Constraint programming (CP) is one of the most effe
ctive techniques for solving practical
operational problems. The outstanding feature of th
e method is a set of constraints affecting a
solution of a problem can be imposed without a need
to explicitly defining a linear relation
among variables, i.e. an equation. Nevertheless, th
e challenge of paramount importance in
using this technique is how to present the operatio
nal problem in a solvable Constraint
Satisfaction Problem (CSP) model. The problem model
ling is problem independent and could be
an exhaustive task at the beginning stage of proble
m solving, particularly when the problem is a
real-world practical problem. This paper investigat
es the application of a simple grid puzzle
game when a player attempts to solve a practical sc
heduling problem. The examination
scheduling is presented as an operational game. The
game‘s rules are set up based on the
operational practice. CP is then applied to solve t
he defined puzzle and the results show the
success of the proposed method. The benefit of usin
g a grid puzzle as the model is that the
method can amplify the simplicity of CP in solving
practical problems.
Solving Scheduling Problems as the Puzzle Games Using Constraint Programmingijpla
Constraint programming (CP) is one of the most effective techniques for solving practical operational
problems. The outstanding feature of the method is a set of constraints affecting a solution of a problem
can be imposed without a need to explicitly defining a linear relation among variables, i.e. an equation.
Nevertheless, the challenge of paramount importance in using this technique is how to present the
operational problem in a solvable Constraint Satisfaction Problem (CSP) model. The problem modelling is
problem independent and could be an exhaustive task at the beginning stage of problem solving,
particularly when the problem is a real-world practical problem. This paper investigates the application of
a simple grid puzzle game when a player attempts to solve practical scheduling problems. The examination
scheduling and logistic fleet scheduling are presented as operational games. The game‘s rules are set up
based on the operational practice. CP is then applied to solve the defined puzzle and the results show the
success of the proposed method. The benefit of using a grid puzzle as the model is that the method can
amplify the simplicity of CP in solving practical problems.
International Journal of Computational Engineering Research(IJCER)ijceronline
International Journal of Computational Engineering Research(IJCER) is an intentional online Journal in English monthly publishing journal. This Journal publish original research work that contributes significantly to further the scientific knowledge in engineering and Technology.
Interactive Fuzzy Goal Programming approach for Tri-Level Linear Programming ...IJERA Editor
The aim of this paper is to present an interactive fuzzy goal programming approach to determine the preferred
compromise solution to Tri-level linear programming problems considering the imprecise nature of the decision
makers’ judgments for the objectives. Using the concept of goal programming, fuzzy set theory, in combination
with interactive programming, and improving the membership functions by means of changing the tolerances of
the objectives provide a satisfactory compromise (near to ideal) solution to the upper level decision makers.
Two numerical examples for three-level linear programming problems have been solved to demonstrate the
feasibility of the proposed approach. The performance of the proposed approach was evaluated by using of
metric distance functions with other approaches.
Unsteady MHD Flow Past A Semi-Infinite Vertical Plate With Heat Source/ Sink:...IJERA Editor
This document presents an approach to solving multi-objective transportation problems using fuzzy goal programming and non-linear membership functions. It defines efficient, weak efficient, and optimal compromise solutions for multi-objective transportation problems. Three non-linear membership functions are proposed: exponential, hyperbolic, and linear. A fuzzy goal programming technique is used to solve the transportation problem, applying the different membership functions to generate equivalent linear or non-linear models. The approach is aimed to determine the impact of using non-linear versus linear membership functions on obtaining the optimal compromise solution.
MULTI-OBJECTIVE ENERGY EFFICIENT OPTIMIZATION ALGORITHM FOR COVERAGE CONTROL ...ijcseit
Many studies have been done in the area of Wireless Sensor Networks (WSNs) in recent years. In this kind of networks, some of the key objectives that need to be satisfied are area coverage, number of active sensors and energy consumed by nodes. In this paper, we propose a NSGA-II based multi-objective algorithm for optimizing all of these objectives simultaneously. The efficiency of our algorithm is demonstrated in the simulation results. This efficiency can be shown as finding the optimal balance point among the maximum coverage rate, the least energy consumption, and the minimum number of active nodes while maintaining the connectivity of the network
Penalty Function Method For Solving Fuzzy Nonlinear Programming Problempaperpublications3
Abstract: In this work, the fuzzy nonlinear programming problem (FNLPP) has been developed and their result have also discussed. The numerical solutions of crisp problems and have been compared and the fuzzy solution and its effectiveness have also been presented and discussed. The penalty function method has been developed and mixed with Nelder and Mend’s algorithm of direct optimization problem solutionhave been used together to solve this FNLPP.
Keyword:Fuzzy set theory, fuzzy numbers, decision making, nonlinear programming, Nelder and Mend’s algorithm, penalty function method.
The document describes a model for visual question answering that uses a co-attention mechanism with a low-rank bilinear model. It extracts image features using a CNN and encodes questions with word, phrase and sentence level representations. A co-attention mechanism is used to generate attention maps for the image and question. A low-rank bilinear model creates a joint embedding of the attended visual and question features for answer prediction. The model is evaluated on the VQA dataset and achieves state-of-the-art performance, demonstrating the effectiveness of using co-attention and a low-rank bilinear model for visual question answering.
The document discusses the concept of duality in linear programming problems. There are five steps to formulate the dual problem from the primal problem: 1) objective functions switch between maximization and minimization, 2) right hand sides of primal constraints become coefficients in the dual objective, 3) primal objective coefficients become right hand side values in the dual constraints, 4) transpose the primal constraint coefficients for the dual constraints, and 5) switch inequality signs. The dual problem maximizes the right hand side values subject to constraints with the primal objective coefficients and reversed inequality signs. The primal and dual problems are symmetric and related through their coefficients, constraints, and objective functions.
Solving Scheduling Problems as the Puzzle Games Using Constraint Programmingijpla
Constraint programming (CP) is one of the most effective techniques for solving practical operational
problems. The outstanding feature of the method is a set of constraints affecting a solution of a problem
can be imposed without a need to explicitly defining a linear relation among variables, i.e. an equation.
Nevertheless, the challenge of paramount importance in using this technique is how to present the
operational problem in a solvable Constraint Satisfaction Problem (CSP) model. The problem modelling is
problem independent and could be an exhaustive task at the beginning stage of problem solving,
particularly when the problem is a real-world practical problem. This paper investigates the application of
a simple grid puzzle game when a player attempts to solve practical scheduling problems. The examination
scheduling and logistic fleet scheduling are presented as operational games. The game‘s rules are set up
based on the operational practice. CP is then applied to solve the defined puzzle and the results show the
success of the proposed method. The benefit of using a grid puzzle as the model is that the method can
amplify the simplicity of CP in solving practical problems.
