This paper proposes a novel metaheuristic approach called Ant Inspired Bacterial Foraging Optimization (ABFO) to solve Mixed Shop Scheduling problems. Mixed Shop Scheduling combines elements of Job Shop, Flow Shop, and Open Shop scheduling and is NP-hard. The ABFO algorithm hybridizes Bacterial Foraging Optimization with principles from Ant Colony Optimization to guide the search for optimal solutions. Computational results on benchmark instances show the ABFO algorithm performs better than existing algorithms at minimizing makespan for Mixed Shop Scheduling problems.
Discrete time prey predator model with generalized holling type interactionZac Darcy
We have introduced a discrete time prey-predator model with Generalized Holling type interaction. Stability nature of the fixed points of the model are determined analytically. Phase diagrams are drawn after solving the system numerically. Bifurcation analysis is done with respect to various parameters of the system. It is shown that for modeling of non-chaotic prey predator ecological systems with Generalized Holling type interaction may be more useful for better prediction and analysis.
IJERA (International journal of Engineering Research and Applications) is International online, ... peer reviewed journal. For more detail or submit your article, please visit www.ijera.com
Discrete time prey predator model with generalized holling type interactionZac Darcy
We have introduced a discrete time prey-predator model with Generalized Holling type interaction. Stability nature of the fixed points of the model are determined analytically. Phase diagrams are drawn after solving the system numerically. Bifurcation analysis is done with respect to various parameters of the system. It is shown that for modeling of non-chaotic prey predator ecological systems with Generalized Holling type interaction may be more useful for better prediction and analysis.
IJERA (International journal of Engineering Research and Applications) is International online, ... peer reviewed journal. For more detail or submit your article, please visit www.ijera.com
Bender’s Decomposition Method for a Large Two-stage Linear Programming Modeldrboon
Linear Programming method (LP) can solve many problems in operations research and can obtain optimal solutions. But, the problems with uncertainties cannot be solved so easily. These uncertainties increase the complexity scale of the problems to become a large-scale LP model. The discussion started with the mathematical models. The objective is to minimize the number of the system variables subjecting to the decision variable coefficients and their slacks and surpluses. Then, the problems are formulated in the form of a Two-stage Stochastic Linear (TSL) model incorporated with the Bender’s Decomposition method. In the final step, the matrix systems are set up to support the MATLAB programming development of the primal-dual simplex and the Bender’s decomposition method, and applied to solve the example problem with the assumed four numerical sets of the decision variable coefficients simultaneously. The simplex method (primal) failed to determine the results and it was computational time-consuming. The comparison of the ordinary primal, primal-random, and dual method, revealed advantageous of the primal-random. The results yielded by the application of Bender’s decomposition method were proven to be the optimal solutions at a high level of confidence.
Discrete penguins search optimization algorithm to solve flow shop schedulin...IJECEIAES
Flow shop scheduling problem is one of the most classical NP-hard optimization problem. Which aims to find the best planning that minimizes the makespan (total completion time) of a set of tasks in a set of machines with certain constraints. In this paper, we propose a new nature inspired metaheuristic to solve the flow shop scheduling problem (FSSP), called penguins search optimization algorithm (PeSOA) based on collaborative hunting strategy of penguins.The operators and parameter values of PeSOA redefined to solve this problem. The performance of the penguins search optimization algorithm is tested on a set of benchmarks instances of FSSP from OR-Library, The results of the tests show that PeSOA is superior to some other metaheuristics algorithms, in terms of the quality of the solutions found and the execution time.
Finding the Extreme Values with some Application of Derivativesijtsrd
There are many different way of mathematics rules. Among them, we express finding the extreme values for the optimization problems that changes in the particle life with the derivatives. The derivative is the exact rate at which one quantity changes with respect to another. And them, we can compute the profit and loss of a process that a company or a system. Variety of optimization problems are solved by using derivatives. There were use derivatives to find the extreme values of functions, to determine and analyze the shape of graphs and to find numerically where a function equals zero. Kyi Sint | Kay Thi Win "Finding the Extreme Values with some Application of Derivatives" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-3 | Issue-6 , October 2019, URL: https://www.ijtsrd.com/papers/ijtsrd29347.pdf Paper URL: https://www.ijtsrd.com/mathemetics/other/29347/finding-the-extreme-values-with-some-application-of-derivatives/kyi-sint
Multi objective predictive control a solution using metaheuristicsijcsit
The application of multi objective model predictive control approaches is significantly limited with
computation time associated with optimization algorithms. Metaheuristics are general purpose heuristics
that have been successfully used in solving difficult optimization problems in a reasonable computation
time. In this work , we use and compare two multi objective metaheuristics, Multi-Objective Particle
swarm Optimization, MOPSO, and Multi-Objective Gravitational Search Algorithm, MOGSA, to generate
a set of approximately Pareto-optimal solutions in a single run. Two examples are studied, a nonlinear
system consisting of two mobile robots tracking trajectories and avoiding obstacles and a linear multi
variable system. The computation times and the quality of the solution in terms of the smoothness of the
control signals and precision of tracking show that MOPSO can be an alternative for real time
applications.
5. Linear Algebra for Machine Learning: Singular Value Decomposition and Prin...Ceni Babaoglu, PhD
The seminar series will focus on the mathematical background needed for machine learning. The first set of the seminars will be on "Linear Algebra for Machine Learning". Here are the slides of the fifth part which is discussing singular value decomposition and principal component analysis.
Here are the slides of the first part which was discussing linear systems: https://www.slideshare.net/CeniBabaogluPhDinMat/linear-algebra-for-machine-learning-linear-systems/1
Here are the slides of the second part which was discussing basis and dimension:
https://www.slideshare.net/CeniBabaogluPhDinMat/2-linear-algebra-for-machine-learning-basis-and-dimension
Here are the slides of the third part which is discussing factorization and linear transformations.
https://www.slideshare.net/CeniBabaogluPhDinMat/3-linear-algebra-for-machine-learning-factorization-and-linear-transformations-130813437
Here are the slides of the fourth part which is discussing eigenvalues and eigenvectors.
https://www.slideshare.net/CeniBabaogluPhDinMat/4-linear-algebra-for-machine-learning-eigenvalues-eigenvectors-and-diagonalization
Application of Bender’s Decomposition Solving a Feed–mix Problem among Supply...drboon
The feed-mix problem is primarily transformed into a mixing situation applying a mathematic formulation with uncertainties. These uncertainties generate the numerous expansions of alternative constraint equations. The given problem has been formulated as mathematic models which correspond to a large-scale Stochastic Programming that cannot be solved by the most popular ordinary calculation method, Simplex Method: LINPROG. This research aims to investigate effective methodology to reveal the optimal solution. The authors have examined the method of Bender’s decomposition: BENDER and developed both methods into MATLAB® program and calculated comparatively. The results revealed that the nearest optimal solutions can be determined by means of a Two-stage Stochastic Programing incorporated with Bender’s decomposition at the most intensive number of uncertainties and take less calculation time than by LINPROG.
