Search results for: Genetic Regulatory Networks (GRNs)

Authors: A. R. Malekpour, A.R. Seifi

Abstract:

This paper discusses a genetic algorithm (GA) based optimal load shedding that can apply for electrical distribution networks with and without dispersed generators (DG). Also, the proposed method has the ability for considering constant and variable capacity deficiency caused by unscheduled outages in the bulked generation and transmission system of bulked power supply. The genetic algorithm (GA) is employed to search for the optimal load shedding strategy in distribution networks considering DGs in two cases of constant and variable modelling of bulked power supply of distribution networks. Electrical power distribution systems have a radial network and unidirectional power flows. With the advent of dispersed generations, the electrical distribution system has a locally looped network and bidirectional power flows. Therefore, installed DG in the electrical distribution systems can cause operational problems and impact on existing operational schemes. Introduction of DGs in electrical distribution systems has introduced many new issues in operational and planning level. Load shedding as one of operational issue has no exempt. The objective is to minimize the sum of curtailed load and also system losses within the frame-work of system operational and security constraints. The proposed method is tested on a radial distribution system with 33 load points for more practical applications.

Keywords: DG, Load shedding, Optimization, Capacity Deficiency Modelling.

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Authors: D. Singh, R. Yousefi, M. Boroushaki

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Intelligent deep-drawing is an instrumental research field in sheet metal forming. A set of 28 different experimental data have been employed in this paper, investigating the roles of die radius, punch radius, friction coefficients and drawing ratios for axisymmetric workpieces deep drawing. This paper focuses an evolutionary neural network, specifically, error back propagation in collaboration with genetic algorithm. The neural network encompasses a number of different functional nodes defined through the established principles. The input parameters, i.e., punch radii, die radii, friction coefficients and drawing ratios are set to the network; thereafter, the material outputs at two critical points are accurately calculated. The output of the network is used to establish the best parameters leading to the most uniform thickness in the product via the genetic algorithm. This research achieved satisfactory results based on demonstration of neural networks.

Keywords: Deep-drawing, Neural network, Genetic algorithm, Sheet metal forming.

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Authors: Xiaoli Shen, Yuehui Chen

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Interactions among proteins are the basis of various life events. So, it is important to recognize and research protein interaction sites. A control set that contains 149 protein molecules were used here. Then 10 features were extracted and 4 sample sets that contained 9 sliding windows were made according to features. These 4 sample sets were calculated by Radial Basis Functional neutral networks which were optimized by Particle Swarm Optimization respectively. Then 4 groups of results were obtained. Finally, these 4 groups of results were integrated by decision fusion (DF) and Genetic Algorithm based Selected Ensemble (GASEN). A better accuracy was got by DF and GASEN. So, the integrated methods were proved to be effective.

Keywords: protein interaction sites, features, sliding windows, radial basis functional neutral networks, genetic algorithm basedselected ensemble.

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Authors: Susmi Routray, A. M. Sherry, B. V. R. Reddy

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Asynchronous Transfer Mode (ATM) is widely used in telecommunications systems to send data, video and voice at a very high speed. In ATM network optimizing the bandwidth through dynamic routing is an important consideration. Previous research work shows that traditional optimization heuristics result in suboptimal solution. In this paper we have explored non-traditional optimization technique. We propose comparison of two such algorithms - Genetic Algorithm (GA) and Tabu search (TS), based on non-traditional Optimization approach, for solving the dynamic routing problem in ATM networks which in return will optimize the bandwidth. The optimized bandwidth could mean that some attractive business applications would become feasible such as high speed LAN interconnection, teleconferencing etc. We have also performed a comparative study of the selection mechanisms in GA and listed the best selection mechanism and a new initialization technique which improves the efficiency of the GA.

Keywords: Asynchronous Transfer Mode(ATM), GeneticAlgorithm(GA), Tabu Search(TS).

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Authors: S. Farzi

Abstract:

Recently, a lot of attention has been devoted to advanced techniques of system modeling. PNN(polynomial neural network) is a GMDH-type algorithm (Group Method of Data Handling) which is one of the useful method for modeling nonlinear systems but PNN performance depends strongly on the number of input variables and the order of polynomial which are determined by trial and error. In this paper, we introduce GPNN (genetic polynomial neural network) to improve the performance of PNN. GPNN determines the number of input variables and the order of all neurons with GA (genetic algorithm). We use GA to search between all possible values for the number of input variables and the order of polynomial. GPNN performance is obtained by two nonlinear systems. the quadratic equation and the time series Dow Jones stock index are two case studies for obtaining the GPNN performance.