International Journal of Computational Engineering Research(IJCER)ijceronline
International Journal of Computational Engineering Research(IJCER) is an intentional online Journal in English monthly publishing journal. This Journal publish original research work that contributes significantly to further the scientific knowledge in engineering and Technology.
Interactive Fuzzy Goal Programming approach for Tri-Level Linear Programming ...IJERA Editor
The aim of this paper is to present an interactive fuzzy goal programming approach to determine the preferred
compromise solution to Tri-level linear programming problems considering the imprecise nature of the decision
makers’ judgments for the objectives. Using the concept of goal programming, fuzzy set theory, in combination
with interactive programming, and improving the membership functions by means of changing the tolerances of
the objectives provide a satisfactory compromise (near to ideal) solution to the upper level decision makers.
Two numerical examples for three-level linear programming problems have been solved to demonstrate the
feasibility of the proposed approach. The performance of the proposed approach was evaluated by using of
metric distance functions with other approaches.
Unsteady MHD Flow Past A Semi-Infinite Vertical Plate With Heat Source/ Sink:...IJERA Editor
This document presents an approach to solving multi-objective transportation problems using fuzzy goal programming and non-linear membership functions. It defines efficient, weak efficient, and optimal compromise solutions for multi-objective transportation problems. Three non-linear membership functions are proposed: exponential, hyperbolic, and linear. A fuzzy goal programming technique is used to solve the transportation problem, applying the different membership functions to generate equivalent linear or non-linear models. The approach is aimed to determine the impact of using non-linear versus linear membership functions on obtaining the optimal compromise solution.
MULTI-OBJECTIVE ENERGY EFFICIENT OPTIMIZATION ALGORITHM FOR COVERAGE CONTROL ...ijcseit
Many studies have been done in the area of Wireless Sensor Networks (WSNs) in recent years. In this kind of networks, some of the key objectives that need to be satisfied are area coverage, number of active sensors and energy consumed by nodes. In this paper, we propose a NSGA-II based multi-objective algorithm for optimizing all of these objectives simultaneously. The efficiency of our algorithm is demonstrated in the simulation results. This efficiency can be shown as finding the optimal balance point among the maximum coverage rate, the least energy consumption, and the minimum number of active nodes while maintaining the connectivity of the network
Penalty Function Method For Solving Fuzzy Nonlinear Programming Problempaperpublications3
Abstract: In this work, the fuzzy nonlinear programming problem (FNLPP) has been developed and their result have also discussed. The numerical solutions of crisp problems and have been compared and the fuzzy solution and its effectiveness have also been presented and discussed. The penalty function method has been developed and mixed with Nelder and Mend’s algorithm of direct optimization problem solutionhave been used together to solve this FNLPP.
Keyword:Fuzzy set theory, fuzzy numbers, decision making, nonlinear programming, Nelder and Mend’s algorithm, penalty function method.
The document describes a model for visual question answering that uses a co-attention mechanism with a low-rank bilinear model. It extracts image features using a CNN and encodes questions with word, phrase and sentence level representations. A co-attention mechanism is used to generate attention maps for the image and question. A low-rank bilinear model creates a joint embedding of the attended visual and question features for answer prediction. The model is evaluated on the VQA dataset and achieves state-of-the-art performance, demonstrating the effectiveness of using co-attention and a low-rank bilinear model for visual question answering.
The document discusses the concept of duality in linear programming problems. There are five steps to formulate the dual problem from the primal problem: 1) objective functions switch between maximization and minimization, 2) right hand sides of primal constraints become coefficients in the dual objective, 3) primal objective coefficients become right hand side values in the dual constraints, 4) transpose the primal constraint coefficients for the dual constraints, and 5) switch inequality signs. The dual problem maximizes the right hand side values subject to constraints with the primal objective coefficients and reversed inequality signs. The primal and dual problems are symmetric and related through their coefficients, constraints, and objective functions.
Comparision of methods for combination of multiple classifiers that predict b...IJERA Editor
Predictive analysis include techniques fromdata mining that analyze current and historical data and make
predictions about the future. Predictive analytics is used in actuarial science, financial services, retail, travel,
healthcare, insurance, pharmaceuticals, marketing, telecommunications and other fields.Predicting patterns can
be considered as a classification problem and combining the different classifiers gives better results. We will
study and compare three methods used to combine multiple classifiers. Bayesian networks perform
classification based on conditional probability. It is ineffective and easy to interpret as it assumes that the
predictors are independent. Tree augmented naïve Bayes (TAN) constructs a maximum weighted spanning tree
that maximizes the likelihood of the training data, to perform classification.This tree structure eliminates the
independent attribute assumption of naïve Bayesian networks. Behavior-knowledge space method works in two
phases and can provide very good performances if large and representative data sets are available.
ANALYTICAL FORMULATIONS FOR THE LEVEL BASED WEIGHTED AVERAGE VALUE OF DISCRET...ijsc
In fuzzy decision-making processes based on linguistic information, operations on discrete fuzzy numbers
are commonly performed. Aggregation and defuzzification operations are some of these often used
operations. Many aggregation and defuzzification operators produce results independent to the decisionmaker’s
strategy. On the other hand, the Weighted Average Based on Levels (WABL) approach can take
into account the level weights and the decision maker's "optimism" strategy. This gives flexibility to the
WABL operator and, through machine learning, can be trained in the direction of the decision maker's
strategy, producing more satisfactory results for the decision maker. However, in order to determine the
WABL value, it is necessary to calculate some integrals. In this study, the concept of WABL for discrete
trapezoidal fuzzy numbers is investigated, and analytical formulas have been proven to facilitate the
calculation of WABL value for these fuzzy numbers. Trapezoidal and their special form, triangular fuzzy
numbers, are the most commonly used fuzzy number types in fuzzy modeling, so in this study, such numbers
have been studied. Computational examples explaining the theoretical results have been performed.