THE STUDY OF CUCKOO OPTIMIZATION ALGORITHM FOR PRODUCTION PLANNING PROBLEMijcax
Constrained Nonlinear programming problems are hard problems, and one of the most widely used and
common problems for production planning problem to optimize. In this study, one of the mathematical
models of production planning is survey and the problem solved by cuckoo algorithm. Cuckoo Algorithm is
efficient method to solve continues non linear problem. Moreover, mentioned models of production
planning solved with Genetic algorithm and Lingo software and the results will compared. The Cuckoo
Algorithm is suitable choice for optimization in convergence of solution
THE STUDY OF CUCKOO OPTIMIZATION ALGORITHM FOR PRODUCTION PLANNING PROBLEMijcax
Constrained Nonlinear programming problems are hard problems, and one of the most widely used and
common problems for production planning problem to optimize. In this study, one of the mathematical
models of production planning is survey and the problem solved by cuckoo algorithm. Cuckoo Algorithm is
efficient method to solve continues non linear problem. Moreover, mentioned models of production
planning solved with Genetic algorithm and Lingo software and the results will compared. The Cuckoo
Algorithm is suitable choice for optimization in convergence of solution
In some industries as foundries, it is not technically feasible to interrupt a processor between jobs. This restriction gives rise to a scheduling problem called no-idle scheduling. This paper deals with scheduling of no-idle open shops to minimize maximum completion time of jobs, called makespan. The problem is first mathematically formulated by three different mixed integer linear programming models. Since open shop scheduling problems are NP-hard, only small instances can be solved to optimality using these models. Thus, to solve large instances, two meta-heuristics based on simulated annealing and genetic algorithms are developed. A complete numerical experiment is conducted and the developed models and algorithms are compared. The results show that genetic algorithm outperforms simulated annealing.
A Study on Differential Equations on the Sphere Using Leapfrog Methodiosrjce
In this article, a new method of analysis of the differential equations on the sphere using Leapfrog
method is presented. To illustrate the effectiveness of the Leapfrog method, an example of the differential
equations on the sphere has been considered and the solutions were obtained using methods taken taken from
the literature [17] and Leapfrog method. The obtained discrete solutions are compared with the exact solutions
of the differential equations on the sphere. Solution graphs for the differential equations on the sphere have
been presented in the graphical form to show the efficiency of this Leapfrog method. This Leapfrog method can
be easily implemented in a digital computer and the solution can be obtained for any length of time
Solving practical economic load dispatch problem using crow search algorithm IJECEIAES
The practical economic load dispatch problem is a non-convex, non-smooth, and non-linear optimization problem due to including practical considerations such as valve-point loading effects and multiple fuel options. An optimization algorithm named crow search algorithm is proposed in this paper to solve the practical non-convex economic load dispatch problem. Three cases with different economic load dispatch configurations are studied. The simulation results and statistical analysis show the efficiency of the proposed crow search algorithm. Also, the simulation results are compared to the other reported algorithms. The comparison of results confirms the high-quality solutions and the effectiveness of the proposed algorithm for solving the non-convex practical economic load dispatch problem.
Formulas for Surface Weighted Numbers on Graphijtsrd
The boundary value problem differential operator on the graph of a specific structure is discussed in this article. The graph has degree 1 vertices and edges that are linked at one common vertex. The differential operator expression with real valued potentials, the Dirichlet boundary conditions, and the conventional matching requirements define the boundary value issue. There are a finite number of eig nv lu s in this problem.The residues of the diagonal elements of the Weyl matrix in the eigenvalues are referred to as weight numbers. The ig nv lu s are monomorphic functions with simple poles.The weight numbers under consideration generalize the weight numbers of differential operators on a finite interval, which are equal to the reciprocals of the squared norms of eigenfunctions. These numbers, along with the eig nv lu s, serve as spectral data for unique operator reconstruction. The contour integration is used to obtain formulas for surfacethe weight numbers, as well as formulas for the sums in the case of superficial near ig nv lu s. On the graphs, the formulas can be utilized to analyze inverse spectral problems. Ghulam Hazrat Aimal Rasa "Formulas for Surface Weighted Numbers on Graph" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-6 | Issue-3 , April 2022, URL: https://www.ijtsrd.com/papers/ijtsrd49573.pdf Paper URL: https://www.ijtsrd.com/mathemetics/calculus/49573/formulas-for-surface-weighted-numbers-on-graph/ghulam-hazrat-aimal-rasa
THE NEW HYBRID COAW METHOD FOR SOLVING MULTI-OBJECTIVE PROBLEMSijfcstjournal
In this article using Cuckoo Optimization Algorithm and simple additive weighting method the hybrid COAW algorithm is presented to solve multi-objective problems. Cuckoo algorithm is an efficient and structured method for solving nonlinear continuous problems. The created Pareto frontiers of the COAW proposed algorithm are exact and have good dispersion. This method has a high speed in finding the
Pareto frontiers and identifies the beginning and end points of Pareto frontiers properly. In order to validation the proposed algorithm, several experimental problems were analyzed. The results of which indicate the proper effectiveness of COAW algorithm for solving multi-objective problems.
ENHANCING ENGLISH WRITING SKILLS THROUGH INTERNET-PLUS TOOLS IN THE PERSPECTI...ijfcstjournal
This investigation delves into incorporating a hybridized memetic strategy within the framework of English
composition pedagogy, leveraging Internet Plus resources. The study aims to provide an in-depth analysis
of how this method influences students’ writing competence, their perceptions of writing, and their
enthusiasm for English acquisition. Employing an explanatory research design that combines qualitative
and quantitative methods, the study collects data through surveys, interviews, and observations of students’
writing performance before and after the intervention. Findings demonstrate a beneficial impact of
integrating the memetic approach alongside Internet Plus tools on the writing aptitude of English as a
Foreign Language (EFL) learners. Students reported increased engagement with writing, attributing it to
the use of Internet plus tools. They also expressed that the memetic approach facilitated a deeper
understanding of cultural and social contexts in writing. Furthermore, the findings highlight a significant
improvement in students’ writing skills following the intervention. This study provides significant insights
into the practical implementation of the memetic approach within English writing education, highlighting
the beneficial contribution of Internet Plus tools in enriching students' learning journeys.
A SURVEY TO REAL-TIME MESSAGE-ROUTING NETWORK SYSTEM WITH KLA MODELLINGijfcstjournal
Messages routing over a network is one of the most fundamental concept in communication which requires
simultaneous transmission of messages from a source to a destination. In terms of Real-Time Routing, it
refers to the addition of a timing constraint in which messages should be received within a specified time
delay. This study involves Scheduling, Algorithm Design and Graph Theory which are essential parts of
the Computer Science (CS) discipline. Our goal is to investigate an innovative and efficient way to present
these concepts in the context of CS Education. In this paper, we will explore the fundamental modelling of
routing real-time messages on networks. We study whether it is possible to have an optimal on-line
algorithm for the Arbitrary Directed Graph network topology. In addition, we will examine the message
routing’s algorithmic complexity by breaking down the complex mathematical proofs into concrete, visual
examples. Next, we explore the Unidirectional Ring topology in finding the transmission’s
“makespan”.Lastly, we propose the same network modelling through the technique of Kinesthetic Learning
Activity (KLA). We will analyse the data collected and present the results in a case study to evaluate the
effectiveness of the KLA approach compared to the traditional teaching method.
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Linear Programming method (LP) can solve many problems in operations research and can obtain optimal solutions. But, the problems with uncertainties cannot be solved so easily. These uncertainties increase the complexity scale of the problems to become a large-scale LP model. The discussion started with the mathematical models. The objective is to minimize the number of the system variables subjecting to the decision variable coefficients and their slacks and surpluses. Then, the problems are formulated in the form of a Two-stage Stochastic Linear (TSL) model incorporated with the Bender’s Decomposition method. In the final step, the matrix systems are set up to support the MATLAB programming development of the primal-dual simplex and the Bender’s decomposition method, and applied to solve the example problem with the assumed four numerical sets of the decision variable coefficients simultaneously. The simplex method (primal) failed to determine the results and it was computational time-consuming. The comparison of the ordinary primal, primal-random, and dual method, revealed advantageous of the primal-random. The results yielded by the application of Bender’s decomposition method were proven to be the optimal solutions at a high level of confidence.
