its illegal copy. Watermarks need to be robust to attacks and maintain data quality. Therefore, we discussed in this paper two approaches for image watermarking, first is based on Particle Swarm Optimization (PSO) and the second approach is based on Genetic Algorithm (GA). Discrete wavelet transformation (DWT) is used with the two approaches separately for embedding process to cover image transformation. Each of PSO and GA is based on co-relation coefficient to detect the high energy coefficient watermark bit in the original image and then hide the watermark in original image. Many experiments were conducted for the two approaches with different values of PSO and GA parameters. From experiments, PSO approach got better results with PSNR equal 53, MSE equal 0.0039. Whereas GA approach got PSNR equal 50.5 and MSE equal 0.0048 when using population size equal to 100, number of iterations equal to 150 and 3×3 block. According to the results, we can note that small block size can affect the quality of image watermarking based PSO/GA because small block size can increase the search area of the watermarking image. Better PSO results were obtained when using swarm size equal to 100.

Keywords: image watermarking, genetic algorithm, particle swarm optimization, discrete wavelet transform

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Authors: Anh Duc Dang, Joachim Horn

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This paper presents a new approach to control robots, which can quickly find their swarm while tracking a moving target through the obstacles of the environment. In this approach, an artificial potential field is generated between each free-robot and the virtual attractive point of the swarm. This artificial potential field will lead free-robots to their swarm. The swarm-finding of these free-robots dose not influence the general motion of their swarm and nor other robots. When one singular robot approaches the swarm then its swarm-search will finish, and it will further participate with its swarm to reach the position of the target. The connections between member-robots with their neighbours are controlled by the artificial attractive/repulsive force field between them to avoid collisions and keep the constant distances between them in ordered formation. The effectiveness of the proposed approach has been verified in simulations.

Keywords: formation control, potential field method, obstacle avoidance, swarm intelligence, multi-agent systems

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Authors: Zhang Tianci, Ding Meng, Zuo Hongfu, Zeng Lina, Sun Zejun

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Automation of airport operations can greatly improve ground movement efficiency. In this paper, we study the speed profile design problem for advanced airport ground movement control and guidance. The problem is constrained by the surface four-dimensional trajectory generated in taxi planning. A decomposed approach of two stages is presented to solve this problem efficiently. In the first stage, speeds are allocated at control points which ensure smooth speed profiles can be found later. In the second stage, detailed speed profiles of each taxi interval are generated according to the allocated control point speeds with the objective of minimizing the overall fuel consumption. We present a swarm intelligence based algorithm for the first-stage problem and a discrete variable driven enumeration method for the second-stage problem since it only has a small set of discrete variables. Experimental results demonstrate the presented methodology performs well on real world speed profile design problems.

Keywords: airport ground movement, fuel consumption, particle swarm optimization, smoothness, speed profile design

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Authors: Tawfik Thelaidjia, Salah Chenikher

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Bearing fault diagnosis has attracted significant attention over the past few decades. It consists of two major parts: vibration signal feature extraction and condition classification for the extracted features. In this paper, feature extraction from faulty bearing vibration signals is performed by a combination of the signal’s Kurtosis and features obtained through the preprocessing of the vibration signal samples using Db2 discrete wavelet transform at the fifth level of decomposition. In this way, a 7-dimensional vector of the vibration signal feature is obtained. After feature extraction from vibration signal, the support vector machine (SVM) was applied to automate the fault diagnosis procedure. To improve the classification accuracy for bearing fault prediction, particle swarm optimization (PSO) is employed to simultaneously optimize the SVM kernel function parameter and the penalty parameter. The results have shown feasibility and effectiveness of the proposed approach

Keywords: condition monitoring, discrete wavelet transform, fault diagnosis, kurtosis, machine learning, particle swarm optimization, roller bearing, rotating machines, support vector machine, vibration measurement

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Authors: Ramin Javadzadeh

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The particle swarm optimization are Meta heuristic optimization method, which are used for clustering and pattern recognition applications are abundantly. These algorithms in multimodal optimization problems are more efficient than genetic algorithms. A major drawback in these algorithms is their slow convergence to global optimum and their weak stability can be considered in various running of these algorithms. In this paper, improved Particle swarm optimization is introduced for the first time to overcome its problems. The fuzzy cellular automata is used for improving the algorithm efficiently. The credibility of the proposed approach is evaluated by simulations, and it is shown that the proposed approach achieves better results can be achieved compared to the Particle swarm optimization algorithms.