Sensitivity Analysis of GRA Method for Interval Valued Intuitionistic Fuzzy M...ijsrd.com
The aim of this paper is to investigate the multiple attribute decision making problems with intuitionistic fuzzy information, in which the information about attribute weights are incompletely known, and the attribute values take the form of intuitionistic fuzzy numbers. In order to get the weight vector of the attribute, we establish an optimization model based on the basic ideal of traditional gray relational analysis (GRA) method, by which the attribute weights can be determined. For the special situations where the information about attribute weights are completely unknown, we establish another optimization model. By solving this model, we get a simple and exact formula, which can be used to determine the attribute weights. Then, based on the traditional GRA method, calculation steps for solving an interval-valued intuitionistic fuzzy environment and developed modified GRA method for interval-valued intuitionistic fuzzy multiple attributes decision-making with incompletely known attribute weight information. This paper provides a new method for sensitivity analysis of MADM problems so that by sing it and changing the weights of attributes, one can determine changes in the final results for a decision making problem. Finally, an illustrative example is given to verify the developed approach and to demonstrate its practicality and effectiveness.
This document describes an expandable Bayesian network (EBN) approach for 3D object description from multiple images and sensor data. The key points are:
- EBNs can dynamically instantiate network structures at runtime based on the number of input images, allowing the use of a varying number of evidence features.
- EBNs introduce the use of hidden variables to handle correlation of evidence features across images, whereas previous approaches did not properly model this.
- The document presents an application of an EBN for building detection and description from aerial images using multiple views and sensor data. Experimental results showed the EBN approach provided significant performance improvements over other methods.
In this paper, Assignment problem with crisp, fuzzy and intuitionistic fuzzy numbers as cost coefficients is investigated. In conventional assignment problem, cost is always certain. This paper develops an approach to solve a mixed intuitionistic fuzzy assignment problem where cost is considered real, fuzzy and an intuitionistic fuzzy numbers. Ranking procedure of Annie Varghese and Sunny Kuriakose [4] is used to transform the mixed intuitionistic fuzzy assignment problem into a crisp one so that the conventional method may be applied to solve the assignment problem. The method is illustrated by a numerical example. The proposed method is very simple and easy to understand. Numerical examples show that an intuitionistic fuzzy ranking method offers an effective tool for handling an intuitionistic fuzzy assignment problem.
A HYBRID COA/ε-CONSTRAINT METHOD FOR SOLVING MULTI-OBJECTIVE PROBLEMSijfcstjournal
In this paper, a hybrid method for solving multi-objective problem has been provided. The proposed method is combining the ε-Constraint and the Cuckoo algorithm. First the multi objective problem transfers into a single-objective problem using ε-Constraint, then the Cuckoo optimization algorithm will optimize the problem in each task. At last the optimized Pareto frontier will be drawn. The advantage of
this method is the high accuracy and the dispersion of its Pareto frontier. In order to testing the efficiency of the suggested method, a lot of test problems have been solved using this method. Comparing the results of this method with the results of other similar methods shows that the Cuckoo algorithm is more suitable for solving the multi-objective problems.
The document discusses duality theory in linear programming. It defines the dual problem as another linear program that is systematically derived from the original or primal problem. The primal and dual problems are closely related, such that solving one provides the optimal solution to the other. There are rules for constructing the dual problem based on whether the primal is a maximization or minimization problem and the constraint types. The document provides examples of writing dual problems and solving them using two methods. It also discusses verifying optimal solutions and the relationship between primal and dual objective values.
Soft computing is likely to play aprogressively important role in many applications including image enhancement. The paradigm for soft computing is the human mind. The soft computing critique has been particularly strong with fuzzy logic. The fuzzy logic is facts representationas a
rule for management of uncertainty. Inthis paperthe Multi-Dimensional optimized problem is addressed by discussing the optimal thresholding usingfuzzyentropyfor Image enhancement. This technique is compared with bi-level and multi-level thresholding and obtained optimal
thresholding values for different levels of speckle noisy and low contrasted images. The fuzzy entropy method has produced better results compared to bi-level and multi-level thresholding techniques.
The Evaluation of Topsis and Fuzzy-Topsis Method for Decision Making System i...IRJET Journal
This document discusses using fuzzy TOPSIS (Technique for Order Preference by Similarity to Ideal Solution) as an analytical tool for decision making in data mining. Fuzzy TOPSIS extends the traditional TOPSIS method to handle uncertainties by using fuzzy set theory. It involves defining ratings and weights as linguistic variables represented by fuzzy numbers. The key steps are normalizing the fuzzy decision matrix, determining fuzzy positive and negative ideal solutions, calculating distances from the ideal solutions, and determining a closeness coefficient to rank the alternatives. The literature review discusses previous research applying fuzzy set concepts to TOPSIS to address limitations of crisp data in modeling real-world decision problems.
The document contains 45 multiple choice questions about linear programming problems (LPP), transportation problems, and assignment problems. Some key points covered are:
- The feasible region in a graphical LPP solution satisfies all constraints simultaneously.
- An LPP deals with problems involving a single objective.
- The optimal solution in an LPP maximizes or minimizes the objective function subject to the constraints.
- Transportation problems aim to minimize total cost and are a special case of LPPs.
- Assignment problems assign origins to destinations at minimum cost when the number of each is equal.
- The document discusses duality theory and sensitivity analysis in linear programming.
- Duality theory states that for every linear programming problem (LPP), there is a corresponding dual LPP. The dual problem can be constructed from the primal problem using specific rules. Solving one problem provides the solution to the other.
- Sensitivity analysis determines how changes in the coefficients or right-hand side values of the LPP affect the optimal solution. It identifies the ranges that parameters can vary without impacting the optimal values of variables. This provides insight into the robustness of the optimal solution.
Event Coreference Resolution using Mincut based Graph Clustering cscpconf
To extract participants of an event instance, it is necessary to identify all the sentences that
describe the event instance. The set of all sentences referring to the same event instance are said
to be corefering each other. Our proposed approach formulates the event coreference resolution
as a graph based clustering model. It identifies the corefering sentences using minimum cut
(mincut) based on similarity score between each pair of sentences at various levels such as
trigger word similarity, time stamp similarity, entity similarity and semantic similarity. It
achieves good B-Cubed F-measure score with some loss in recall.
Sensitivity analysis linear programming copyKiran Jadhav
This document discusses sensitivity analysis in linear programming. It begins by defining sensitivity analysis as investigating how changes to a linear programming model's parameters, like objective function coefficients or constraint coefficients, affect the optimal solution. It then discusses the basic parameter changes that can impact the solution, like right-hand side constants or new variables/constraints. The document also covers duality in linear programming and how the dual problem is derived from the primal problem by setting coefficient values to the resource costs at optimality. An example is provided to demonstrate how the dual problem is formulated.