Discrete penguins search optimization algorithm to solve flow shop schedulin...IJECEIAES
Flow shop scheduling problem is one of the most classical NP-hard optimization problem. Which aims to find the best planning that minimizes the makespan (total completion time) of a set of tasks in a set of machines with certain constraints. In this paper, we propose a new nature inspired metaheuristic to solve the flow shop scheduling problem (FSSP), called penguins search optimization algorithm (PeSOA) based on collaborative hunting strategy of penguins.The operators and parameter values of PeSOA redefined to solve this problem. The performance of the penguins search optimization algorithm is tested on a set of benchmarks instances of FSSP from OR-Library, The results of the tests show that PeSOA is superior to some other metaheuristics algorithms, in terms of the quality of the solutions found and the execution time.
Finding the Extreme Values with some Application of Derivativesijtsrd
There are many different way of mathematics rules. Among them, we express finding the extreme values for the optimization problems that changes in the particle life with the derivatives. The derivative is the exact rate at which one quantity changes with respect to another. And them, we can compute the profit and loss of a process that a company or a system. Variety of optimization problems are solved by using derivatives. There were use derivatives to find the extreme values of functions, to determine and analyze the shape of graphs and to find numerically where a function equals zero. Kyi Sint | Kay Thi Win "Finding the Extreme Values with some Application of Derivatives" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-3 | Issue-6 , October 2019, URL: https://www.ijtsrd.com/papers/ijtsrd29347.pdf Paper URL: https://www.ijtsrd.com/mathemetics/other/29347/finding-the-extreme-values-with-some-application-of-derivatives/kyi-sint
Multi objective predictive control a solution using metaheuristicsijcsit
The application of multi objective model predictive control approaches is significantly limited with
computation time associated with optimization algorithms. Metaheuristics are general purpose heuristics
that have been successfully used in solving difficult optimization problems in a reasonable computation
time. In this work , we use and compare two multi objective metaheuristics, Multi-Objective Particle
swarm Optimization, MOPSO, and Multi-Objective Gravitational Search Algorithm, MOGSA, to generate
a set of approximately Pareto-optimal solutions in a single run. Two examples are studied, a nonlinear
system consisting of two mobile robots tracking trajectories and avoiding obstacles and a linear multi
variable system. The computation times and the quality of the solution in terms of the smoothness of the
control signals and precision of tracking show that MOPSO can be an alternative for real time
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5. Linear Algebra for Machine Learning: Singular Value Decomposition and Prin...Ceni Babaoglu, PhD
The seminar series will focus on the mathematical background needed for machine learning. The first set of the seminars will be on "Linear Algebra for Machine Learning". Here are the slides of the fifth part which is discussing singular value decomposition and principal component analysis.
Here are the slides of the first part which was discussing linear systems: https://www.slideshare.net/CeniBabaogluPhDinMat/linear-algebra-for-machine-learning-linear-systems/1
Here are the slides of the second part which was discussing basis and dimension:
https://www.slideshare.net/CeniBabaogluPhDinMat/2-linear-algebra-for-machine-learning-basis-and-dimension
Here are the slides of the third part which is discussing factorization and linear transformations.
https://www.slideshare.net/CeniBabaogluPhDinMat/3-linear-algebra-for-machine-learning-factorization-and-linear-transformations-130813437
Here are the slides of the fourth part which is discussing eigenvalues and eigenvectors.
https://www.slideshare.net/CeniBabaogluPhDinMat/4-linear-algebra-for-machine-learning-eigenvalues-eigenvectors-and-diagonalization
Application of Bender’s Decomposition Solving a Feed–mix Problem among Supply...drboon
The feed-mix problem is primarily transformed into a mixing situation applying a mathematic formulation with uncertainties. These uncertainties generate the numerous expansions of alternative constraint equations. The given problem has been formulated as mathematic models which correspond to a large-scale Stochastic Programming that cannot be solved by the most popular ordinary calculation method, Simplex Method: LINPROG. This research aims to investigate effective methodology to reveal the optimal solution. The authors have examined the method of Bender’s decomposition: BENDER and developed both methods into MATLAB® program and calculated comparatively. The results revealed that the nearest optimal solutions can be determined by means of a Two-stage Stochastic Programing incorporated with Bender’s decomposition at the most intensive number of uncertainties and take less calculation time than by LINPROG.
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Constrained Nonlinear programming problems are hard problems, and one of the most widely used and
common problems for production planning problem to optimize. In this study, one of the mathematical
models of production planning is survey and the problem solved by cuckoo algorithm. Cuckoo Algorithm is
efficient method to solve continues non linear problem. Moreover, mentioned models of production
planning solved with Genetic algorithm and Lingo software and the results will compared. The Cuckoo
Algorithm is suitable choice for optimization in convergence of solution
THE STUDY OF CUCKOO OPTIMIZATION ALGORITHM FOR PRODUCTION PLANNING PROBLEMijcax
Constrained Nonlinear programming problems are hard problems, and one of the most widely used and
common problems for production planning problem to optimize. In this study, one of the mathematical
models of production planning is survey and the problem solved by cuckoo algorithm. Cuckoo Algorithm is
efficient method to solve continues non linear problem. Moreover, mentioned models of production
planning solved with Genetic algorithm and Lingo software and the results will compared. The Cuckoo
Algorithm is suitable choice for optimization in convergence of solution
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A Study on Differential Equations on the Sphere Using Leapfrog Methodiosrjce
In this article, a new method of analysis of the differential equations on the sphere using Leapfrog
method is presented. To illustrate the effectiveness of the Leapfrog method, an example of the differential
equations on the sphere has been considered and the solutions were obtained using methods taken taken from
the literature [17] and Leapfrog method. The obtained discrete solutions are compared with the exact solutions
of the differential equations on the sphere. Solution graphs for the differential equations on the sphere have
been presented in the graphical form to show the efficiency of this Leapfrog method. This Leapfrog method can
be easily implemented in a digital computer and the solution can be obtained for any length of time
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The practical economic load dispatch problem is a non-convex, non-smooth, and non-linear optimization problem due to including practical considerations such as valve-point loading effects and multiple fuel options. An optimization algorithm named crow search algorithm is proposed in this paper to solve the practical non-convex economic load dispatch problem. Three cases with different economic load dispatch configurations are studied. The simulation results and statistical analysis show the efficiency of the proposed crow search algorithm. Also, the simulation results are compared to the other reported algorithms. The comparison of results confirms the high-quality solutions and the effectiveness of the proposed algorithm for solving the non-convex practical economic load dispatch problem.
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The boundary value problem differential operator on the graph of a specific structure is discussed in this article. The graph has degree 1 vertices and edges that are linked at one common vertex. The differential operator expression with real valued potentials, the Dirichlet boundary conditions, and the conventional matching requirements define the boundary value issue. There are a finite number of eig nv lu s in this problem.The residues of the diagonal elements of the Weyl matrix in the eigenvalues are referred to as weight numbers. The ig nv lu s are monomorphic functions with simple poles.The weight numbers under consideration generalize the weight numbers of differential operators on a finite interval, which are equal to the reciprocals of the squared norms of eigenfunctions. These numbers, along with the eig nv lu s, serve as spectral data for unique operator reconstruction. The contour integration is used to obtain formulas for surfacethe weight numbers, as well as formulas for the sums in the case of superficial near ig nv lu s. On the graphs, the formulas can be utilized to analyze inverse spectral problems. Ghulam Hazrat Aimal Rasa "Formulas for Surface Weighted Numbers on Graph" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-6 | Issue-3 , April 2022, URL: https://www.ijtsrd.com/papers/ijtsrd49573.pdf Paper URL: https://www.ijtsrd.com/mathemetics/calculus/49573/formulas-for-surface-weighted-numbers-on-graph/ghulam-hazrat-aimal-rasa
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In this article using Cuckoo Optimization Algorithm and simple additive weighting method the hybrid COAW algorithm is presented to solve multi-objective problems. Cuckoo algorithm is an efficient and structured method for solving nonlinear continuous problems. The created Pareto frontiers of the COAW proposed algorithm are exact and have good dispersion. This method has a high speed in finding the
Pareto frontiers and identifies the beginning and end points of Pareto frontiers properly. In order to validation the proposed algorithm, several experimental problems were analyzed. The results of which indicate the proper effectiveness of COAW algorithm for solving multi-objective problems.
