Pub Date : 2019-04-01DOI: 10.11113/MATEMATIKA.V35.N1.1032
M. Tifroute, H. Bouzahir
The wind farm layout optimization problem is similar to the classical mathematical problem of finding the Steiner Minimal Tree Problem (SMTP) of a weighted undirected graph. Due to the cable current-carrying capacity limitation, the cable sectional area should be carefully selected to meet the system operational requirement and this constraint should be considered during the SMTP formulation process. Hence, traditional SMTP algorithm cannot ensure a minimal cable investment layout. In this paper, a hybrid algorithm based on modified Ants Colony Optimization (ACO) and Artificial Immune Algorithm (AIA) for solving SMTP is introduced. Since the Steiner Tree Problem is NP-hard, we design an algorithm to construct high quality Steiner trees in a short time which is suitable for real time multicast routing in networks. After the breadth - first traversal of the minimal graph obtained by ACO, the terminal points are divided into different convex hull sets, and the full Steiner tree is structured from the convex hull sets partition. The Steiner points can then be vaccinated by AIA to get an optimal graph. The average optimization effect of AIA is shorter than the minimal graph obtained using ACO, and the performance of the algorithm is shown. We give an example of application in optimization for onshore wind farm Cable. The possibility of using different sectional area’s cable is also considered in this paper.
{"title":"Optimization for Onshore Wind Farm Cable: Connection Layout using ACO-AIA algorithm","authors":"M. Tifroute, H. Bouzahir","doi":"10.11113/MATEMATIKA.V35.N1.1032","DOIUrl":"https://doi.org/10.11113/MATEMATIKA.V35.N1.1032","url":null,"abstract":"The wind farm layout optimization problem is similar to the classical mathematical problem of finding the Steiner Minimal Tree Problem (SMTP) of a weighted undirected graph. Due to the cable current-carrying capacity limitation, the cable sectional area should be carefully selected to meet the system operational requirement and this constraint should be considered during the SMTP formulation process. Hence, traditional SMTP algorithm cannot ensure a minimal cable investment layout. In this paper, a hybrid algorithm based on modified Ants Colony Optimization (ACO) and Artificial Immune Algorithm (AIA) for solving SMTP is introduced. Since the Steiner Tree Problem is NP-hard, we design an algorithm to construct high quality Steiner trees in a short time which is suitable for real time multicast routing in networks. After the breadth - first traversal of the minimal graph obtained by ACO, the terminal points are divided into different convex hull sets, and the full Steiner tree is structured from the convex hull sets partition. The Steiner points can then be vaccinated by AIA to get an optimal graph. The average optimization effect of AIA is shorter than the minimal graph obtained using ACO, and the performance of the algorithm is shown. We give an example of application in optimization for onshore wind farm Cable. The possibility of using different sectional area’s cable is also considered in this paper.","PeriodicalId":43733,"journal":{"name":"Matematika","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2019-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42596686","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-04-01DOI: 10.11113/MATEMATIKA.V35.N1.1127
N. Aziz, Choong Jing Yee
Inventory Routing Problem (IRP) has been continuously developed and improved due to pressure from global warming issue particularly related to greenhouse gases (GHGs) emission. The burning of fossil fuel for transportations such as cars, trucks, ships, trains, and planes primarily emits GHGs. Carbon dioxide (CO2) from burning of fossil fuel to power transportation and industrial process is the largest contributor to global GHGs emission. Therefore, the focus of this study is on solving a multi-period inventory routing problem (MIRP) involving carbon emission consideration based on carbon cap and offset policy. Hybrid genetic algorithm (HGA) based on allocation first and routing second is used to compute a solution for the MIRP in this study. The objective of this study is to solve the proposed MIRP model with HGA then validate the effectiveness of the proposed HGA on data of different sizes. Upon validation, the proposed MIRP model and HGA is applied on real-world data. The HGA is found to be able to solve small size and large size instances effectively by providing near optimal solution in relatively short CPU execution time.