INTRA BLOCK AND INTER BLOCK NEIGHBORING JOINT DENSITY BASED APPROACH FOR JPEG...ijsc
Steganalysis is the method used to detect the presence of any hidden message in a cover medium. A novel
approach based on feature mining on the discrete cosine transform (DCT) domain based approach,
machine learning for steganalysis of JPEG images is proposed. The neighboring joint density on both
intra-block and inter-block are extracted from the DCT coefficient array. After the feature space has been
constructed, it uses SVM like binary classifier for training and classification. The performance of the
proposed method on different Steganographic systems named F5, Pixel Value Differencing, Model Based
Steganography with and without deblocking, JPHS, Steghide etc are analyzed. Individually each feature
and combined features classification accuracy is checked and concludes which provides better
classification.
Inventory Model with Price-Dependent Demand Rate and No Shortages: An Interva...orajjournal
In this paper, an interval-valued inventory optimization model is proposed. The model involves the price dependent
demand and no shortages. The input data for this model are not fixed, but vary in some real bounded intervals. The aim is to determine the optimal order quantity, maximizing the total profit and minimizing the holding cost subjecting to three constraints: budget constraint, space constraint, and
budgetary constraint on ordering cost of each item. We apply the linear fractional programming approach based on interval numbers. To apply this approach, a linear fractional programming problem is modeled with interval type uncertainty. This problem is further converted to an optimization problem with interval valued
objective function having its bounds as linear fractional functions. Two numerical examples in crisp
case and interval-valued case are solved to illustrate the proposed approach.
This document contains 20 multiple choice questions about integer programming models and techniques for solving integer programming problems like branch and bound. The questions cover topics such as the different types of integer programming models including mixed integer, 0-1 integer, and total integer models. They also address concepts like linear programming relaxation, implicit enumeration, and rounding solutions.
This document discusses modeling the skewness and kurtosis of box office revenue data using the Box-Cox power exponential (BCPE) distribution within the generalized additive models for location, scale and shape (GAMLSS) framework. It finds that the BCPE distribution provides a better fit than the traditionally used Pareto–Levy–Mandelbrot distribution. The flexible four-parameter BCPE distribution allows modeling the location, scale, skewness, and kurtosis parameters of box office revenues as smooth functions of explanatory variables like opening revenues and number of screens. This overcomes limitations of previous models and provides a better understanding of box office revenues across different time periods.
10122603 劉倪均internet based grammar instruction in the esl classroom(NEW)Cathy Liu
The document discusses a study that examined the effectiveness of Internet-based grammar instruction (IBGI) compared to conventional pen-and-paper instruction (CPBI) for English language learners. The study found that students who received IBGI made fewer grammatical errors and scored higher on tests of parts-of-speech, subject-verb agreement, and tenses than students who received CPBI. However, not all grammatical items could be effectively taught using Internet-based instruction.
The document proposes a new model for solving Weighted Constraint Satisfaction Problems (WCSPs) using a Hopfield neural network approach. It formulates WCSPs as a 0-1 quadratic programming problem subject to linear constraints, which can be solved using the Hopfield neural network. The model was tested on benchmark WCSP instances and was able to find optimal solutions, with the same time complexity as other known methods. The approach recognizes optimal solutions for WCSPs by minimizing an original energy function using the Hopfield neural network.
A constraint is defined as a logical relation among several unknown quantities or variables, each taking a value in a given
domain. Constraint Programming (CP) is an emergent field in operations research. Constraint programming is based on feasibility
which means finding a feasible solution rather than optimization which means finding an optimal solution and focuses on the
constraints and variables domain rather than the objective functions. While defining a set of constraints, this may seem a simple way to
model a real-world problem but finding a good model that works well with a chosen solver is not that easy. A model could be very
hard to solve if it is poorly chosen
Dear students get fully solved SMU MBA Fall 2014 assignments
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Dear students get fully solved SMU MBA Fall 2014 assignments
Send your semester & Specialization name to our mail id :
“ help.mbaassignments@gmail.com ”
or
Call us at : 08263069601
Comparision of methods for combination of multiple classifiers that predict b...IJERA Editor
Predictive analysis include techniques fromdata mining that analyze current and historical data and make
predictions about the future. Predictive analytics is used in actuarial science, financial services, retail, travel,
healthcare, insurance, pharmaceuticals, marketing, telecommunications and other fields.Predicting patterns can
be considered as a classification problem and combining the different classifiers gives better results. We will
study and compare three methods used to combine multiple classifiers. Bayesian networks perform
classification based on conditional probability. It is ineffective and easy to interpret as it assumes that the
predictors are independent. Tree augmented naïve Bayes (TAN) constructs a maximum weighted spanning tree
that maximizes the likelihood of the training data, to perform classification.This tree structure eliminates the
independent attribute assumption of naïve Bayesian networks. Behavior-knowledge space method works in two
phases and can provide very good performances if large and representative data sets are available.
ANALYTICAL FORMULATIONS FOR THE LEVEL BASED WEIGHTED AVERAGE VALUE OF DISCRET...ijsc
In fuzzy decision-making processes based on linguistic information, operations on discrete fuzzy numbers
are commonly performed. Aggregation and defuzzification operations are some of these often used
operations. Many aggregation and defuzzification operators produce results independent to the decisionmaker’s
strategy. On the other hand, the Weighted Average Based on Levels (WABL) approach can take
into account the level weights and the decision maker's "optimism" strategy. This gives flexibility to the
WABL operator and, through machine learning, can be trained in the direction of the decision maker's
strategy, producing more satisfactory results for the decision maker. However, in order to determine the
WABL value, it is necessary to calculate some integrals. In this study, the concept of WABL for discrete
trapezoidal fuzzy numbers is investigated, and analytical formulas have been proven to facilitate the
calculation of WABL value for these fuzzy numbers. Trapezoidal and their special form, triangular fuzzy
numbers, are the most commonly used fuzzy number types in fuzzy modeling, so in this study, such numbers
have been studied. Computational examples explaining the theoretical results have been performed.
Sensitivity Analysis of GRA Method for Interval Valued Intuitionistic Fuzzy M...ijsrd.com
The aim of this paper is to investigate the multiple attribute decision making problems with intuitionistic fuzzy information, in which the information about attribute weights are incompletely known, and the attribute values take the form of intuitionistic fuzzy numbers. In order to get the weight vector of the attribute, we establish an optimization model based on the basic ideal of traditional gray relational analysis (GRA) method, by which the attribute weights can be determined. For the special situations where the information about attribute weights are completely unknown, we establish another optimization model. By solving this model, we get a simple and exact formula, which can be used to determine the attribute weights. Then, based on the traditional GRA method, calculation steps for solving an interval-valued intuitionistic fuzzy environment and developed modified GRA method for interval-valued intuitionistic fuzzy multiple attributes decision-making with incompletely known attribute weight information. This paper provides a new method for sensitivity analysis of MADM problems so that by sing it and changing the weights of attributes, one can determine changes in the final results for a decision making problem. Finally, an illustrative example is given to verify the developed approach and to demonstrate its practicality and effectiveness.