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This investigation delves into incorporating a hybridized memetic strategy within the framework of English
composition pedagogy, leveraging Internet Plus resources. The study aims to provide an in-depth analysis
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enthusiasm for English acquisition. Employing an explanatory research design that combines qualitative
and quantitative methods, the study collects data through surveys, interviews, and observations of students’
writing performance before and after the intervention. Findings demonstrate a beneficial impact of
integrating the memetic approach alongside Internet Plus tools on the writing aptitude of English as a
Foreign Language (EFL) learners. Students reported increased engagement with writing, attributing it to
the use of Internet plus tools. They also expressed that the memetic approach facilitated a deeper
understanding of cultural and social contexts in writing. Furthermore, the findings highlight a significant
improvement in students’ writing skills following the intervention. This study provides significant insights
into the practical implementation of the memetic approach within English writing education, highlighting
the beneficial contribution of Internet Plus tools in enriching students' learning journeys.
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refers to the addition of a timing constraint in which messages should be received within a specified time
delay. This study involves Scheduling, Algorithm Design and Graph Theory which are essential parts of
the Computer Science (CS) discipline. Our goal is to investigate an innovative and efficient way to present
these concepts in the context of CS Education. In this paper, we will explore the fundamental modelling of
routing real-time messages on networks. We study whether it is possible to have an optimal on-line
algorithm for the Arbitrary Directed Graph network topology. In addition, we will examine the message
routing’s algorithmic complexity by breaking down the complex mathematical proofs into concrete, visual
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bowel (intestine) examination in human. The Pill Camera (Endoscopy Capsule) is made up of sealed
biocompatible material to withstand acid, enzymes and other antibody chemicals in the stomach is a
technology that helps the medical practitioners especially the general physicians and the
gastroenterologists to examine and re-examine the intestine for possible bleeding or infection. Before the
advent of the Pill camera (Endoscopy Capsule) the colonoscopy was the local method used but research
showed that some parts (bowel) of the intestine can’t be reach by mere traditional method hence the need
for Pill Camera. Countless number of deaths from stomach disease such as polyps, inflammatory bowel
(Crohn”s diseases), Cancers, Ulcer, anaemia and tumours of small intestines which ordinary would have
been detected by sophisticated technology like Pill Camera has become norm in the developing nations.
Nevertheless, not only will this paper examine and re-evaluate the Pill Camera Innovation, theory,
Structural dynamics and evolution it unravelled and aimed to create awareness for both medical
practitioners and the public.
AN OPTIMIZED HYBRID APPROACH FOR PATH FINDINGijfcstjournal
Path finding algorithm addresses problem of finding shortest path from source to destination avoiding
obstacles. There exist various search algorithms namely A*, Dijkstra's and ant colony optimization. Unlike
most path finding algorithms which require destination co-ordinates to compute path, the proposed
algorithm comprises of a new method which finds path using backtracking without requiring destination
co-ordinates. Moreover, in existing path finding algorithm, the number of iterations required to find path is
large. Hence, to overcome this, an algorithm is proposed which reduces number of iterations required to
traverse the path. The proposed algorithm is hybrid of backtracking and a new technique(modified 8-
neighbor approach). The proposed algorithm can become essential part in location based, network, gaming
applications. grid traversal, navigation, gaming applications, mobile robot and Artificial Intelligence.
EAGRO CROP MARKETING FOR FARMING COMMUNITYijfcstjournal
The Major Occupation in India is the Agriculture; the people involved in the Agriculture belong to the poor
class and category. The people of the farming community are unaware of the new techniques and Agromachines, which would direct the world to greater heights in the field of agriculture. Though the farmers
work hard, they are cheated by agents in today’s market. This serves as a opportunity to solve
all the problems that farmers face in the current world. The eAgro crop marketing will serve as a better
way for the farmers to sell their products within the country with some mediocre knowledge about using
the website. This would provide information to the farmers about current market rate of agro-products,
their sale history and profits earned in a sale. This site will also help the farmers to know about the market
information and to view agricultural schemes of the Government provided to farmers.
EDGE-TENACITY IN CYCLES AND COMPLETE GRAPHSijfcstjournal
It is well known that the tenacity is a proper measure for studying vulnerability and reliability in graphs.
Here, a modified edge-tenacity of a graph is introduced based on the classical definition of tenacity.
Properties and bounds for this measure are introduced; meanwhile edge-tenacity is calculated for cycle
graphs and also for complete graphs.
COMPARATIVE STUDY OF DIFFERENT ALGORITHMS TO SOLVE N QUEENS PROBLEMijfcstjournal
This Paper provides a brief description of the Genetic Algorithm (GA), the Simulated Annealing (SA)
Algorithm, the Backtracking (BT) Algorithm and the Brute Force (BF) Search Algorithm and attempts to
explain the way as how the Proposed Genetic Algorithm (GA), the Proposed Simulated Annealing (SA)
Algorithm using GA, the Backtracking (BT) Algorithm and the Brute Force (BF) Search Algorithm can be
employed in finding the best solution of N Queens Problem and also, makes a comparison between these
four algorithms. It is entirely a review based work. The four algorithms were written as well as
implemented. From the Results, it was found that, the Proposed Genetic Algorithm (GA) performed better
than the Proposed Simulated Annealing (SA) Algorithm using GA, the Backtracking (BT) Algorithm and
the Brute Force (BF) Search Algorithm and it also provided better fitness value (solution) than the
Proposed Simulated Annealing Algorithm (SA) using GA, the Backtracking (BT) Algorithm and the Brute
Force (BF) Search Algorithm, for different N values. Also, it was noticed that, the Proposed GA took more
time to provide result than the Proposed SA using GA.
PSTECEQL: A NOVEL EVENT QUERY LANGUAGE FOR VANET’S UNCERTAIN EVENT STREAMSijfcstjournal
In recent years, the complex event processing technology has been used to process the VANET’s temporal
and spatial event streams. However, we usually cannot get the accurate data because the device sensing
accuracy limitations of the system. We only can get the uncertain data from the complex and limited
environment of the VANET. Because the VANET’s event streams are consist of the uncertain data, so they
are also uncertain. How effective to express and process these uncertain event streams has become the core
issue for the VANET system. To solve this problem, we propose a novel complex event query language
PSTeCEQL (probabilistic spatio-temporal constraint event query language). Firstly, we give the definition
of the possible world model of VANET’s uncertain event streams. Secondly, we propose an event query
language PSTeCEQL and give the syntax and the operational semantics of the language. Finally, we
illustrate the validity of the PSTeCEQL by an example.