Keywords: cellular automata, cellular learning automata, local search, optimization, particle swarm optimization

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Authors: T. K. Hung

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Terrorism acts have occurred across both developed and developing states, with well-identified motivation and causes. For many years, terrorism eradication has become a major topic yet only passive actions were taken in response to acts. The linkage between the location of terrorism occurrence and breeding ground is not well-documented, resulting in the passive approach used in counter-terrorism nowadays. The evaluation investigates all post-9/11 terrorism affairs considering their state capacity, safety, ease of border access control, religion diversity, and technology access, to measure the level of breeding ground of the states. Those "weak" states with poor border access control, resources capacity and domestic safety are the best breeding ground for terrorists. Although many attacks were caused by religious motivation, religion diversity does not predict the breeding ground. States with censored technology access, particular computer-mediated communication, predict on the terrorism breeding ground, moderated by the level of breeding ground of neighboring states.

Keywords: counter-terrorism, lethality, security, terrorism

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Authors: Muneeb Ahmad, Ali Raza

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A computational method inspired by the immune system (IS) is presented, leveraging its shared characteristics of robustness, fault tolerance, scalability, and adaptability with swarm intelligence. This method aims to showcase flocking behaviors in a swarm of robots (SR). The innate part of the IS offers a variety of reactive and probabilistic cell functions alongside its self-regulation mechanism which have been translated to enable swarming behaviors. Although, the research is specially focused on flocking behaviors in a variety of simulated environments using e-puck robots in a physics-based simulator (CoppeliaSim); the artificial innate immune system (AIIS) can exhibit other swarm behaviors as well. The effectiveness of the immuno-inspired approach has been established with extensive experimentations, for scalability and adaptability, using standard swarm benchmarks as well as the immunological regulatory functions (i.e., Dendritic Cells’ Maturity and Inflammation). The AIIS-based approach has proved to be a scalable and adaptive solution for emulating the flocking behavior of SR.

Keywords: artificial innate immune system, flocking swarm, immune system, swarm intelligence

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Authors: Faruque Miah, Hafij Ali, Enaya Jannat, Tanmoy Modok Shuvra, M. Niamul Naser

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In this study, breeding biology and induced breeding of freshwater mud eel, Monopterus cuchia was observed during the experimental period from February to June, 2013. Breeding biology of freshwater mud eel, Monopterus cuchia was considered in terms of gonadosomatic index, length-weight relationship of gonad, ova diameter and fecundity. The ova diameter was recorded from 0.3 mm to 4.30 mm and the individual fecundity was recorded from 155 to 1495 while relative fecundity was found from 2.64 to 12.45. The fecundity related to body weight and length of fish was also discussed. A peak of GSI was observed 2.14±0.2 in male and 5.1 ±1.09 in female. Induced breeding of freshwater mud eel, Monopterus cuchia was also practiced with different doses of different inducing agents like pituitary gland (PG), human chorionic gonadotropin (HCG), Gonadotropin releasing hormone (GnRH) and Ovuline-a synthetic hormone in different environmental conditions. However, it was observed that the artificial breeding of freshwater mud eel, Monopterus cuchia was not yet succeeded through inducing agents in captive conditions, rather the inducing agent showed negative impacts on fecundity and ovarian tissues. It was seen that mature eggs in the oviduct were reduced, absorbed and some eggs were found in spoiled condition.