This document describes an expandable Bayesian network (EBN) approach for 3D object description from multiple images and sensor data. The key points are:
- EBNs can dynamically instantiate network structures at runtime based on the number of input images, allowing the use of a varying number of evidence features.
- EBNs introduce the use of hidden variables to handle correlation of evidence features across images, whereas previous approaches did not properly model this.
- The document presents an application of an EBN for building detection and description from aerial images using multiple views and sensor data. Experimental results showed the EBN approach provided significant performance improvements over other methods.
In this paper, Assignment problem with crisp, fuzzy and intuitionistic fuzzy numbers as cost coefficients is investigated. In conventional assignment problem, cost is always certain. This paper develops an approach to solve a mixed intuitionistic fuzzy assignment problem where cost is considered real, fuzzy and an intuitionistic fuzzy numbers. Ranking procedure of Annie Varghese and Sunny Kuriakose [4] is used to transform the mixed intuitionistic fuzzy assignment problem into a crisp one so that the conventional method may be applied to solve the assignment problem. The method is illustrated by a numerical example. The proposed method is very simple and easy to understand. Numerical examples show that an intuitionistic fuzzy ranking method offers an effective tool for handling an intuitionistic fuzzy assignment problem.
A HYBRID COA/ε-CONSTRAINT METHOD FOR SOLVING MULTI-OBJECTIVE PROBLEMSijfcstjournal
In this paper, a hybrid method for solving multi-objective problem has been provided. The proposed method is combining the ε-Constraint and the Cuckoo algorithm. First the multi objective problem transfers into a single-objective problem using ε-Constraint, then the Cuckoo optimization algorithm will optimize the problem in each task. At last the optimized Pareto frontier will be drawn. The advantage of
this method is the high accuracy and the dispersion of its Pareto frontier. In order to testing the efficiency of the suggested method, a lot of test problems have been solved using this method. Comparing the results of this method with the results of other similar methods shows that the Cuckoo algorithm is more suitable for solving the multi-objective problems.
The document discusses duality theory in linear programming. It defines the dual problem as another linear program that is systematically derived from the original or primal problem. The primal and dual problems are closely related, such that solving one provides the optimal solution to the other. There are rules for constructing the dual problem based on whether the primal is a maximization or minimization problem and the constraint types. The document provides examples of writing dual problems and solving them using two methods. It also discusses verifying optimal solutions and the relationship between primal and dual objective values.
Soft computing is likely to play aprogressively important role in many applications including image enhancement. The paradigm for soft computing is the human mind. The soft computing critique has been particularly strong with fuzzy logic. The fuzzy logic is facts representationas a
rule for management of uncertainty. Inthis paperthe Multi-Dimensional optimized problem is addressed by discussing the optimal thresholding usingfuzzyentropyfor Image enhancement. This technique is compared with bi-level and multi-level thresholding and obtained optimal
thresholding values for different levels of speckle noisy and low contrasted images. The fuzzy entropy method has produced better results compared to bi-level and multi-level thresholding techniques.
The Evaluation of Topsis and Fuzzy-Topsis Method for Decision Making System i...IRJET Journal
This document discusses using fuzzy TOPSIS (Technique for Order Preference by Similarity to Ideal Solution) as an analytical tool for decision making in data mining. Fuzzy TOPSIS extends the traditional TOPSIS method to handle uncertainties by using fuzzy set theory. It involves defining ratings and weights as linguistic variables represented by fuzzy numbers. The key steps are normalizing the fuzzy decision matrix, determining fuzzy positive and negative ideal solutions, calculating distances from the ideal solutions, and determining a closeness coefficient to rank the alternatives. The literature review discusses previous research applying fuzzy set concepts to TOPSIS to address limitations of crisp data in modeling real-world decision problems.
The document contains 45 multiple choice questions about linear programming problems (LPP), transportation problems, and assignment problems. Some key points covered are:
- The feasible region in a graphical LPP solution satisfies all constraints simultaneously.
- An LPP deals with problems involving a single objective.
- The optimal solution in an LPP maximizes or minimizes the objective function subject to the constraints.
- Transportation problems aim to minimize total cost and are a special case of LPPs.
- Assignment problems assign origins to destinations at minimum cost when the number of each is equal.
- The document discusses duality theory and sensitivity analysis in linear programming.
- Duality theory states that for every linear programming problem (LPP), there is a corresponding dual LPP. The dual problem can be constructed from the primal problem using specific rules. Solving one problem provides the solution to the other.
- Sensitivity analysis determines how changes in the coefficients or right-hand side values of the LPP affect the optimal solution. It identifies the ranges that parameters can vary without impacting the optimal values of variables. This provides insight into the robustness of the optimal solution.
Event Coreference Resolution using Mincut based Graph Clustering cscpconf
To extract participants of an event instance, it is necessary to identify all the sentences that
describe the event instance. The set of all sentences referring to the same event instance are said
to be corefering each other. Our proposed approach formulates the event coreference resolution
as a graph based clustering model. It identifies the corefering sentences using minimum cut
(mincut) based on similarity score between each pair of sentences at various levels such as
trigger word similarity, time stamp similarity, entity similarity and semantic similarity. It
achieves good B-Cubed F-measure score with some loss in recall.
Sensitivity analysis linear programming copyKiran Jadhav
This document discusses sensitivity analysis in linear programming. It begins by defining sensitivity analysis as investigating how changes to a linear programming model's parameters, like objective function coefficients or constraint coefficients, affect the optimal solution. It then discusses the basic parameter changes that can impact the solution, like right-hand side constants or new variables/constraints. The document also covers duality in linear programming and how the dual problem is derived from the primal problem by setting coefficient values to the resource costs at optimality. An example is provided to demonstrate how the dual problem is formulated.
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demand and no shortages. The input data for this model are not fixed, but vary in some real bounded intervals. The aim is to determine the optimal order quantity, maximizing the total profit and minimizing the holding cost subjecting to three constraints: budget constraint, space constraint, and
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This document contains 20 multiple choice questions about integer programming models and techniques for solving integer programming problems like branch and bound. The questions cover topics such as the different types of integer programming models including mixed integer, 0-1 integer, and total integer models. They also address concepts like linear programming relaxation, implicit enumeration, and rounding solutions.