CLUSTBIGFIM-FREQUENT ITEMSET MINING OF BIG DATA USING PRE-PROCESSING BASED ON...ijfcstjournal
Now a day enormous amount of data is getting explored through Internet of Things (IoT) as technologies
are advancing and people uses these technologies in day to day activities, this data is termed as Big Data
having its characteristics and challenges. Frequent Itemset Mining algorithms are aimed to disclose
frequent itemsets from transactional database but as the dataset size increases, it cannot be handled by
traditional frequent itemset mining. MapReduce programming model solves the problem of large datasets
but it has large communication cost which reduces execution efficiency. This proposed new pre-processed
k-means technique applied on BigFIM algorithm. ClustBigFIM uses hybrid approach, clustering using kmeans algorithm to generate Clusters from huge datasets and Apriori and Eclat to mine frequent itemsets
from generated clusters using MapReduce programming model. Results shown that execution efficiency of
ClustBigFIM algorithm is increased by applying k-means clustering algorithm before BigFIM algorithm as
one of the pre-processing technique.
A MUTATION TESTING ANALYSIS AND REGRESSION TESTINGijfcstjournal
Software testing is a testing which conducted a test to provide information to client about the quality of the
product under test. Software testing can also provide an objective, independent view of the software to
allow the business to appreciate and understand the risks of software implementation. In this paper we
focused on two main software testing –mutation testing and mutation testing. Mutation testing is a
procedural testing method, i.e. we use the structure of the code to guide the test program, A mutation is a
little change in a program. Such changes are applied to model low level defects that obtain in the process
of coding systems. Ideally mutations should model low-level defect creation. Mutation testing is a process
of testing in which code is modified then mutated code is tested against test suites. The mutations used in
source code are planned to include in common programming errors. A good unit test typically detects the
program mutations and fails automatically. Mutation testing is used on many different platforms, including
Java, C++, C# and Ruby. Regression testing is a type of software testing that seeks to uncover
new software bugs, or regressions, in existing functional and non-functional areas of a system after
changes such as enhancements, patches or configuration changes, have been made to them. When defects
are found during testing, the defect got fixed and that part of the software started working as needed. But
there may be a case that the defects that fixed have introduced or uncovered a different defect in the
software. The way to detect these unexpected bugs and to fix them used regression testing. The main focus
of regression testing is to verify that changes in the software or program have not made any adverse side
effects and that the software still meets its need. Regression tests are done when there are any changes
made on software, because of modified functions.
GREEN WSN- OPTIMIZATION OF ENERGY USE THROUGH REDUCTION IN COMMUNICATION WORK...ijfcstjournal
Advances in micro fabrication and communication techniques have led to unimaginable proliferation of
WSN applications. Research is focussed on reduction of setup operational energy costs. Bulk of operational
energy costs are linked to communication activities of WSN. Any progress towards energy efficiency has a
potential of huge savings globally. Therefore, every energy efficient step is an endeavour to cut costs and
‘Go Green’. In this paper, we have proposed a framework to reduce communication workload through: Innetwork compression and multiple query synthesis at the base-station and modification of query syntax
through introduction of Static Variables. These approaches are general approaches which can be used in
any WSN irrespective of application.
A NEW MODEL FOR SOFTWARE COSTESTIMATION USING HARMONY SEARCHijfcstjournal
Accurate and realistic estimation is always considered to be a great challenge in software industry.
Software Cost Estimation (SCE) is the standard application used to manage software projects. Determining
the amount of estimation in the initial stages of the project depends on planning other activities of the
project. In fact, the estimation is confronted with a number of uncertainties and barriers’, yet assessing the
previous projects is essential to solve this problem. Several models have been developed for the analysis of
software projects. But the classical reference method is the COCOMO model, there are other methods
which are also applied such as Function Point (FP), Line of Code(LOC); meanwhile, the expert`s opinions
matter in this regard. In recent years, the growth and the combination of meta-heuristic algorithms with
high accuracy have brought about a great achievement in software engineering. Meta-heuristic algorithms
which can analyze data from multiple dimensions and identify the optimum solution between them are
analytical tools for the analysis of data. In this paper, we have used the Harmony Search (HS)algorithm for
SCE. The proposed model which is a collection of 60 standard projects from Dataset NASA60 has been
assessed.The experimental results show that HS algorithm is a good way for determining the weight
similarity measures factors of software effort, and reducing the error of MRE.
AGENT ENABLED MINING OF DISTRIBUTED PROTEIN DATA BANKSijfcstjournal
Mining biological data is an emergent area at the intersection between bioinformatics and data mining
(DM). The intelligent agent based model is a popular approach in constructing Distributed Data Mining
(DDM) systems to address scalable mining over large scale distributed data. The nature of associations
between different amino acids in proteins has also been a subject of great anxiety. There is a strong need to
develop new models and exploit and analyze the available distributed biological data sources. In this study,
we have designed and implemented a multi-agent system (MAS) called Agent enriched Quantitative
Association Rules Mining for Amino Acids in distributed Protein Data Banks (AeQARM-AAPDB). Such
globally strong association rules enhance understanding of protein composition and are desirable for
synthesis of artificial proteins. A real protein data bank is used to validate the system.
International Journal on Foundations of Computer Science & Technology (IJFCST)ijfcstjournal
International Journal on Foundations of Computer Science & Technology (IJFCST) is a Bi-monthly peer-reviewed and refereed open access journal that publishes articles which contribute new results in all areas of the Foundations of Computer Science & Technology. Over the last decade, there has been an explosion in the field of computer science to solve various problems from mathematics to engineering. This journal aims to provide a platform for exchanging ideas in new emerging trends that needs more focus and exposure and will attempt to publish proposals that strengthen our goals. Topics of interest include, but are not limited to the following:
Because the technology is used largely in the last decades; cybercrimes have become a significant
international issue as a result of the huge damage that it causes to the business and even to the ordinary
users of technology. The main aims of this paper is to shed light on digital crimes and gives overview about
what a person who is related to computer science has to know about this new type of crimes. The paper has
three sections: Introduction to Digital Crime which gives fundamental information about digital crimes,
Digital Crime Investigation which presents different investigation models and the third section is about
Cybercrime Law.
DISTRIBUTION OF MAXIMAL CLIQUE SIZE UNDER THE WATTS-STROGATZ MODEL OF EVOLUTI...ijfcstjournal
In this paper, we analyze the evolution of a small-world network and its subsequent transformation to a
random network using the idea of link rewiring under the well-known Watts-Strogatz model for complex
networks. Every link u-v in the regular network is considered for rewiring with a certain probability and if
chosen for rewiring, the link u-v is removed from the network and the node u is connected to a randomly
chosen node w (other than nodes u and v). Our objective in this paper is to analyze the distribution of the
maximal clique size per node by varying the probability of link rewiring and the degree per node (number
of links incident on a node) in the initial regular network. For a given probability of rewiring and initial
number of links per node, we observe the distribution of the maximal clique per node to follow a Poisson
distribution. We also observe the maximal clique size per node in the small-world network to be very close
to that of the average value and close to that of the maximal clique size in a regular network. There is no
appreciable decrease in the maximal clique size per node when the network transforms from a regular
network to a small-world network. On the other hand, when the network transforms from a small-world
network to a random network, the average maximal clique size value decreases significantly
Essentials of Automations: Optimizing FME Workflows with ParametersSafe Software
Are you looking to streamline your workflows and boost your projects’ efficiency? Do you find yourself searching for ways to add flexibility and control over your FME workflows? If so, you’re in the right place.
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Here’s what you’ll gain:
- Essentials of FME Parameters: Understand the pivotal role of parameters, including Reader/Writer, Transformer, User, and FME Flow categories. Discover how they are the key to unlocking automation and optimization within your workflows.