Keywords: breeding biology, induced breeding, Monopterus cuchia, human chorionic gonadotropin

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Authors: Jeryes Danial, Yosi Ben Asher

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Algorithms for controlling a swarm of robots is an active research field, out of which cattle herding is one of the most complex problems to solve. In this paper, we derive an independent herding algorithm that is specifically designed for a swarm of quadcopters. The algorithm works by devising flight trajectories that cause the cows to run-away in the desired direction and hence herd cows that are distributed in a given field towards a common gathering point. Unlike previously proposed swarm herding algorithms, this algorithm does not use a flocking model but rather stars each cow separately. The effectiveness of this algorithm is verified experimentally using a simulator. We use a special set of experiments attempting to demonstrate that the herding times of this algorithm correspond to field diameter small constant regardless of the number of cows in the field. This is an optimal result indicating that the algorithm groups the cows into intermediate groups and herd them as one forming ever closing bigger groups.

Keywords: swarm, independent, distributed, algorithm

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Authors: P. W. Tsai, J. W. Chen, C. W. Chen, C. Y. Chen

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In recent years, many researchers are involved in the field of fuzzy theory. However, there are still a lot of issues to be resolved. Especially on topics related to controller design such as the field of robot, artificial intelligence, and nonlinear systems etc. Besides fuzzy theory, algorithms in swarm intelligence are also a popular field for the researchers. In this paper, a concept of utilizing one of the swarm intelligence method, which is called Bacterial-GA Foraging, to find the stabilized common P matrix for the fuzzy controller system is proposed. An example is given in in the paper, as well.

Keywords: half-circle fuzzy numbers, predictions, swarm intelligence, Lyapunov method

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Authors: Elimhan N. Mahmudov

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The paper concerns the necessary and sufficient conditions of optimality for Cauchy problem of fourth order discrete (PD) and discrete-approximate (PDA) inclusions. The main problem is formulation of the fourth order adjoint discrete and discrete-approximate inclusions and transversality conditions, which are peculiar to problems including fourth order derivatives and approximate derivatives. Thus the necessary and sufficient conditions of optimality are obtained incorporating the Euler-Lagrange and Hamiltonian forms of inclusions. Derivation of optimality conditions are based on the apparatus of locally adjoint mapping (LAM). Moreover in the application of these results we consider the fourth order linear discrete and discrete-approximate inclusions.

Keywords: difference, optimization, fourth, approximation, transversality

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Authors: Diogo Silva, Fadul Rodor, Carlos Moraes

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This work compares the results of multidimensional function approximation using two algorithms: the classical Particle Swarm Optimization (PSO) and the Quantum Particle Swarm Optimization (QPSO). These algorithms were both tested on three functions - The Rosenbrock, the Rastrigin, and the sphere functions - with different characteristics by increasing their number of dimensions. As a result, this study shows that the higher the function space, i.e. the larger the function dimension, the more evident the advantages of using the QPSO method compared to the PSO method in terms of performance and number of necessary iterations to reach the stop criterion.

Keywords: PSO, QPSO, function approximation, AI, optimization, multidimensional functions

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Authors: Fuzhang Zhao

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Particle swarm optimization (PSO) is becoming one of the most important swarm intelligent paradigms for solving global optimization problems. Although some progress has been made to improve PSO algorithms over the last two decades, additional work is still needed to balance parameters to achieve better numerical properties of accuracy, efficiency, and stability. In the optimal PSO algorithm, the optimal weightings of (√ 5 − 1)/2 and (3 − √5)/2 are used for the cognitive factor and the social factor, respectively. By the same token, the same optimal weightings have been applied for intensification searches and diversification searches, respectively. Perturbation and constriction effects are optimally balanced. Simulations of the de Jong, the Rosenbrock, and the Griewank functions show that the optimal PSO algorithm indeed achieves better numerical properties and outperforms the canonical PSO algorithm.