Keywords: GMDH, GPNN, GA, PNN.

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Authors: Robin Gremlich, Andreas Hamfelt, Héctor de Pereda, Vladislav Valkovsky

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By introducing the concept of Oracle we propose an approach for improving the performance of genetic algorithms for large-scale asymmetric Traveling Salesman Problems. The results have shown that the proposed approach allows overcoming some traditional problems for creating efficient genetic algorithms.

Keywords: Genetic algorithms, Traveling Salesman Problem, optimal decision distribution, oracle.

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Authors: Saleh Mesbah Elkaffas, Ahmed A. Toony

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This paper details the application of a genetic programming framework for induction of useful classification rules from a database of income statements, balance sheets, and cash flow statements for North American public companies. Potentially interesting classification rules are discovered. Anomalies in the discovery process merit further investigation of the application of genetic programming to the dataset for the problem domain.

Keywords: Genetic programming, data mining classification rule.

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Authors: Galal H. Senussi, Muamar Benisa, Sanja Vasin

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In our business field today, one of the most important issues for any enterprises is cost minimization and profit maximization. Second issue is how to develop a strong and capable model that is able to give us desired forecasting of these two issues. Many researches deal with these issues using different methods. In this study, we developed a model for multi-criteria production program optimization, integrated with Artificial Neural Network.

The prediction of the production cost and profit per unit of a product, dealing with two obverse functions at same time can be extremely difficult, especially if there is a great amount of conflict information about production parameters.

Feed-Forward Neural Networks are suitable for generalization, which means that the network will generate a proper output as a result to input it has never seen. Therefore, with small set of examples the network will adjust its weight coefficients so the input will generate a proper output.

This essential characteristic is of the most important abilities enabling this network to be used in variety of problems spreading from engineering to finance etc.

From our results as we will see later, Feed-Forward Neural Networks has a strong ability and capability to map inputs into desired outputs.

Keywords: Project profitability, multi-objective optimization, genetic algorithm, Pareto set, Neural Networks.

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Authors: S. Bag, S. Ramaiah, P. Anitha, K. M. Kumar, P. Lavanya, V. Sivasakhthi, A. Anbarasu

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Gene networks present a graphical view at the level of gene activities and genetic functions and help us to understand complex interactions in a meaningful manner. In the present study, we have analyzed the gene interaction of PPAR-γ (peroxisome proliferator-activated receptor gamma) by search tool for retrieval of interacting genes. We find PPAR-γ is highly networked by genetic interactions with 10 genes: RXRA (retinoid X receptor, alpha), PPARGC1A (peroxisome proliferator-activated receptor gamma, coactivator 1 alpha), NCOA1 (nuclear receptor coactivator 1), NR0B2 (nuclear receptor subfamily 0, group B, member 2), HDAC3 (histone deacetylase 3), MED1 (mediator complex subunit 1), INS (insulin), NCOR2 (nuclear receptor co-repressor 2), PAX8 (paired box 8), ADIPOQ (adiponectin) and it augurs well for the fact that obesity and several other metabolic disorders are inter related.

Keywords: Gene networks, NCOA1, PPARγ, PPARGC1A, RXRA.

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Authors: Truong Quang Dang Khoa, Masahiro Nakagawa

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In this paper, a novel associative memory model will be proposed and applied to memory retrievals based on the conventional continuous time model. The conventional model presents memory capacity is very low and retrieval process easily converges to an equilibrium state which is very different from the stored patterns. Genetic Algorithms is well-known with the capability of global optimal search escaping local optimum on progress to reach a global optimum. Based on the well-known idea of Genetic Algorithms, this work proposes a heuristic rule to make a mutation when the state of the network is trapped in a spurious memory. The proposal heuristic associative memory show the stored capacity does not depend on the number of stored patterns and the retrieval ability is up to ~ 1.

Keywords: Artificial Intelligent, Soft Computing, NeuralNetworks, Genetic Algorithms, Hopfield Neural Networks, andAssociative Memories.

