This paper represents a non linear bi-criterion generalized multi-index transportation problem (BGMTP) is considered. The generalized transportation problem (GTP) arises in many real-life applications. It has the form of a classical transportation problem, with the additional assumption that the quantities of goods change during the transportation process. Here the fuzzy constraints are used in the demand and in the budget. An efficient new solution procedure is developed keeping the budget as the first priority. All efficient time-cost trade-off pairs are obtained. D1-distance is calculated to each trade-off pair from the ideal solution. Finally optimum solution is reached by using D1-distance.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
Multi – Objective Two Stage Fuzzy Transportation Problem with Hexagonal Fuzzy...IJERA Editor
Fuzzy geometric programming approach is used to determine the optimal solution of a multi-objective two stage fuzzy transportation problem in which supplies, demands are hexagonal fuzzy numbers and fuzzy membership of the objective function is defined. This paper aims to find out the best compromise solution among the set of feasible solutions for the multi-objective two stage transportation problem. To illustrate the proposed method, example is used
The peer-reviewed International Journal of Engineering Inventions (IJEI) is started with a mission to encourage contribution to research in Science and Technology. Encourage and motivate researchers in challenging areas of Sciences and Technology.
New Method for Finding an Optimal Solution of Generalized Fuzzy Transportatio...BRNSS Publication Hub
In this paper, a proposed method, namely, zero average method is used for solving fuzzy transportation problems by assuming that a decision-maker is uncertain about the precise values of the transportation costs, demand, and supply of the product. In the proposed method, transportation costs, demand, and supply are represented by generalized trapezoidal fuzzy numbers. To illustrate the proposed method, a numerical example is solved. The proposed method is easy to understand and apply to real-life transportation problems for the decision-makers.
The paper talks about the pentagonal Neutrosophic sets and its operational law. The paper presents the cut of single valued pentagonal Neutrosophic numbers and additionally introduced the arithmetic operation of single-valued pentagonal Neutrosophic numbers. Here, we consider a transportation problem with pentagonal Neutrosophic numbers where the supply, demand and transportation cost is uncertain. Taking the benefits of the properties of ranking functions, our model can be changed into a relating deterministic form, which can be illuminated by any method. Our strategy is easy to assess the issue and can rank different sort of pentagonal Neutrosophic numbers. To legitimize the proposed technique, some numerical tests are given to show the adequacy of the new model.
Transportation Problem (TP) is an important network structured linear programming problem that arises in several contexts and has deservedly received a great deal of attention in the literature. The central concept in this problem is to find the least total transportation cost of a commodity in order to satisfy demands at destinations using available supplies at origins in a crisp environment. In real life situations, the decision maker may not be sure about the precise values of the coefficients belonging to the transportation problem. The aim of this paper is to introduce a formulation of TP involving Triangular fuzzy numbers for the transportation costs and values of supplies and demands. We propose a two-step method for solving fuzzy transportation problem where all of the parameters are represented by non-negative triangular fuzzy numbers i.e., an Interval Transportation Problems (TPIn) and a Classical Transport Problem (TP). Since the proposed approach is based on classical approach it is very easy to understand and to apply on real life transportation problems for the decision makers. To illustrate the proposed approach two application examples are solved. The results show that the proposed method is simpler and computationally more efficient than existing methods in the literature.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
Multi – Objective Two Stage Fuzzy Transportation Problem with Hexagonal Fuzzy...IJERA Editor
Fuzzy geometric programming approach is used to determine the optimal solution of a multi-objective two stage fuzzy transportation problem in which supplies, demands are hexagonal fuzzy numbers and fuzzy membership of the objective function is defined. This paper aims to find out the best compromise solution among the set of feasible solutions for the multi-objective two stage transportation problem. To illustrate the proposed method, example is used
The peer-reviewed International Journal of Engineering Inventions (IJEI) is started with a mission to encourage contribution to research in Science and Technology. Encourage and motivate researchers in challenging areas of Sciences and Technology.
New Method for Finding an Optimal Solution of Generalized Fuzzy Transportatio...BRNSS Publication Hub
In this paper, a proposed method, namely, zero average method is used for solving fuzzy transportation problems by assuming that a decision-maker is uncertain about the precise values of the transportation costs, demand, and supply of the product. In the proposed method, transportation costs, demand, and supply are represented by generalized trapezoidal fuzzy numbers. To illustrate the proposed method, a numerical example is solved. The proposed method is easy to understand and apply to real-life transportation problems for the decision-makers.
The paper talks about the pentagonal Neutrosophic sets and its operational law. The paper presents the cut of single valued pentagonal Neutrosophic numbers and additionally introduced the arithmetic operation of single-valued pentagonal Neutrosophic numbers. Here, we consider a transportation problem with pentagonal Neutrosophic numbers where the supply, demand and transportation cost is uncertain. Taking the benefits of the properties of ranking functions, our model can be changed into a relating deterministic form, which can be illuminated by any method. Our strategy is easy to assess the issue and can rank different sort of pentagonal Neutrosophic numbers. To legitimize the proposed technique, some numerical tests are given to show the adequacy of the new model.