Keywords: diversification search, intensification search, optimal weighting, particle swarm optimization

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Authors: Phawin Sangsuvan, Chutimet Srinilta

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This Paper presents the applications of Particle Swarm Optimization (PSO) Method for Thai optical character recognition (OCR). OCR consists of the pre-processing, character recognition and post-processing. Before enter into recognition process. The Character must be “Prepped” by pre-processing process. The PSO is an optimization method that belongs to the swarm intelligence family based on the imitation of social behavior patterns of animals. Route of each particle is determined by an individual data among neighborhood particles. The interaction of the particles with neighbors is the advantage of Particle Swarm to determine the best solution. So PSO is interested by a lot of researchers in many difficult problems including character recognition. As the previous this research used a Projection Histogram to extract printed digits features and defined the simple Fitness Function for PSO. The results reveal that PSO gives 67.73% for testing dataset. So in the future there can be explored enhancement the better performance of PSO with improve the Fitness Function.

Keywords: character recognition, histogram projection, particle swarm optimization, pattern recognition techniques

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Authors: Lihua Zhu, Jianfeng Du, Yu Wang, Zhiqiang Wu

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Collision avoidance problems of a swarm of unmanned air vehicles (UAVs) flying in an obstacle-laden environment are investigated in this paper. Given that the UAV swarm needs to adapt to the obstacle distribution in dynamic operation, a priority configuration is designed to guide the UAVs to pass through the obstacles in turn. Based on the collision cone approach and the prediction of the collision time, a collision evaluation model is established to judge the urgency of the imminent collision of each UAV, and the evaluation result is used to assign the priority of each UAV to further instruct them going through the obstacles in descending order. At last, the simulation results provide the promising validation in terms of the efficiency and scalability of the proposed approach.

Keywords: UAV swarm, collision avoidance, complex environment, online priority design

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Authors: Hans Schumann, Colin Domnauer, Louis Rosenberg

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In this study, machine learning techniques were deployed on real-time human swarm data to forecast the likelihood of outcomes for English Premier League matches in the 2020/21 season. These techniques included ensemble models in combination with neural networks and were tested against an industry standard of Vegas Oddsmakers. Predictions made from the collective intelligence of human swarm participants managed to achieve a positive return on investment over a full season on matches, empirically proving the usefulness of a new artificial intelligence valuing human instinct and intelligence.

Keywords: artificial intelligence, data science, English Premier League, human swarming, machine learning, sports betting, swarm intelligence

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Authors: Daham Owaid Matrood, Naqaa Hussein Raheem

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Evolutionary algorithms and Artificial neural networks (ANN) are two relatively young research areas that were subject to a steadily growing interest during the past years. This paper examines the use of Particle Swarm Optimization (PSO) to train a multi-layer feed forward neural network for demand forecasting. We use in this paper weekly demand data for packed cement and towels, which have been outfitted by the Northern General Company for Cement and General Company of prepared clothes respectively. The results showed superiority of trained neural networks using particle swarm optimization on neural networks trained using error back propagation because their ability to escape from local optima.

Keywords: artificial neural network, demand forecasting, particle swarm optimization, weight optimization

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Authors: Mohsin Raza, Arne Bilberg, Thomas Ditlev Brunø, Ann-Louise Andersen, Filip SKärin

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Shifting from a dedicated or flexible manufacturing system to a reconfigurable manufacturing system (RMS) requires a significant amount of time, money, and effort. Therefore, it is vital to verify beforehand that the potential reconfigurable solution will be able to achieve the organizational objectives. Discrete event simulation offers the opportunity of assessing several reconfigurable alternatives against the set objectives. This study signifies the importance of using discrete-event simulation as a tool to verify several reconfiguration options. Two different industrial cases have been presented in the study to elaborate on the role of discrete event simulation in the implementation methodology of RMSs. The study concluded that discrete event simulation is one of the important tools to consider in the RMS implementation methodology.