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10122603 劉倪均internet based grammar instruction in the esl classroom(NEW)Cathy Liu
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The document proposes a new model for solving Weighted Constraint Satisfaction Problems (WCSPs) using a Hopfield neural network approach. It formulates WCSPs as a 0-1 quadratic programming problem subject to linear constraints, which can be solved using the Hopfield neural network. The model was tested on benchmark WCSP instances and was able to find optimal solutions, with the same time complexity as other known methods. The approach recognizes optimal solutions for WCSPs by minimizing an original energy function using the Hopfield neural network.
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constraints and variables domain rather than the objective functions. While defining a set of constraints, this may seem a simple way to
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Dear students get fully solved SMU MBA Fall 2014 assignments
Send your semester & Specialization name to our mail id :
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MIXED 0−1 GOAL PROGRAMMING APPROACH TO INTERVAL-VALUED BILEVEL PROGRAMMING PR...cscpconf
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DSCPs. With the increasing complexity and problem size of the application problems in AI, the required
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This document discusses variations of the interval linear assignment problem. It begins with an introduction to assignment problems and defines them as problems that assign resources to activities to minimize cost or maximize profit on a one-to-one basis. It then provides the mathematical model for standard assignment problems and discusses variations such as non-square matrices, maximization/minimization objectives, constrained assignments, and alternate optimal solutions. The document also gives examples of managerial applications and provides two numerical examples solving interval linear assignment problems using an interval Hungarian method.
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1) Achieving a piecewise inner-approximation of the concave function using an auxiliary linear program, leading to a bilevel program that provides a lower bound to the original problem.
2) Reducing the bilevel program to a single level formulation using Karush-Kuhn-Tucker conditions and linearizing the complementary slackness conditions with BigM.
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Template matching is a basic method in image analysis to extract useful information from images. In this
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dimensional image into one dimensional vector. Also all sub-windows (same size of template) in the
reference image will transform into one dimensional vectors. The three similarity measures SAD, SSD, and
Euclidean are used to compute the likeness between template and all sub-windows in the reference image
to find the best match. The experimental results show the superior performance of the proposed method
over the conventional methods on various template of different sizes.
Assisting Domain Experts To Formulate And Solve Constraint Satisfaction ProblemsJim Jimenez
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▪ Developed a mathematical puzzle solver using brute force algorithm and Constraint Satisfaction Problems in C++
▪ Employed backtracking methodology to ensure guaranteed solution to Sudoku Problem in order of milliseconds
▪ Implemented AI practices like Forwarding Checking, Most Constrained Heuristic & ARC-Consistency in an incremental manner
IMAGE SEGMENTATION BY MODIFIED MAP-ML ESTIMATIONScscpconf
This document summarizes an image segmentation algorithm called Modified MAP-ML Estimations. It begins with an abstract describing the algorithm and its benefits of faster execution time compared to existing algorithms. It then reviews related work in image segmentation techniques and their limitations. The document describes the probabilistic model used in the algorithm, which formulates segmentation as a labeling problem. It explains the MAP estimation approach used to estimate label configurations, and the ML estimation used to estimate region properties. The algorithm iterates between these two estimations to perform segmentation.
This document summarizes an image segmentation algorithm called Modified MAP-ML Estimations. It begins with an abstract describing the algorithm and its benefits of faster execution time compared to existing algorithms. It then reviews related work in image segmentation techniques and their limitations. The document describes the probabilistic model used in the algorithm, which formulates segmentation as a labeling problem. It explains the MAP estimation approach used to estimate label configurations, defining energy functions minimized through graph cuts. ML estimation is then used to update the region feature estimates in an iterative process. In summary, this algorithm modifies an existing MAP-ML approach to achieve comparable segmentation results to other algorithms, but in a faster execution time without human intervention.
Image segmentation by modified map ml estimationsijesajournal
Though numerous algorithms exist to perform image segmentation there are several issues
related to execution time of these algorithm. Image Segmentation is nothing but label relabeling
problem under probability framework. To estimate the label configuration, an iterative
optimization scheme is implemented to alternately carry out the maximum a posteriori (MAP)
estimation and the maximum likelihood (ML) estimations. In this paper this technique is
modified in such a way so that it performs segmentation within stipulated time period. The
extensive experiments shows that the results obtained are comparable with existing algorithms.
This algorithm performs faster execution than the existing algorithm to give automatic
segmentation without any human intervention. Its result match image edges very closer to
human perception.
IRJET - Factors Affecting Deployment of Deep Learning based Face Recognition ...IRJET Journal
This document discusses factors affecting the deployment of deep learning models for face recognition on smartphones. It examines training data requirements, suitable neural network architectures, and effective loss functions. Larger datasets with more subjects and images are preferred for training models that generalize well. Residual networks like ResNet have achieved good accuracy while being efficient for face recognition. Loss functions like center loss and triplet loss help learn discriminative features by reducing intra-class and increasing inter-class variations.
APPLYING TRANSFORMATION CHARACTERISTICS TO SOLVE THE MULTI OBJECTIVE LINEAR F...ijcsit
For some management programming problems, multiple objectives to be optimized rather than a single objective, and objectives can be expressed with ratio equations such as return/investment, operating
profit/net-sales, profit/manufacturing cost, etc. In this paper, we proposed the transformation characteristics to solve the multi objective linear fractional programming (MOLFP) problems. If a MOLFP problem with both the numerators and the denominators of the objectives are linear functions and some
technical linear restrictions are satisfied, then it is defined as a multi objective linear fractional programming problem MOLFPP in this research. The transformation characteristics are illustrated and the solution procedure and numerical example are presented.
For some management programming problems, multiple objectives to be optimized rather than a single objective, and objectives can be expressed with ratio equations such as return/investment, operating profit/net-sales, profit/manufacturing cost, etc. In this paper, we proposed the transformation characteristics to solve the multi objective linear fractional programming (MOLFP) problems. If a MOLFP problem with both the numerators and the denominators of the objectives are linear functions and some technical linear restrictions are satisfied, then it is defined as a multi objective linear fractional programming problem MOLFPP in this research. The transformation characteristics are illustrated and the solution procedure and numerical example are presented.
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2. 10 Computer Science & Information Technology (CS & IT)
problems and using CP solvers to solve the problems. There are several available CP solvers for
both CSP and CSOP including: Choco, Ilog, ECLiPSe®, Gecode, Comet, CHIP, and Jsolve.