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Authors: Mohsen Ebrahimi, Milad M. Rabieh

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In this paper, two very different optimization algorithms, Genetic and DIRECT algorithms, are used to history match a bottomhole pressure response for a reservoir with wellbore storage and skin with the best possible analytical model. No initial guesses are available for reservoir parameters. The results show that the matching process is much faster and more accurate for DIRECT method in comparison with Genetic algorithm. It is furthermore concluded that the DIRECT algorithm does not need any initial guesses, whereas Genetic algorithm needs to be tuned according to initial guesses.

Keywords: DIRECT algorithm, Genetic algorithm, Analytical modeling, History match

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Authors: T. Cholastova, D. Knotova

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Utilization of diverse germplasm is needed to enhance the genetic diversity of cultivars. The objective of this study was to evaluate the genetic relationships of 98 alfalfa germplasm accessions using morphological traits and SSR markers. From the 98 tested populations, 81 were locals originating in Europe, 17 were introduced from USA, Australia, New Zealand and Canada. Three primers generated 67 polymorphic bands. The average polymorphic information content (PIC) was very high (> 0.90) over all three used primer combinations. Cluster analysis using Unweighted Pair Group Method with Arithmetic Means (UPGMA) and Jaccard´s coefficient grouped the accessions into 2 major clusters with 4 sub-clusters with no correlation between genetic and morphological diversity. The SSR analysis clearly indicated that even with three polymorphic primers, reliable estimation of genetic diversity could be obtained.

Keywords: genetic diversity, Medicago sativa L., morphological traits, SSR markers

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Authors: Mustafa Yorgancılar, Emine Atalay, Necdet Akgün, Ali Topal

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In this study, polymerase chain reaction based Inter-simple sequence repeat (ISSR) from DNA fingerprinting techniques were used to investigate the genetic relationships among barley crossbreed genotypes in Turkey. It is important that selection based on the genetic base in breeding programs via ISSR, in terms of breeding time. 14 ISSR primers generated a total of 97 bands, of which 81 (83.35%) were polymorphic. The highest total resolution power (RP) value was obtained from the F2 (0.53) and M16 (0.51) primers. According to the ISSR result, the genetic similarity index changed between 0.64–095; Lane 3 with Line 6 genotypes were the closest, while Line 36 were the most distant ones. The ISSR markers were found to be promising for assessing genetic diversity in barley crossbreed genotypes.

Keywords: Barley, crossbreed, genetic similarity, ISSR.

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Authors: Ju-Chun Chien

Abstract:

The Ottawa Charter for Health Promotion proposed that the role of health services should shift the focus from cure to prevention. Nowadays, besides having physical examinations, people could also conduct genetic tests to provide important information for diagnosing, treating, and/or preventing illnesses. However, because of the incompletion of the Chinese Genetic Database, people in Taiwan were still unfamiliar with genetic testing. The purposes of the present study were to: (1) Figure out people’s attitudes towards genetic testing. (2) Examine factors that influence people’s intention to pursue genetic testing by means of the Health Belief Model (HBM). A pilot study was conducted on 249 Taiwanese in 2017 to test the feasibility of the self-developed instrument. The reliability and construct validity of scores on the self-developed questionnaire revealed that this HBM-based questionnaire with 40 items was a well-developed instrument. A total of 542 participants were recruited and the valid participants were 535 (99%) between the ages of 20 and 86. Descriptive statistics, one-way ANOVA, two-way contingency table analysis, Pearson’s correlation, and stepwise multiple regression analysis were used in this study. The main results were that only 32 participants (6%) had already undergone genetic testing; moreover, their attitude towards genetic testing was more positive than those who did not have the experience. Compared with people who never underwent genetic tests, those who had gone for genetic testing had higher self-efficacy, greater intention to pursue genetic testing, had academic majors in health-related fields, had chronic and genetic diseases, possessed Catastrophic Illness Cards, and all of them had heard about genetic testing. The variables that best predicted people’s intention to pursue genetic testing were cues to action, self-efficacy, and perceived benefits (the three variables all correlated with one another positively at high magnitudes). To sum up, the HBM could be effective in designing and identifying the needs and priorities of the target population to pursue genetic testing.

Keywords: Genetic testing, intention to pursue genetic testing, Taiwan, health belief model.