Keywords: reconfigurable manufacturing system, discrete event simulation, Tecnomatix plant simulation, RMS

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Authors: Houda Abadlia, Nadia Smairi, Khaled Ghedira

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Multiobjective Particle Swarm Optimization (MOPSO) has shown an effective performance for solving test functions and real-world optimization problems. However, this method has a premature convergence problem, which may lead to lack of diversity. In order to improve its performance, this paper presents a hybrid approach which embedded the MOPSO into the island model and integrated a local search technique, Variable Neighborhood Search, to enhance the diversity into the swarm. Experiments on two series of test functions have shown the effectiveness of the proposed approach. A comparison with other evolutionary algorithms shows that the proposed approach presented a good performance in solving multiobjective optimization problems.

Keywords: particle swarm optimization, migration, variable neighborhood search, multiobjective optimization

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Authors: Maja Andrić, Josip Pečarić

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Over the last five decades, an enormous amount of work has been done on Opial’s integral inequality, dealing with new proofs, various generalizations, extensions and discrete analogs. The Opial inequality is recognized as a fundamental result in the analysis of qualitative properties of solution of differential equations. We use submultiplicative convex functions, appropriate representations of functions and inequalities involving means to obtain generalizations and extensions of certain known multidimensional integral and discrete Opial-type inequalities.

Keywords: Opial's inequality, Jensen's inequality, integral inequality, discrete inequality

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Authors: Mukhtiar Singh, Sumeet Nagar

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Vehicle routing problem (VRP) is a combinatorial optimization and nonlinear programming problem aiming to optimize decisions regarding given set of routes for a fleet of vehicles in order to provide cost-effective and efficient delivery of both services and goods to the intended customers. This paper proposes the application of integrated particle swarm optimization (PSO) and genetic optimization algorithm (GA) to address the Vehicle routing problem in sugarcane industry in India. Suger industry is very prominent agro-based industry in India due to its impacts on rural livelihood and estimated to be employing around 5 lakhs workers directly in sugar mills. Due to various inadequacies, inefficiencies and inappropriateness associated with the current vehicle routing model it costs huge money loss to the industry which needs to be addressed in proper context. The proposed algorithm utilizes the crossover operation that originally appears in genetic algorithm (GA) to improve its flexibility and manipulation more readily and avoid being trapped in local optimum, and simultaneously for improving the convergence speed of the algorithm, level set theory is also added to it. We employ the hybrid approach to an example of VRP and compare its result with those generated by PSO, GA, and parallel PSO algorithms. The experimental comparison results indicate that the performance of hybrid algorithm is superior to others, and it will become an effective approach for solving discrete combinatory problems.

Keywords: fuzzy logic, genetic algorithm, particle swarm optimization, vehicle routing problem

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Authors: Arslan Ellahi, Syed Amjad Hussain, Fawaz Saleem Bokhari

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Optimization of software architecture can be done with respect to a quality attributes (QA). In this paper, there is an analysis of multiple research papers from different dimensions that have been used to classify those attributes. We have proposed a technique of swarm intelligence Meta heuristic ant colony optimization algorithm as a contribution to solve this critical optimization problem of software architecture. We have ranked quality attributes and run our algorithm on every QA, and then we will rank those on the basis of accuracy. At the end, we have selected the most accurate quality attributes. Ant colony algorithm is an effective algorithm and will perform best in optimizing the QA’s and ranking them.

Keywords: complexity, rapid evolution, swarm intelligence, dimensions

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Authors: Baye Berihun Getahun, Mulugeta Atnaf Tiruneh, Richard G. F. Visser