Problem modelling is one of the key steps of using CP to solve problems successfully. This paper
will focus on a grid puzzle-game as inspiration to model and solve the problem. The rest of the
paper is organised as follows; Section 2 discusses the current CP applications, Section 3 provides
a background of typical grid puzzle game, Section 4 demonstrates the using of grid puzzle to
model a scheduling problem, Section 5 discusses the CP implementation, Section 6 discussed the
result of the paper and, Section 7 is the conclusion.
2. CP APPLICATIONS
CP has been applied to solve several applications successfully. In healthcare, CP is used to assign
shifts to medical staffs. Several rules can be imposed to solve the problem and create the realistic
schedule including; assignments meet the demand for every shift, staff availability status, and the
fairness of the generated schedule for every assigned staff [7]. Further requirements to schedule
working time for medical residents are addressed in [8]. The requirements that make this
scheduling different from the typical medical staff come from the fact that a resident is not only
the medical staff, he or she is also a student in training i.e. the schedule have to provide a good
balance between education and medical service activities. CP is also used for scheduling facilities
in healthcare such as an operation theatre[9]. At airports, [10] investigates the use of CP to
schedule aircraft departure to avoid traffic congestion, while [11] focuses the study on generating
a contingency plan to handle unexpected failures affecting a regular traffic schedules. At
academic institutes, manual timetabling can be a very time-consuming task, [12] presents CP
based school timetabling to minimise idle hours between the daily teaching responsibilities of all
teachers. [13] develops an examination timetabling to tackle important constrains such as
schedule clashing, room capacity, and avoiding an allocation of two difficult subjects in
consecutive time slot.
3. GRID PUZZLES
Grid Puzzles are board games contained within an NxM lattice where players are usually required
to locate symbols or number to meet the objective of the game. There have been several studies
using CP to solve grid puzzle games. Akari, Kakuro, Nurikabe have been studied [14]. Akuro is a
game that provides clues for a number of tokens, which the game called ‘lights’, for certain grid,
players are asked to locate tokens such that all conditions are satisfied. Kakuro requires players
to fill a numbers to grids to generate sums to meet vertical and horizontal clues. Another classical
puzzle game problem that is usually mentioned in CP literature is the N-queen problem. In this
problem, one is asked to place N queens on the N× N chess board, where N ≥ 3, so that they do
not attack each other. Better known puzzle games are Crosswords and Sudoku, and MineSweeper.
Crosswords are games in which one is required to fill pre-defined vocabulary into the NxN grids
in a way that none of the words are used more than once. Sudoku is usually played on 9 x 9 grids
with some grids having pre-defined values. The game‘s rule involves giving a value assignment
so that all rows and column as well as sub-regions 3 x3 grid are pairwise different. Finally,
Minesweeper is one of the most popular ‘time-killer’ computer games which has the objective to
determine the ‘mine’ on a grid where the game might provide hints for a number of mines in the
grids. The example of the Grid puzzle games are shown as Figure 1.
3. Computer Science & Information Technology (CS & IT) 11
Figure 1. Typical grid puzzle games and their solutions [14-17]
4. CP APPLICATIONS
The mechanism of tackling CSP using CP typically relies on the domain reduction process. To
solve a problem, a set of constraints related to the problem needs to be identified and later on
applied to a problem. Some of the constraints are associated with each other to formulate a
constraint network. Each constraint applied to the model is usually associated with finite domain
variables. Solving the problem is a process of reducing the domain of each variable until there are
no conflicted domains remaining. So, constraint programmers will need to understand the
variables, domain and constrains of the problem. Particularly they need to have a comprehensive
understanding of the relationship among associated constraints and variables. This can be
exhaustive task when solving complicated practical problems. Figure 2 visualises an abstraction
of a constraint network and variable network of CP as describe above.
Figure 2. CP problem solving
Grid puzzles representations, i.e. using 2 Dimension (2D), NxM , lattice to represent
finite values/states of variables,which can be applied to model many practical problems. With
that, the relationship between variables can be visualised. Rules of the games can be set up to
4. 12 Computer Science & Information Technology (CS & IT)
reflect businesses rules, and typical constraints can be applied to the model just as what shown in
solving general puzzle games. This paper demonstrates the use of grid puzzles for solving an
examination scheduling problem which is outlined as follows:
Problem definition: The problem is an examination scheduling problem. It is mainly concerned
with assignment of subjects for exam into given time slot during examination period. The
generated result shall be able to indicate the day of the week the exam is allocated together with
the room assigned. The assumption of this problem is that this schedule is for a package
registration system in which student in the same year will study the same subjects. The problem is
concerned with practical constraints such as certain subjects requiring larger room and every
student cannot take exams in more than 2 subjects in a day. Solving this problem manually, i.e.
using human decision making, is highly time-consuming and prone to mistakes such as schedule
conflicted issues. This research will apply the grid puzzle, shown in Figure 3, to tackle the
described problem.
0
Figure 3. Grid puzzle for examination scheduling problem
From Figure 3, it can be seen that the columns represent rooms or venue of the exam. There are 2
types of rooms in this problem: 1) regular-sized rooms indicated by the white-grids and 2) larger
sized rooms indicated by the shaded-grids. Rows of the puzzle represent time slots of the exam.
Assuming there are 3 timeslots per day, the thick horizontal lines are used to separate days during
the exam period. Thus, Figure 3 is shown that there are 6 rooms available for the exam with 2
large rooms and the exam period lasts 3 days. The objective of the defining game is to assign
subject ID to the puzzle such that operational constraints are satisfied. The rules of the game are
setup to match the businesses rules of the problem as detailed in Table 1.
Table 1 Business‘s and game‘s rules of the problem
Business ‘s rules Game ‘s rules
A. All subjects have to be assigned to the
schedule and each subject takes only 1
exam
A. All the numbers indicating subject IDs, can be
used only once
B. Students should not take more than 2
exams in a same day
B. In a day sub-region, the number of assigned
subjects for each year cannot be over 2
C. Some subjects require large rooms
C The subjects that requires large rooms should be
assigned to the given area only
Day1
Day2
Day3
5. Computer Science & Information Technology (CS & IT) 13
5. IMPLEMENTATION
The problems is implemented by using Choco, a Java based CP library. The constraints declared
in Section 4 as the rules of this game can be solved by CP as follows:
5.1 “All the numbers indicating subject IDs, can be used only once”
Global constraint is a category of constraints that are defined for solving practical problems where
association between variables are not limited to ‘local’ consideration [18]. Global constraints are
well documented to define 423 constraints in [19]. Global cardinality is a global constraints used
to tackle this requirement. The constraint enable limiting the lower bound and upper bound
together with the number of times that those values can be used. Imposing the Global cardinality
constraint to satisfy this rule in Choco is as the following simplified statement.