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We’ll wrap up with a glimpse into future webinars, followed by a Q&A session to address your specific questions surrounding this topic.
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The Art of the Pitch: WordPress Relationships and SalesLaura Byrne
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In this insightful webinar, Inflectra explores how artificial intelligence (AI) is transforming software development and testing. Discover how AI-powered tools are revolutionizing every stage of the software development lifecycle (SDLC), from design and prototyping to testing, deployment, and monitoring.
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• The Future of Testing: How AI is shifting testing towards verification, analysis, and higher-level skills, while reducing repetitive tasks.
• Test Automation: How AI-powered test case generation, optimization, and self-healing tests are making testing more efficient and effective.
• Visual Testing: Explore the emerging capabilities of AI in visual testing and how it's set to revolutionize UI verification.
• Inflectra's AI Solutions: See demonstrations of Inflectra's cutting-edge AI tools like the ChatGPT plugin and Azure Open AI platform, designed to streamline your testing process.
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JMeter webinar - integration with InfluxDB and GrafanaRTTS
Watch this recorded webinar about real-time monitoring of application performance. See how to integrate Apache JMeter, the open-source leader in performance testing, with InfluxDB, the open-source time-series database, and Grafana, the open-source analytics and visualization application.
In this webinar, we will review the benefits of leveraging InfluxDB and Grafana when executing load tests and demonstrate how these tools are used to visualize performance metrics.
Length: 30 minutes
Session Overview
-------------------------------------------
During this webinar, we will cover the following topics while demonstrating the integrations of JMeter, InfluxDB and Grafana:
- What out-of-the-box solutions are available for real-time monitoring JMeter tests?
- What are the benefits of integrating InfluxDB and Grafana into the load testing stack?
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To view the webinar recording, go to:
https://www.rttsweb.com/jmeter-integration-webinar
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This video focuses on the notifications, alerts, and approval requests using Slack for Bonterra Impact Management. The solutions covered in this webinar can also be deployed for Microsoft Teams.
Interested in deploying notification automations for Bonterra Impact Management? Contact us at sales@sidekicksolutionsllc.com to discuss next steps.
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1. Insights into SAP testing best practices
2. Heatmap utilization for testing
3. Optimization of testing processes
4. Demo
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Execution from the test manager
Orchestrator execution result
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All of this illustrated with link prediction over knowledge graphs, but the argument is general.
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Gopinath Rebala
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Knowledge engineering: from people to machines and back
A Novel Metaheuristics To Solve Mixed Shop Scheduling Problems
1. International Journal in Foundations of Computer Science & Technology (IJFCST), Vol. 3, No.2, March 2013
A NOVEL METAHEURISTICS TO SOLVE MIXED
SHOP SCHEDULING PROBLEMS
V. Ravibabu
Centre for Information Technology and Engineering,
Manonmaniam Sundaranar University, Tirunelveli, India
v_ravibabu@yahoo.com
ABSTRACT
This paper represents the metaheuristics proposed for solving a class of Shop Scheduling problem. The
Bacterial Foraging Optimization algorithm is featured with Ant Colony Optimization algorithm and
proposed as a natural inspired computing approach to solve the Mixed Shop Scheduling problem. The
Mixed Shop is the combination of Job Shop, Flow Shop and Open Shop scheduling problems. The sample
instances for all mentioned Shop problems are used as test data and Mixed Shop survive its computational
complexity to minimize the makespan. The computational results show that the proposed algorithm is
gentler to solve and performs better than the existing algorithms.
KEYWORDS
Combinatorial Optimization, Bacterial Foraging Optimization, Ant Colony Optimization, Metaheuristics,
Mixed Shop Scheduling Problem.
1. INTRODUCTION
Effective scheduling is an essential activity in manufacturing industry which leads to
improvement in the efficiency and utilization of resources. This kind of problems in scheduling is
called Shop Scheduling problems. A real world system may need the mixture of shop scheduling
problems. In general, the Mixed Shop Scheduling problem is a NP-hard problem which is closely
related and also the combination of the scheduling problems such as Job Shop, Flow Shop and
Open Shop Scheduling problems. The Mixed Shop Scheduling problem can be assigned as n x m,
where 'n' is the number of Jobs (J= {j1, j2... jn}) can be processed on 'm' number of Machines (M=
{m1, m2,...,mm}). Each Job ‘ji’ consists of ‘m’ operations represented as ‘Mij’ processed on
machine ‘mj’ for ‘Pij’ time units without pre-emption. One machine can process only one
operation of same job at a time without interruption. The Mixed Shop Scheduling problem
calculates the minimum makespan (Cmax) for all operations in the order of n x m dimensions.
The Mixed Shop Scheduling problem is also called two production problems such as Single-stage
problem and Multi-stage problem. A Single-stage system requires one operation for each job,
whereas in a Multi-stage System there are jobs that require operations on different machines [2].
The Single-stage problem process on a single machine known as Single Machine Scheduling
problem and the problem processing on more than one machines is known as the Parallel
Machine Scheduling Problem. The Multi-stage problem is a Mixed Shop Scheduling problem
which processes on three basic shop scheduling problems such as Job Shop, Flow Shop and Open
Shop Scheduling Problems. In Job Shop Scheduling problem, the operation precedence constraint
on the job is that the order of operations of job is fixed and the processing of an operation cannot
DOI:10.5121/ijfcst.2013.3204 31
2. International Journal in Foundations of Computer Science & Technology (IJFCST), Vol. 3, No.2, March 2013
be interrupted and concurrent. The machine processing constraint is that only a single job can be
processed at the same time on the same machine. In Flow Shop Scheduling problem, each job is
processed on machines in a fixed unidirectional order. In Open Shop Scheduling problem, each
machine can process only one job at a time and each job can be processed by one machine at any
time. Here, the routing of all operations is free.
2. RELATED WORKS
Yuri N. Sotskov, Natalia V.shakhlevich., surveyed the computational complexity of Mixed Shop
Scheduling problem where the problem is a combination of Job Shop and Open Shop. Also the
other classical scheduling assumptions were used for multi stage systems. This paper has no
benchmark problems to discuss Mixed Shop problem in detail [1].
S.Q.Liu and H.L.Ong., presented the metaheuristics for the Mixed Shop Scheduling problem. In
this paper, three metaheuristics were proposed for solving a class of basic shop and mixed shop
scheduling problems. They proved that mixed shop is flexible compared to basic shop scheduling
problems for 39 LA [01-39] benchmark instances [2].
Hanning Chen, Yunlong Zhu, and Kunyuan Hu., discussed a new variation, Cooperative Bacterial
Foraging Optimization which improved the original Bacterial Foraging algorithm to solve the
complex optimization problem. They solved for two cooperative approaches through the Bacterial
Foraging Optimization algorithm, the serial heterogeneous on the implicit and hybrid space
decomposition levels. This proposed method was compared with Particle Swarm Optimization,
Bacterial Foraging Optimization and Genetic Algorithm [7].
Sambarta Dasgupta, Swagatam Das, Ajith Abraham, and Arijit Biswas (2009), represented a
mathematical analysis of the chemotactics step in Bacterial Foraging Optimization from the
viewpoint of the classical gradient descent search. They used two simple schemes for adapting the
chemotactics step were height have been proposed and investigated. The adaptive variants of
Bacterial Foraging Optimization were applied to the frequency-modulated sound wave synthesis
problem [9].
E. Taillard [1989] has proposed a paper about Benchmarks’ for Basic Scheduling Problems about
260 scheduling problems whose rare examples were published. Those kinds of problems
correspond to real dimensions of industrial problems. In this paper he solved the flow shop, the
job shop and the open shop scheduling problems and provides all benchmark results [10].