{"title":"Inventory Routing Problem with Carbon Emission Consideration","authors":"N. Aziz, Choong Jing Yee","doi":"10.11113/MATEMATIKA.V35.N1.1127","DOIUrl":"https://doi.org/10.11113/MATEMATIKA.V35.N1.1127","url":null,"abstract":"Inventory Routing Problem (IRP) has been continuously developed and improved due to pressure from global warming issue particularly related to greenhouse gases (GHGs) emission. The burning of fossil fuel for transportations such as cars, trucks, ships, trains, and planes primarily emits GHGs. Carbon dioxide (CO2) from burning of fossil fuel to power transportation and industrial process is the largest contributor to global GHGs emission. Therefore, the focus of this study is on solving a multi-period inventory routing problem (MIRP) involving carbon emission consideration based on carbon cap and offset policy. Hybrid genetic algorithm (HGA) based on allocation first and routing second is used to compute a solution for the MIRP in this study. The objective of this study is to solve the proposed MIRP model with HGA then validate the effectiveness of the proposed HGA on data of different sizes. Upon validation, the proposed MIRP model and HGA is applied on real-world data. The HGA is found to be able to solve small size and large size instances effectively by providing near optimal solution in relatively short CPU execution time.","PeriodicalId":43733,"journal":{"name":"Matematika","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2019-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45783462","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-04-01DOI: 10.11113/MATEMATIKA.V35.N1.1102
N. I. Alimon, N. Sarmin, A. Erfanian
Topological indices are numerical values that can be analysed to predict the chemical properties of the molecular structure and the topological indices are computed for a graph related to groups. Meanwhile, the conjugacy class graph of is defined as a graph with a vertex set represented by the non-central conjugacy classes of . Two distinct vertices are connected if they have a common prime divisor. The main objective of this article is to find various topological indices including the Wiener index, the first Zagreb index and the second Zagreb index for the conjugacy class graph of dihedral groups of order where the dihedral group is the group of symmetries of regular polygon, which includes rotations and reflections. Many topological indices have been determined for simple and connected graphs in general but not graphs related to groups. In this article, the Wiener index and Zagreb index of conjugacy class graph of dihedral groups are generalized.
{"title":"The Wiener and Zagreb Indices of Conjugacy Class Graph of the Dihedral Groups","authors":"N. I. Alimon, N. Sarmin, A. Erfanian","doi":"10.11113/MATEMATIKA.V35.N1.1102","DOIUrl":"https://doi.org/10.11113/MATEMATIKA.V35.N1.1102","url":null,"abstract":"Topological indices are numerical values that can be analysed to predict the chemical properties of the molecular structure and the topological indices are computed for a graph related to groups. Meanwhile, the conjugacy class graph of is defined as a graph with a vertex set represented by the non-central conjugacy classes of . Two distinct vertices are connected if they have a common prime divisor. The main objective of this article is to find various topological indices including the Wiener index, the first Zagreb index and the second Zagreb index for the conjugacy class graph of dihedral groups of order where the dihedral group is the group of symmetries of regular polygon, which includes rotations and reflections. Many topological indices have been determined for simple and connected graphs in general but not graphs related to groups. In this article, the Wiener index and Zagreb index of conjugacy class graph of dihedral groups are generalized.","PeriodicalId":43733,"journal":{"name":"Matematika","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2019-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44424990","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-04-01DOI: 10.11113/MATEMATIKA.V35.N1.1059
Rabiha Mahmoud, Amira Fadina Ahmad Fadzil, N. Sarmin, A. Erfanian
Let G be a dihedral group and its conjugacy class graph. The Laplacian energy of the graph, is defined as the sum of the absolute values of the difference between the Laplacian eigenvalues and the ratio of twice the edges number divided by the vertices number. In this research, the Laplacian matrices of the conjugacy class graph of some dihedral groups, generalized quaternion groups, quasidihedral groups and their eigenvalues are first computed. Then, the Laplacian energy of the graphs are determined.
{"title":"The Laplacian Energy of Conjugacy Class Graph of Some Finite Groups","authors":"Rabiha Mahmoud, Amira Fadina Ahmad Fadzil, N. Sarmin, A. Erfanian","doi":"10.11113/MATEMATIKA.V35.N1.1059","DOIUrl":"https://doi.org/10.11113/MATEMATIKA.V35.N1.1059","url":null,"abstract":"Let G be a dihedral group and its conjugacy class graph. The Laplacian energy of the graph, is defined as the sum of the absolute values of the difference between the Laplacian eigenvalues and the ratio of twice the edges number divided by the vertices number. In this research, the Laplacian matrices of the conjugacy class graph of some dihedral groups, generalized quaternion groups, quasidihedral groups and their eigenvalues are first computed. Then, the Laplacian energy of the graphs are determined.","PeriodicalId":43733,"journal":{"name":"Matematika","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2019-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47055101","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-04-01DOI: 10.11113/MATEMATIKA.V35.N1.1042
Manoj Kumar, Pratik Gupta
Signcryption schemes are compact and specially suited for efficiency-critical applications such as smart card dependent systems. Several researchers have performed a large number of significant applications of signcryption such as authenticated key recovery and key establishment in one mall data packet, secure ATM networks as well as light weight electronic transaction protocols and multi-casting over the internet. In this paper we have proposed an efficient and efficient scheme of signcryption symmetric key solutions, using elliptic curves by reducing senders computational cost. It needs two elliptic curve point multiplication for sender and comparative study of computational cost for sender and recipient as well as there is no any inverse computation for sender and recipient. This makes it more crucial than others.