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Authors: Warattapop Chainate, Peeraya Thapatsuwan, Pupong Pongcharoen

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The hybridisation of genetic algorithm with heuristics has been shown to be one of an effective way to improve its performance. In this work, genetic algorithm hybridised with four heuristics including a new heuristic called neighbourhood improvement were investigated through the classical travelling salesman problem. The experimental results showed that the proposed heuristic outperformed other heuristics both in terms of quality of the results obtained and the computational time.

Keywords: Genetic Algorithm, Hybridisation, Metaheuristics, Travelling Salesman Problem.

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Authors: C. Chitra, P. Subbaraj

Abstract:

The shortest path routing problem is a multiobjective nonlinear optimization problem with constraints. This problem has been addressed by considering Quality of service parameters, delay and cost objectives separately or as a weighted sum of both objectives. Multiobjective evolutionary algorithms can find multiple pareto-optimal solutions in one single run and this ability makes them attractive for solving problems with multiple and conflicting objectives. This paper uses an elitist multiobjective evolutionary algorithm based on the Non-dominated Sorting Genetic Algorithm (NSGA), for solving the dynamic shortest path routing problem in computer networks. A priority-based encoding scheme is proposed for population initialization. Elitism ensures that the best solution does not deteriorate in the next generations. Results for a sample test network have been presented to demonstrate the capabilities of the proposed approach to generate well-distributed pareto-optimal solutions of dynamic routing problem in one single run. The results obtained by NSGA are compared with single objective weighting factor method for which Genetic Algorithm (GA) was applied.

Keywords: Multiobjective optimization, Non-dominated Sorting Genetic Algorithm, Routing, Weighted sum.

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Authors: Z. G. Wang, M. Rahman, Y. S. Wong, K. S. Neo

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In this paper, a new hybrid of genetic algorithm (GA) and simulated annealing (SA), referred to as GSA, is presented. In this algorithm, SA is incorporated into GA to escape from local optima. The concept of hierarchical parallel GA is employed to parallelize GSA for the optimization of multimodal functions. In addition, multi-niche crowding is used to maintain the diversity in the population of the parallel GSA (PGSA). The performance of the proposed algorithms is evaluated against a standard set of multimodal benchmark functions. The multi-niche crowding PGSA and normal PGSA show some remarkable improvement in comparison with the conventional parallel genetic algorithm and the breeder genetic algorithm (BGA).

Keywords: Crowding, genetic algorithm, parallel geneticalgorithm, simulated annealing.

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Authors: Ahmed A. A. Radwan, Bahgat A. Abdel Latef, Abdel Mgeid A. Ali, Osman A. Sadek

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This study investigates the use of genetic algorithms in information retrieval. The method is shown to be applicable to three well-known documents collections, where more relevant documents are presented to users in the genetic modification. In this paper we present a new fitness function for approximate information retrieval which is very fast and very flexible, than cosine similarity fitness function.

Keywords: Cosine similarity, Fitness function, Genetic Algorithm, Information Retrieval, Query learning.

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Authors: V. R. Asghari, M. Ardebilipour

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In the context of spectrum surveillance, a method to recover the code of spread spectrum signal is presented, whereas the receiver has no knowledge of the transmitter-s spreading sequence. The approach is based on a genetic algorithm (GA), which is forced to model the received signal. Genetic algorithms (GAs) are well known for their robustness in solving complex optimization problems. Experimental results show that the method provides a good estimation, even when the signal power is below the noise power.

Keywords: Code estimation, genetic algorithms, spread spectrum.

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Authors: Mohammad Ali Jabraeil Jamali, Ahmad Khademzadeh, Hasan Asil, Amir Asil

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This method decrease usage power (expenditure) in networks on chips (NOC). This method data coding for data transferring in order to reduces expenditure. This method uses data compression reduces the size. Expenditure calculation in NOC occurs inside of NOC based on grown models and transitive activities in entry ports. The goal of simulating is to weigh expenditure for encoding, decoding and compressing in Baseline networks and reduction of switches in this type of networks. KeywordsNetworks on chip, Compression, Encoding, Baseline networks, Banyan networks.