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Resource-poor farmers practice low-input farming systems, and yet, most breeding programs give less attention to this huge farming system, which serves as a source of food and income for several people in developing countries. The high-input conventional breeding system appears to have failed to adequately meet the needs and requirements of 'difficult' environments operating under this system. Moreover, the unavailability of resources for crop production is getting for their peaks, the environment is maltreated by excessive use of agrochemicals, crop productivity reaches its plateau stage, particularly in the developed nations, the world population is increasing, and food shortage sustained to persist for poor societies. In various parts of the world, genetic gain at the farmers' level remains low which could be associated with low adoption of crop varieties, which have been developed under high input systems. Farmers usually use their local varieties and apply minimum inputs as a risk-avoiding and cost-minimizing strategy. This evidence indicates that the conventional high-input plant breeding system has failed to feed the world population, and the world is moving further away from the United Nations' goals of ending hunger, food insecurity, and malnutrition. In this review, we discussed the rationality of focused breeding programs for low-input farming systems and, the technical aspect of crop breeding that accommodates future food needs and its significance for developing countries in the decreasing scenario of resources required for crop production. To this end, the application of exotic introgression techniques like polyploidization, pan-genomics, comparative genomics, and De novo domestication as a pre-breeding technique has been discussed in the review to exploit the untapped genetic diversity of the crop wild relatives (CWRs). Desired recombinants developed at the pre-breeding stage are exploited through appropriate breeding approaches such as evolutionary plant breeding (EPB), rhizosphere-related traits breeding, and participatory plant breeding approaches. Populations advanced through evolutionary breeding like composite cross populations (CCPs) and rhizosphere-associated traits breeding approach that provides opportunities for improving abiotic and biotic soil stress, nutrient acquisition capacity, and crop microbe interaction in improved varieties have been reviewed. Overall, we conclude that low input farming system is a huge farming system that requires distinctive breeding approaches, and the exotic pre-breeding introgression techniques and the appropriate breeding approaches which deploy the skills and knowledge of both breeders and farmers are vital to develop heterogeneous landrace populations, which are effective for farmers practicing low input farming across the world.

Keywords: low input farming, evolutionary plant breeding, composite cross population, participatory plant breeding

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Authors: Riffi Mohammed Amine

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A cloud is made up of small particles of liquid water or ice suspended in the atmosphere, which generally do not reach the ground. Various methods are used to classify clouds. This article focuses specifically on a technique known as particle swarm optimization (PSO), an AI approach inspired by the collective behaviors of animals living in groups, such as schools of fish and flocks of birds, and a method used to solve complex classification and optimization problems with approximate solutions. The proposed technique was evaluated using a series of second-generation METOSAT images taken by the MSG satellite. The acquired results indicate that the proposed method gave acceptable results.

Keywords: remote sensing, particle swarm optimization, clouds, meteorological image

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Authors: Ž. Nikolić, H. Smoljanović, N. Živaljić

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This paper presents numerical model based on finite-discrete element method for analysis of the structural response of dry stone masonry structures under static and dynamic loads. More precisely, each discrete stone block is discretized by finite elements. Material non-linearity including fracture and fragmentation of discrete elements as well as cyclic behavior during dynamic load are considered through contact elements which are implemented within a finite element mesh. The application of the model was conducted on several examples of these structures. The performed analysis shows high accuracy of the numerical results in comparison with the experimental ones and demonstrates the potential of the finite-discrete element method for modelling of the response of dry stone masonry structures.

Keywords: dry stone masonry structures, dynamic load, finite-discrete element method, static load

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Authors: Jorge Gonzalez Camus, Valentin Keyantuo, Mahamadi Warma

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In this work, we obtain representation results for solutions of a time-fractional differential equation involving the discrete fractional Laplace operator in terms of generalized Wright functions. Such equations arise in the modeling of many physical systems, for example, chain processes in chemistry and radioactivity. The focus is on the linear problem of the simplified Moore - Gibson - Thompson equation, where the discrete fractional Laplacian and the Caputo fractional derivate of order on (0,2] are involved. As a particular case, we obtain the explicit solution for the discrete heat equation and discrete wave equation. Furthermore, we show the explicit solution for the equation involving the perturbed Laplacian by the identity operator. The main tool for obtaining the explicit solution are the Laplace and discrete Fourier transforms, and Stirling's formula. The methodology mainly is to apply both transforms in the equation, to find the inverse of each transform, and to prove that this solution is well defined, using Stirling´s formula.

Keywords: discrete fractional Laplacian, explicit representation of solutions, fractional heat and wave equations, fundamental

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