3. METAHEURISTICS
Metaheuristics makes assumptions on most of NP-Hard problems such as optimizing problems,
decision making and search problems to be optimized and provides an unguaranteed optimal
solution [15]. Optimization problems use computation method to search for an optimal solution
and randomization method to get a least running time of the problem. The metaheuristics should
be keen form of local search and starts with an initial solution. The search method should be
efficient for Mixed Shop Scheduling Problem and satisfy the constraints by processing all
operations without repetition.
32
3. International Journal in Foundations of Computer Science & Technology (IJFCST), Vol. 3, No.2, March 2013
3.1. Metaheuristics for Mixed Shop scheduling problem
The Bacterial Foraging Optimization algorithm is an evolutionary computation algorithm
proposed by Passino.K.M (2002). This algorithm mimics the foraging behaviour of Escherichia
Coli bacteria that living in human intestines. Escherichia Coli swims or moves by rotating its
flagella on anti-clockwise direction and tumbles clockwise to choose new direction to swim for
searching the nutrients. The foraging behaviour of Escherichia Coli process under three stages
such as Chemotactics, Reproduction and Elimination and Dispersal Events. [12]
In Chemotactics, the health of the bacteria will be calculated by Nc + 1
i
j health = ∑ j= 1
j(i, j, k , l)
For Өi (j,k,l), the bacteria ‘i’ undergoes j th chemotactics step by swimming and tumbling, the k is
the reproduction step taken by total number of bacterium group ’S’. The group of bacteria
arranged in terms of health and best half from the group is divided by two. The remaining
bacteria will populated twice to make group in constant. The ‘l’ is the elimination and dispersal
process which eliminates the rest of the population and dispersal makes random replacements in
bacterium group.
The chemotactics process can be computed by C(i) while swimming and the run length of each
bacteria can be calculated by Өi (j+1,k,l) = Өi (j,k,l) + C(i) ∆ T ∆ ( (i ).i ) ∆ ( i ) ,where Δ(i) represents
direction vector of the chemotactics.
The minimization of Jisw = Ji +Jcc(θi,θ) can be calculated for bacteria’s total cost value such that
swarming function can be calculated by
S k2 S k2
∑ ∑
−W a i
− −W r i
−
− M e − e
J cc ( i
)
, = K =1 K =1 (1)
, w ith s w a r m
0 ,w ith o u t s w a r m
where M is the magnitude of the cell to cell signaling and Wa and Wr is the size of the attractant
and repellent signals represented in Euclidean form [8].
The behavior of ant helps to explore the search space and each ant search for food at random by
depositing pheromone in its path. The pheromone helps other ants to follow the same route. Each
ant makes its own map. The pheromone value can be calculated through local update for single
ant and global updates for group of ant at end of the tour.
The local pheromone represented by
(r , s ) ← (1 − ) . (r , s ) + . 0
(2)
where ρ denotes the pheromone lies between [0, 1].
Once all the ants reached their destination, the amount of pheromone values modified again and
the global pheromone update represented by
(r , s ) ← (1 − ). (r , s ) + .∆ (r , s ) (3)
33
4. International Journal in Foundations of Computer Science & Technology (IJFCST), Vol. 3, No.2, March 2013
Where ∆ ( r , s ) = ( L ) − 1 , if (r , s ) ∈
global − best − tour
gb
0 , otherwise
Here α denotes the pheromone decay parameter lies between [0, 1], Lgb is the length of the
globally best tour from the beginning of the trial and ∆τ(r,s) is the pheromone addition on edge (r,
s) [5].
Metaheuristics of ACO is to apply an ant tour repeatedly on all nodes to find the shortest path and
this method also called stochastic greedy rule for optimal solution.[13]
a r g
s =
m a u ∈x (
J ) {
r ( r u) (,
) r , u
} (
≤ , 0 )i f q , q(4)
S , o t h e r w i s e
where (r,u) represents an edge between point r and u, and τ(r, u) stands for the pheromone on
edge (r, u). η(r, u) is the desirability of edge (r, u), which is defined as the inverse of the length of
edge (r, u). q is a random number uniformly distributed in [0, 1], q0 is a user-defined parameter
lies between [0, 1] where q and q0 is exploitation, β is the parameter controlling the relative
importance of the desirability. J (r) is the set of edges available at decision point r [5]. S is a
random variable selected according to the probability distribution represented by
( r , u) , ( )r ,
u
, i f ( S∈ (J )) r
( )s = ∑ ( r , u) ( )r , u
(5)
P r, ,
u∈ J( )r
0 ,o t h e r w i s e
3.2. An Ant Inspired Bacterial Foraging Optimization Algorithm
for Elimination-dispersal loop do
for Reproduction loop do
Tumble: Generate a secure random vector q ∈ decimal.
for Chemotaxis loop do
for Bacterium i do
Generate a secure random vector l ∈ operation,
If q < q0 then
Generate a secure random vector l ∈ operation,
ph[job][operation] based on equation 4.
Else
Move: Generate a secure random vector lnew ∈ operation.
ph[job][operation] based on equation 5.
end
Swim:
if time[job][l] < time[job][ lnew] then
current_operation = l
Else
current_operation = l new
end
end
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5. International Journal in Foundations of Computer Science & Technology (IJFCST), Vol. 3, No.2, March 2013
end
end
Sort bacteria in Jst.
Sr = S/2 bacteria with the highest J value die,
Sr bacteria with the updated value of J and Jst .
end
Eliminate and disperse with ped.
Update J and Jst.
End
Note: Refer Appendix for Nomenclature
4. IMPLEMENTATION
The Mixed Shop Scheduling problem can be represented in terms of O = n x m where O is the
number of nodes and n denotes the job and m denotes the machines. The Pij is processing time of
operations.
Table 1. Mixed Shop Problem
M1 M2 M3
JJ 2 2 3
JF 1 3 2
JO 3 1 2
The sample test problem generated by 3 jobs and 3 machines such that the completion time based
on Mixed Shop scheduling problem, the mixture of Job Shop, Open Shop and Flow Shop were
shown in table 1. Each job is allocated based on the constraints of each Shop Scheduling
problems such as JJ, JF and JO is apportioned with Job Shop, Flow Shop and Open Shop. The
computational result shows that the makespan is minimum for the Mixed Shop Scheduling
Problem is 7 were shown in table 2, where remaining shop problems completes its process with
makespan value of 11, 11 and 8.
Table 2. Result for Mixed Shop Scheduling Problem
M3 O3 J3 F3
M2 J2 F2 O2 ------
M1 F1 ------ O1 J1
0 1 2 3 4 5 6 7
The Mixed Shop Scheduling problem has constraints of Job Shop, Flow Show and Open Shop for
each machines and obtained minimum completion time is 7 where Open Shop Scheduling
problem has no restrictions in its operations and obtained minimum completion time is 8. The
Mixed Shop Scheduling problem achieves better minimum makespan in Hybrid Bacterial
Foraging Optimization algorithm when compared to Job Shop, Flow Shop and Open Shop
Scheduling problems. The same techniques were used to test the complexity of Mixed Shop by
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6. International Journal in Foundations of Computer Science & Technology (IJFCST), Vol. 3, No.2, March 2013
computing it for all relevant benchmark problems. Since there were no direct instances for Mixed
Shop Scheduling, the sample instances (RND) were generated under the constraints of Shop
Scheduling problems and used as test data for Job Shop, Flow Shop, Open Shop and Mixed Shop
Scheduling problems.