{"title":"An Efficient and Authentication Signcryption Scheme Based on Elliptic Curves","authors":"Manoj Kumar, Pratik Gupta","doi":"10.11113/MATEMATIKA.V35.N1.1042","DOIUrl":"https://doi.org/10.11113/MATEMATIKA.V35.N1.1042","url":null,"abstract":"Signcryption schemes are compact and specially suited for efficiency-critical applications such as smart card dependent systems. Several researchers have performed a large number of significant applications of signcryption such as authenticated key recovery and key establishment in one mall data packet, secure ATM networks as well as light weight electronic transaction protocols and multi-casting over the internet. In this paper we have proposed an efficient and efficient scheme of signcryption symmetric key solutions, using elliptic curves by reducing senders computational cost. It needs two elliptic curve point multiplication for sender and comparative study of computational cost for sender and recipient as well as there is no any inverse computation for sender and recipient. This makes it more crucial than others.","PeriodicalId":43733,"journal":{"name":"Matematika","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2019-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43111661","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-04-01DOI: 10.11113/MATEMATIKA.V35.N1.1062
M. A. Tahan, B. Davvaz
Algebraic hyperstructures represent a natural extension of classical algebraic structures and they have many applications in various sciences. The main purpose of this paper is to provide a new application of $n$-ary weak hyperstructures in Chemistry. More precisely, we present three different examples of ternary hyperstructures associated with electrochemical cells. In which we prove that our defined hyperstructures are ternary $H_{v}$-semigroups.
{"title":"Electrochemical Cells as Experimental Verifications of n-ary Hyperstructures","authors":"M. A. Tahan, B. Davvaz","doi":"10.11113/MATEMATIKA.V35.N1.1062","DOIUrl":"https://doi.org/10.11113/MATEMATIKA.V35.N1.1062","url":null,"abstract":"Algebraic hyperstructures represent a natural extension of classical algebraic structures and they have many applications in various sciences. The main purpose of this paper is to provide a new application of $n$-ary weak hyperstructures in Chemistry. More precisely, we present three different examples of ternary hyperstructures associated with electrochemical cells. In which we prove that our defined hyperstructures are ternary $H_{v}$-semigroups.","PeriodicalId":43733,"journal":{"name":"Matematika","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2019-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45763396","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-04-01DOI: 10.11113/MATEMATIKA.V35.N1.1073
O. Babarinsa, H. Kamarulhaili
The proposed modified methods of Cramer's rule consider the column vector as well as the coefficient matrix concurrently in the linear system. The modified methods can be applied since Cramer's rule is typically known for solving the linear systems in $WZ$ factorization to yield Z-matrix. Then, we presented our results to show that there is no tangible difference in performance time between Cramer's rule and the modified methods in the factorization from improved versions of MATLAB. Additionally, the Frobenius norm of the modified methods in the factorization is better than using Cramer's rule irrespective of the version of MATLAB used.
{"title":"Modified Cramer’s Rule and its Application to Solve Linear Systems in WZ Factorization","authors":"O. Babarinsa, H. Kamarulhaili","doi":"10.11113/MATEMATIKA.V35.N1.1073","DOIUrl":"https://doi.org/10.11113/MATEMATIKA.V35.N1.1073","url":null,"abstract":"The proposed modified methods of Cramer's rule consider the column vector as well as the coefficient matrix concurrently in the linear system. The modified methods can be applied since Cramer's rule is typically known for solving the linear systems in $WZ$ factorization to yield Z-matrix. Then, we presented our results to show that there is no tangible difference in performance time between Cramer's rule and the modified methods in the factorization from improved versions of MATLAB. Additionally, the Frobenius norm of the modified methods in the factorization is better than using Cramer's rule irrespective of the version of MATLAB used.","PeriodicalId":43733,"journal":{"name":"Matematika","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2019-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46807787","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-04-01DOI: 10.11113/MATEMATIKA.V35.N1.1037
M. I. A. Aziz, N. Nasir, A. Banitalebi
Successful palm oil plantation should have high returns profit, clean and environmental friendly. Since oil palm trees have a long life and it takes years to be fully grown, controlling the felling rate of the palm oil trees is a fundamental challenge. It needs to be addressed in order to maximize oil production. However, a good arrangement of the felling palm oil trees may still affect the amount of carbon absorption. The objective of this study is to develop an optimal felling model of the palm oil plantation system taking into account both oil production and carbon absorption. The model facilitates in providing the optimal control of felling rate that results in maximizing both oil production and carbon absorption. With this aim, the model is formulated considering palm oil biomass, carbon absorption rate, oil production rate and the average prices of carbon and oil palm. A set of real data is used to estimate the parameters of the model and numerical simulation is conducted to highlight the application of the proposed model. The resulting parameter estimation is solved that leads to an optimal control of felling rate problem.