Keywords: Networks on chip, Compression, Encoding, Baseline networks, Banyan networks

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Authors: Dorota Galeza

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This paper argues that networks, such as the ECN and the American network, are affected by certain small events which are inherent to path dependence and preclude the full evolution towards efficiency. It is advocated that the American network is superior to the ECN in many respects due to its greater flexibility and longer history. This stems in particular from the creation of the American network, which was based on a small number of cases. Such a structure encourages further changes and modifications which are not necessarily radical. The ECN, by contrast, was established by legislative action, which explains its rigid structure and resistance to change. This paper is an attempt to transpose the superiority of the American network on to the ECN. It looks at concepts such as judicial cooperation, harmonisation of procedure, peer review and regulatory impact assessments (RIAs), and dispute resolution procedures.

Keywords: Antitrust, Competition, Networks, Path Dependence.

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Authors: Abduladheem A. Ali, Easa A. Abd

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The robot is a repeated task plant. The control of such a plant under parameter variations and load disturbances is one of the important problems. The aim of this work is to design Geno-Fuzzy controller suitable for online applications to control single link rigid robot arm plant. The genetic-fuzzy online controller (indirect controller) has two genetic-fuzzy blocks, the first as controller, the second as identifier. The identification method is based on inverse identification technique. The proposed controller it tested in normal and load disturbance conditions.

Keywords: Fuzzy network, genetic algorithm, robot control, online genetic control, parameter identification.

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Authors: Yi-Chang Chen, Shan-Lin Chang, Chia-Chun Wu

Abstract:

Unlike this study focused extensively on trading behavior of option market, those researches were just taken their attention to model-driven option pricing. For example, Black-Scholes (B-S) model is one of the most famous option pricing models. However, the arguments of B-S model are previously mentioned by some pricing models reviewing. This paper following suggests the importance of the dynamic character for option pricing, which is also the reason why using the genetic algorithm (GA). Because of its natural selection and species evolution, this study proposed a hybrid model, the Genetic-BS model which combining GA and B-S to estimate the price more accurate. As for the final experiments, the result shows that the output estimated price with lower MAE value than the calculated price by either B-S model or its enhanced one, Gram-Charlier garch (G-C garch) model. Finally, this work would conclude that the Genetic-BS pricing model is exactly practical.

Keywords: genetic algorithm, Genetic-BS, option pricing model.

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Authors: V. K. Banga, Y. Singh, R. Kumar

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In this paper, we have proposed a low cost optimized solution for the movement of a three-arm manipulator using Genetic Algorithm (GA) and Analytical Hierarchy Process (AHP). A scheme is given for optimizing the movement of robotic arm with the help of Genetic Algorithm so that the minimum energy consumption criteria can be achieved. As compared to Direct Kinematics, Inverse Kinematics evolved two solutions out of which the best-fit solution is selected with the help of Genetic Algorithm and is kept in search space for future use. The Inverse Kinematics, Fitness Value evaluation and Binary Encoding like tasks are simulated and tested. Although, three factors viz. Movement, Friction and Least Settling Time (or Min. Vibration) are used for finding the Fitness Function / Fitness Values, however some more factors can also be considered.

Keywords: Inverse Kinematics, Genetic Algorithm (GA), Analytical Hierarchy Process (AHP), Fitness Value, Fitness Function.

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Authors: Grigorios N. Beligiannis, Georgios A. Tsirogiannis, Panayotis E. Pintelas

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In this contribution, the use of a new genetic operator is proposed. The main advantage of using this operator is that it is able to assist the evolution procedure to converge faster towards the optimal solution of a problem. This new genetic operator is called ''intuition'' operator. Generally speaking, one can claim that this operator is a way to include any heuristic or any other local knowledge, concerning the problem, that cannot be embedded in the fitness function. Simulation results show that the use of this operator increases significantly the performance of the classic Genetic Algorithm by increasing the convergence speed of its population.

Keywords: Genetic algorithms, intuition operator, reasonable genomes, complex search space, nonlinear fitness functions

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Authors: Soottipoom Yaowiwat, Manoj Lohatepanont, Proadpran Punyabukkana

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Several approaches such as linear programming, network modeling, greedy heuristic and decision support system are well-known approaches in solving irregular airline operation problem. This paper presents an alternative approach based on Multi Objective Micro Genetic Algorithm. The aim of this research is to introduce the concept of Multi Objective Micro Genetic Algorithm as a tool to solve irregular airline operation, combine and reroute problem. The experiment result indicated that the model could obtain optimal solutions within a few second.

Keywords: Irregular Airline Operation, Combine and RerouteRoutine, Genetic Algorithm, Micro Genetic Algorithm, Multi ObjectiveOptimization, Evolutionary Algorithm.