The RND instances were implemented based on the Bacterial Foraging Algorithm (BFO) were
shown in table 3 and the figure 1 indicates the results of table 3 in chart representation. The
Bacterial Foraging Optimization Algorithm was compared for Job Shop, Flow Shop, Open Shop
and Mixed Shop Scheduling problem were the results are not much comparable. So the Bacterial
Foraging Optimization Algorithm is altered according to the shortest path selection method and
implemented as an Ant Inspired Bacterial Foraging Optimization Algorithm (ABFO) for Job
Shop, Flow Shop, Open Shop and Mixed Shop Scheduling problems were shown in table 4 and
the figure 2 indicates the results of table 4 in chart representation.
Table 3. Comparison Result for Job Shop, Flow Shop, Open Shop and Mixed Shop Scheduling Problems
using BFO
INSTANCE [SIZE] JOB FLOW OPEN MIXED
SHOP SHOP SHOP SHOP
RND [3X3] 310 310 240 240
RND [5X5] 495 515 350 345
RND [7X7] 720 727 690 672
RND[10X10] 1240 1320 890 810
RND[15X15] 1720 1810 1540 1415
RND[20X20] 2814 2730 2240 1940
Table 4. Comparison Result for Job Shop, Flow Shop, Open Shop and Mixed Shop Scheduling Problems
ABFO
INSTANCE [SIZE] JOB FLOW OPEN MIXED
SHOP SHOP SHOP SHOP
RND [3X3] 285 285 201 201
RND [5X5] 452 452 313 305
RND [7X7] 664 664 481 469
RND[10X10] 1045 1080 764 749
RND[15X15] 1653 1662 1213 1155
RND[20X20] 2314 2343 1721 1672
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7. International Journal in Foundations of Computer Science & Technology (IJFCST), Vol. 3, No.2, March 2013
Figure 1. Comparison Result for Job Shop, Flow Shop, Open Shop and Mixed Shop Scheduling
Problems BFO
Figure 2. Comparison Result for Job Shop, Flow Shop, Open Shop and Mixed Shop Scheduling
Problems using ABFO
The implementation was done in Java 6.0; the Pseudo Random Number Generator (PRNG) is
used to provide secure random class for choosing next node in search space. The constant values
were used as parameter to check the performance of the problems. The Mixed Shop Scheduling
Problem achieves the best optimum values of the all other shop scheduling problems using Ant
Inspired Bacterial Foraging Algorithm.
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8. International Journal in Foundations of Computer Science & Technology (IJFCST), Vol. 3, No.2, March 2013
5. CONCLUSIONS
In computational experiments the performance of Mixed Shop Scheduling problem was evaluated
by applying the sample test data of the basic shop scheduling problems and the metaheuristics
shows that the proposed Ant Inspired Bacterial Foraging Optimization algorithm performs well
on Mixed Shop Scheduling problem and can achieve minimum makes span than Job Shop and
Flow Shop. The Open shop scheduling has been achieved to its best optimum value and also the
same instance implemented on Mixed Shop problem achieved the least optimum values for most
instances. However, the Ant Inspired Bacterial Foraging Optimization Algorithm performs well
on all these kind of shop scheduling problems.
6. APPENDIX
NOMENCLATURE
C(i) - Step size
i - Bacterium number
j - Counter for chemotactic step
J(i, j, k, l) - Cost at the location of ith bacterium
Jcc - Swarm attractant cost
J ihealth - Health of bacteria
Jisw - Swarming effect
k - Counter for reproduction step
l - Counter for elimination-dispersal step
Nc - Maximum number chemotactic steps
Ned - Number of elimination dispersal event
Nre - Maximum reproduction steps
Ns - Maximum number of swims
P - Dimension of the optimization
Ped - Probability of occurrence of
Elimination-dispersal events
S - Population of the E. coli bacteria
θi(j, k, l)- Location of the ith bacterium at
jth chemotactic step,
kth reproduction step, and
lth elimination-dispersal step
JJ - Job Shop Constraints
JF - Flow Shop Constraints
JO - Open Shop Constraints
REFERENCES
[1] Yuri N. Sotskov, Natalia V. Shakhlevich, “Mixed Shop Scheduling Problems,’ INTAS (project 96
0820) and ISTC (project B 104 98).
[2] S. Q. Liu and H. L. Ong, “Metaheuristics for the Mixed Shop Scheduling Problem,” Asia-Pacific
Journal of Operational Research, Vol. 21, No. 4, 2004, pp. 97-115.
[3] W. J. Tang, Q. H. Wu, and J. R. Saunders, “Bacterial Foraging Algorithm For Dynamic
Environments,” IEEE Congress on Evolutionary Computation, July 2006, pp. 16-21.
[4] Hai Shen et al, “Bacterial Foraging Optimization Algorithm with Particle Swarm Optimization
Strategy for Global Numerical Optimization,”GEC’09, June 2009.
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9. International Journal in Foundations of Computer Science & Technology (IJFCST), Vol. 3, No.2, March 2013
[5] Jun Zhang, Xiaomin Hu, X.Tan, J.H Zhong and Q. Huang., “Implementation of an Ant Colony
Optimization Technique for Job Shop Scheduling Problem,” Transactions of the Institute of
Measurement and Control 28, pp. 93_/108, 2006.
[6] Peter Bruker, “Scheduling Algorithms,” Fifth Edition, Springer-Verlag Berlin Heidelberg, 2007.
[7] Hanning Chen, Yunlong Zhu, and Kunyuan Hu ., “Cooperative Bacterial Foraging Optimization,”
Hindawi Publishing Corporation, Discrete Dynamics in Nature and Society, Article ID 815247,
Volume 2009.
[8] Jing Dang, Anthony Brabazon, Michael O’Neill, and David Edition., “Option Model Calibration
using a Bacterial Foraging Optimization Algorithm”, LNCS 4974, 2008.
[9] Sambarta Dasgupta, Swagatam Das, Ajith Abraham, Senior Member, IEEE, and Arijit Biswas.,
“Adaptive Computational Chemotaxis in Bacterial Foraging Optimization: An Analysis,” IEEE
Transactions on Evolutionary Computation, vol. 13, no. 4, August 2009.
[10] E. Taillard, “BenchMarks For Basic Scheduling Problems,” European Journal of Operations
Research, 64, 1993, pp. 278-285.
[11] Jason Brownlee., “Clever Algorithms: Nature-Inspired Programming Recipes,” First Edition, January
2011.
[12] Kevin M. Passino., “Bacterial Foraging for Optimization,” International Journal of Swarm
Intelligence Research, 1(1), January – March, 2010, pp. 1-16.
[13] Ravibabu. V, Amudha. T, “An Ant Inspired Bacterial Foraging Methodology Proposed To Solve
Open Shop Scheduling Problems”, International Journal of Advanced Research in Computer Science
and Electronics Engineering (IJARCSEE), ISSN: 2277-9043, August 2012.
[14] J. E. Beasley, OR-Library Web page for Instances, http://people.brunel.ac.uk/~mastjjb/jeb/info.html
[15] Naoyuki Tamura, CSP2SAT: Open Shop Scheduling Problems Web page, http://bach.istc.kobe-
u.ac.jp/csp2sat/oss/
[16] http://www.metaheuristics.org/
Authors
Mr.V.Ravibabu received his B.Sc Degree in Computer Science and MCA Degree in
Computer Applications in 2009 and 2012 respectively, from Bharathiar University,
Coimbatore, India. His area of interest includes Agent based computing and Bio-
inspired computing. He has attended National / International Conferences and 1
research publication for his credit in International Journal. He is a member of
International Association of Engineers.
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