The representation for this constraint is depicted in Figure 4. In this application, each variable
Subject ID (S) = {1, 2, 3, 4…20) represents a sequence of continuous subject ID. A dummy
value 0 is required to indicate that there is no assignment given to that timeslot. Therefore, the
domain of this variable, i.e. for 20 subjects, is ranged from [0, 20). The global cardinality is
enforced every S, except 0, appearing only once
Figure 4. Problem modelling to tackle constraint 5.1
5.2 “In a day sub-region, the number of assigned subjects for each year cannot be over 2”
The model of the year of subject is similar the Subject ID as shown in Figure 5. There are four
year of students from 1 to 4. However, similar to the previous constraint, a dummy value (0) is
required to indicate a ‘no-assignment’. The domain for this variable is therefore ranged from [0,
4].
Impose globalCardinality(S,[0,20],all the number in the range except 0 is only assigned 1 time)
6. 14 Computer Science & Information Technology (CS & IT)
Figure 5. Problem modelling to tackle constraint 5.2
Due to the fact that rows in the puzzle indicate time slot of the exam, Globalcardinality is used to
control the number of the domain 1-4 appearing at most twice in each day region. The algorithm
for tackling this rules of the defined puzzle is shown in Figure 6.
FOR Each day
Impose GlobalCardinality(Year, [0,4],all the number in the range except 0 is only
assigned 2 time)
ENDFOR
Figure 6. Algorithm for tackling the constraint 5.2
5.3 “The subjects that requires large-rooms should be assigned to the defined areas only”
Two larger rooms are defined for the first two columns as shown in Figure 7. Assignment to this
area are limited to the subject that required. The subject that require larger room have to be
defined in a problem statement, and this value will never be assigned outside that area.
Figure 7 Problem modelling to tackle constraint 5.3
To implement this constraint in Choco, the constraint ‘among’ is applied to limit a subject ID
assignment bounded in a predefined list of large rooms. This constraint is only applied to the
shaded area of the puzzle. So a constraint is defined within a nested loop. The algorithm is
depicted as Figure 7a.
7. Computer Science & Information Technology (CS & IT) 15
FOR i = 0 To LastRow
For j = To LastColumnLargeRoom
Impose among (S[i][j], LargeroomList)
ENDFOR
ENDFOR
Figure 7a. Problem modelling to tackle constraint 5.3
5.4” Associating IDs to other attributes”
Being that a grid puzzle is 2D, the limitation in problem modelling is an unknown variable that
can be solved one at a time. In practice, there are multiple variables to consider in one problem.
For example, the example problem involved with Subject ID and year of the subject. Modelling
the problem using a grid puzzle requires to solve the problem separately. The internal constraint
beside the explicit constraints of the problem is required to associate with other solving variables.
This can be done by imposing constraints to associate variables. In CP, a compatibility between
variable can be enforced by declaring a feasible pair i.e. between subject ID and the year variable.
This will enable interpretation of which subject is belong to. The algorithm for binding 2
variables is indicated as Figure 8.
FOR i = 0 To LastRow
For j = To LastColumnLargeRoom
Impose feasiblepair (S[i][j],Yr[i][j],DefinedPair)
ENDFOR
ENDFOR
Figure 8. Algorithm for associating Subject ID with its year
6. RESULTS AND DISCUSSION
This Section demonstrates the use of the grid puzzle defined to solve the exam scheduling
problem. The sample question is given in Table 2, and brief clarification on the problem is as
follows:
8. 16 Computer Science & Information Technology (CS & IT)
Table 2. Requirements of the problem
Subject
ID
Year Large section (yes or no)
1 1 Yes
2 1 No
3 1 No
4 1 No
5 1 No
6 2 No
7 2 Yes
8 2 No
9 2 No
10 2 No
11 3 No
12 3 Yes
13 3 No
14 3 No
15 3 No
16 4 No
17 4 No
18 4 No
19 4 Yes
20 4 No
From Table 2., there are 5 subjects for each year i.e. subject 1-5 for the first year, 6-10 for the
second year, 11-15 for the third year, and 16-20 for the fourth year. 5 subjects require larger
room: 1, 3, 7, 12, and, 19. Solving this grid puzzle using our proposed method can result in the
following scheduling as depicted in Figure 7.
Figure 7. Scheduling result
The result indicates that 3 defined major constrains are satisfied; 1) all subjects are allocated to
the schedule 2) there are no more than 2 exams for every year subject and 3) the subject that has
larger class-sizes are allocated to the larger room.
9. Computer Science & Information Technology (CS & IT) 17
In this paper schedule result is generated under CSP focus. Figure 7 show only one possible
solution, actually several more possible solutions can be generated. CSP solving does not specify
which solution is better than the other, when an optimal solution is required, the problem can be
simply expanded to the “Constraint Satisfaction Optimisation Problem (CSOP)” by applying
objective function to the model e.g. minimise spanning time.
7. CONCLUSION
This paper aims at tackling the problem formulation issue of using CP solving CSP. Applying
grid puzzles to represent the problem is an alternative solution to get started solving practical
problem. The paper shows the success of using the grid puzzle to solve simple examination
scheduling problem. Three operational constraints are addressed; 1) all the subjects are scheduled
the exam 2) students can take at most 2 subjects per a days and 3) the schedule allocates the
rooms to meet capacity requirement. The future work of this research is to impose more constraint
to this problem also applying the model to similar scheduling problems. This work has led to the
new research question is the proposed method simple enough for non-computing user? The
planned field evaluation is to conduct to evaluation of the proposed method by university
administration staff. Subject to success of the proposed method, anyone not limited to computing
users who understand the problem can contribute in the problem solving process using CP. In
practice, operational workers might be able to formulate a CSP model to cooperate with a
Constraint Programmer to shorten problem solving time, or they can even solve the problem by
themselves.
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AUTHOR
Noppon Choosri: is a director of the Software, Management and Animation by Radical
Technologies (SMART) Research centre, College of Arts, Media and Technologies,
Chiang Mai University, Thailand. He is also a lecturer at Software Engineering
Department. He received his B.Sc. in Computer Science and M.Sc. in Information
Management on Environment and Resources from Mahidol University, Thailand and
PhD in Computing Science from Staffordshire University, U.K. His research interest
involves applying information technologies to solve practical operational problem in
various areas including logistics, knowledge management, tourism, medical science,
and environmental studies