{"title":"The Optimal Felling Rate in the Palm Oil Plantation System","authors":"M. I. A. Aziz, N. Nasir, A. Banitalebi","doi":"10.11113/MATEMATIKA.V35.N1.1037","DOIUrl":"https://doi.org/10.11113/MATEMATIKA.V35.N1.1037","url":null,"abstract":"Successful palm oil plantation should have high returns profit, clean and environmental friendly. Since oil palm trees have a long life and it takes years to be fully grown, controlling the felling rate of the palm oil trees is a fundamental challenge. It needs to be addressed in order to maximize oil production. However, a good arrangement of the felling palm oil trees may still affect the amount of carbon absorption. The objective of this study is to develop an optimal felling model of the palm oil plantation system taking into account both oil production and carbon absorption. The model facilitates in providing the optimal control of felling rate that results in maximizing both oil production and carbon absorption. With this aim, the model is formulated considering palm oil biomass, carbon absorption rate, oil production rate and the average prices of carbon and oil palm. A set of real data is used to estimate the parameters of the model and numerical simulation is conducted to highlight the application of the proposed model. The resulting parameter estimation is solved that leads to an optimal control of felling rate problem.","PeriodicalId":43733,"journal":{"name":"Matematika","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2019-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48652847","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-04-01DOI: 10.11113/MATEMATIKA.V35.N1.1063
Vakkas Uluçay, A. Kılıç, M. Sahin, Harun Deniz
In recent times, refined neutrosophic sets introduced by Deli [6] has been one of the most powerful and flexible approaches for dealing with complex and uncertain situations of real world. In particular, the decision making methods between refined neutrosophic sets are important since it has applications in various areas such as image segmentation, decision making, medical diagnosis, pattern recognition and many more. The aim of this paper is to introduce a new distance-based similarity measure for refined neutrosophic sets. The properties of the proposed new distance-based similarity measure have been studied and the findings are applied in medical diagnosis of some diseases with a common set of symptoms.
{"title":"A New Hybrid Distance-Based Similarity Measure for Refined Neutrosophic sets and its Application in Medical Diagnosis","authors":"Vakkas Uluçay, A. Kılıç, M. Sahin, Harun Deniz","doi":"10.11113/MATEMATIKA.V35.N1.1063","DOIUrl":"https://doi.org/10.11113/MATEMATIKA.V35.N1.1063","url":null,"abstract":" In recent times, refined neutrosophic sets introduced by Deli [6] has been one of the most powerful and flexible approaches for dealing with complex and uncertain situations of real world. In particular, the decision making methods between refined neutrosophic sets are important since it has applications in various areas such as image segmentation, decision making, medical diagnosis, pattern recognition and many more. The aim of this paper is to introduce a new distance-based similarity measure for refined neutrosophic sets. The properties of the proposed new distance-based similarity measure have been studied and the findings are applied in medical diagnosis of some diseases with a common set of symptoms.","PeriodicalId":43733,"journal":{"name":"Matematika","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2019-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42980082","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2018-12-31DOI: 10.11113/MATEMATIKA.V34.N3.1146
A. I. Baqi, A. Nazra, Zulakmal Zulakmal, L. Yulianti, M. Muhafzan
It is well known the descriptor systems have a wide application field. Usually it appear as a mathematical model of a real problem, mainly the model that involves the input output relationship. It is well known that a descriptor linear system has an unique solution if the pencil matrix of the system is regular. However, there are some systems that are not regular. Moreover, even though the system is regular the solution can contain the noncausal behavior. Therefore, it is necessary to normalize the descriptor system so as it has well behavior. In this paper, we propose a feedback to normalize a discrete descriptor system under disturbance. Furthermore, we establish a sufficient condition in order for the discrete descriptor system under disturbance can be normalized positively.
{"title":"Positive Normalization of Discrete Descriptor System under Disturbance","authors":"A. I. Baqi, A. Nazra, Zulakmal Zulakmal, L. Yulianti, M. Muhafzan","doi":"10.11113/MATEMATIKA.V34.N3.1146","DOIUrl":"https://doi.org/10.11113/MATEMATIKA.V34.N3.1146","url":null,"abstract":"It is well known the descriptor systems have a wide application field. Usually it appear as a mathematical model of a real problem, mainly the model that involves the input output relationship. It is well known that a descriptor linear system has an unique solution if the pencil matrix of the system is regular. However, there are some systems that are not regular. Moreover, even though the system is regular the solution can contain the noncausal behavior. Therefore, it is necessary to normalize the descriptor system so as it has well behavior. In this paper, we propose a feedback to normalize a discrete descriptor system under disturbance. Furthermore, we establish a sufficient condition in order for the discrete descriptor system under disturbance can be normalized positively.","PeriodicalId":43733,"journal":{"name":"Matematika","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2018-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43044947","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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