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Authors: Omid S. Fard, Akbar H. Borzabadi

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In this paper we apply one of approaches in category of heuristic methods as Genetic Algorithms for obtaining approximate solution of optimal control problems. The firs we convert optimal control problem to a quasi Assignment Problem by defining some usual characters as defined in Genetic algorithm applications. Then we obtain approximate optimal control function as an piecewise constant function. Finally the numerical examples are given.

Keywords: Optimal control, Integer programming, Genetic algorithm, Discrete approximation, Linear programming.

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Authors: Kolar Jan, Dvorak Vaclav

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In this study, an optimization of supersonic air-to-air ejector is carried out by a recently developed single-objective genetic algorithm based on adaption of sequence of individuals. Adaptation of sequence is based on Shape-based distance of individuals and embedded micro-genetic algorithm. The optimal sequence found defines the succession of CFD-aimed objective calculation within each generation of regular micro-genetic algorithm. A spring-based deformation mutates the computational grid starting the initial individualvia adapted population in the optimized sequence. Selection of a generation initial individual is knowledge-based. A direct comparison of the newly defined and standard micro-genetic algorithm is carried out for supersonic air-to-air ejector. The only objective is to minimize the loose of total stagnation pressure in the ejector. The result is that sequence-adopted micro-genetic algorithm can provide comparative results to standard algorithm but in significantly lower number of overall CFD iteration steps.

Keywords: Grid deformation, Micro-genetic algorithm, shapebased sequence, supersonic ejector.

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Authors: Feng-Sheng Wang, Wu-Hsiung Wu, Kai-Cheng Hsu

Abstract:

The optimization of biological systems, which is a branch of metabolic engineering, has generated a lot of industrial and academic interest for a long time. In the last decade, metabolic engineering approaches based on mathematical optimizations have been used extensively for the analysis and manipulation of metabolic networks. In practical optimization of metabolic reaction networks, designers have to manage the nature of uncertainty resulting from qualitative characters of metabolic reactions, e.g., the possibility of enzyme effects. A deterministic approach does not give an adequate representation for metabolic reaction networks with uncertain characters. Fuzzy optimization formulations can be applied to cope with this problem. A fuzzy multi-objective optimization problem can be introduced for finding the optimal engineering interventions on metabolic network systems considering the resilience phenomenon and cell viability constraints. The accuracy of optimization results depends heavily on the development of essential kinetic models of metabolic networks. Kinetic models can quantitatively capture the experimentally observed regulation data of metabolic systems and are often used to find the optimal manipulation of external inputs. To address the issues of optimizing the regulatory structure of metabolic networks, it is necessary to consider qualitative effects, e.g., the resilience phenomena and cell viability constraints. Combining the qualitative and quantitative descriptions for metabolic networks makes it possible to design a viable strain and accurately predict the maximum possible flux rates of desired products. Considering the resilience phenomena in metabolic networks can improve the predictions of gene intervention and maximum synthesis rates in metabolic engineering. Two case studies will present in the conference to illustrate the phenomena.

Keywords: Fuzzy multi-objective optimization problem, kinetic model, metabolic engineering.

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Authors: S. Makal, L. Ozyilmaz, S. Palavaroglu

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Gene, principal unit of inheritance, is an ordered sequence of nucleotides. The genes of eukaryotic organisms include alternating segments of exons and introns. The region of Deoxyribonucleic acid (DNA) within a gene containing instructions for coding a protein is called exon. On the other hand, non-coding regions called introns are another part of DNA that regulates gene expression by removing from the messenger Ribonucleic acid (RNA) in a splicing process. This paper proposes to determine splice junctions that are exon-intron boundaries by analyzing DNA sequences. A splice junction can be either exon-intron (EI) or intron exon (IE). Because of the popularity and compatibility of the artificial neural network (ANN) in genetic fields; various ANN models are applied in this research. Multi-layer Perceptron (MLP), Radial Basis Function (RBF) and Generalized Regression Neural Networks (GRNN) are used to analyze and detect the splice junctions of gene sequences. 10-fold cross validation is used to demonstrate the accuracy of networks. The real performances of these networks are found by applying Receiver Operating Characteristic (ROC) analysis.

Keywords: Gene, neural networks, ROC analysis, splice junctions.

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