Transportation Problem (TP) is an important network structured linear programming problem that arises in several contexts and has deservedly received a great deal of attention in the literature. The central concept in this problem is to find the least total transportation cost of a commodity in order to satisfy demands at destinations using available supplies at origins in a crisp environment. In real life situations, the decision maker may not be sure about the precise values of the coefficients belonging to the transportation problem. The aim of this paper is to introduce a formulation of TP involving Triangular fuzzy numbers for the transportation costs and values of supplies and demands. We propose a two-step method for solving fuzzy transportation problem where all of the parameters are represented by non-negative triangular fuzzy numbers i.e., an Interval Transportation Problems (TPIn) and a Classical Transport Problem (TP). Since the proposed approach is based on classical approach it is very easy to understand and to apply on real life transportation problems for the decision makers. To illustrate the proposed approach two application examples are solved. The results show that the proposed method is simpler and computationally more efficient than existing methods in the literature.
Biogeography Based Optimization (BBO) is a new evolutionary algorithm for global optimization that was introduced in
2008. BBO is an application of biogeography to evolutionary algorithms. Biogeography is the study of the distribution of biodiversity
over space and time. It aims to analyze where organisms live, and in what abundance. BBO has certain features in common with other population-based optimization methods. Like GA and PSO, BBO can share information between solutions. This makes BBO applicable to many of the same types of problems that GA and PSO are used for, including unimodal, multimodal and deceptive functions. This paper explains the methodology of application of BBO algorithm for the constrained task scheduling problems.
A New Method to Solving Generalized Fuzzy Transportation Problem-Harmonic Mea...AI Publications
Transportation Problem is one of the models in the Linear Programming problem. The objective of this paper is to transport the item from the origin to the destination such that the transport cost should be minimized, and we should minimize the time of transportation. To achieve this, a new approach using harmonic mean method is proposed in this paper. In this proposed method transportation costs are represented by generalized trapezoidal fuzzy numbers. Further comparative studies of the new technique with other existing algorithms are established by means of sample problems.
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.
In conventional transportation problem (TP), all the parameters are always certain. But, many of the real life situations in industry or organization, the parameters (supply, demand and cost) of the TP are not precise which are imprecise in nature in different factors like the market condition, variations in rates of diesel, traffic jams, weather in hilly areas, capacity of men and machine, long power cut, labourer’s over time work, unexpected failures in machine, seasonal changesandmanymore. Tocountertheseproblems,dependingonthenatureoftheparameters, theTPisclassifiedintotwocategoriesnamelytype-2andtype-4fuzzytransportationproblems (FTPs) under uncertain environment and formulates the problem and utilizes the trapezoidal fuzzy number (TrFN) to solve the TP. The existing ranking procedure of Liou and Wang (1992)isusedtotransformthetype-2andtype-4FTPsintoacrisponesothattheconventional method may be applied to solve the TP. Moreover, the solution procedure differs from TP to type-2 and type-4 FTPs in allocation step only. Therefore a simple and efficient method denoted by PSK (P. Senthil Kumar) method is proposed to obtain an optimal solution in terms of TrFNs. From this fuzzy solution, the decision maker (DM) can decide the level of acceptance for the transportation cost or profit. Thus, the major applications of fuzzy set theory are widely used in areas such as inventory control, communication network, aggregate planning, employment scheduling, and personnel assignment and so on.
Heptagonal Fuzzy Numbers by Max Min MethodYogeshIJTSRD
In this paper, we propose another methodology for the arrangement of fuzzy transportation problem under a fuzzy environment in which transportation costs are taken as fuzzy Heptagonal numbers. The fuzzy numbers and fuzzy values are predominantly used in various fields. Here, we are converting fuzzy Heptagonal numbers into crisp value by using range technique and then solved by the MAX MIN method for the transportation problem. M. Revathi | K. Nithya "Heptagonal Fuzzy Numbers by Max-Min Method" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-5 | Issue-3 , April 2021, URL: https://www.ijtsrd.com/papers/ijtsrd38280.pdf Paper URL: https://www.ijtsrd.com/mathemetics/applied-mathamatics/38280/heptagonal-fuzzy-numbers-by-maxmin-method/m-revathi
Phenomenological Decomposition Heuristics for Process Design Synthesis of Oil...Alkis Vazacopoulos
The processing of a raw material is a phenomenon that varies its quantity and quality along a specific network and logics and logistics to transform it into final products. To capture the production framework in a mathematical programming model, a full space formulation integrating discrete design variables and quantity-quality relations gives rise to large scale non-convex mixed-integer nonlinear models, which are often difficult to solve. In order to overcome this problem, we propose a phenomenological decomposition heuristic to solve separately in a first stage the quantity and logic variables in a mixed-integer linear model, and in a second stage the quantity and quality variables in a nonlinear programming formulation. By considering different fuel demand scenarios, the problem becomes a two-stage stochastic programming model, where nonlinear models for each demand scenario are iteratively restricted by the process design results. Two examples demonstrate the tailor-made decomposition scheme to construct the complex oil-refinery process design in a quantitative manner.
HOPX Crossover Operator for the Fixed Charge Logistic Model with Priority Bas...IJECEIAES
In this paper, we are interested to an important Logistic problem modelised us optimization problem. It is the fixed charge transportation problem (FCTP) where the aim is to find the optimal solution which minimizes the objective function containig two costs, variable costs proportional to the amount shipped and fixed cost regardless of the quantity transported. To solve this kind of problem, metaheuristics and evolutionary methods should be applied. Genetic algorithms (GAs) seem to be one of such hopeful approaches which is based both on probability operators (Crossover and mutation) responsible for widen the solution space. The different characteristics of those operators influence on the performance and the quality of the genetic algorithm. In order to improve the performance of the GA to solve the FCTP, we propose a new adapted crossover operator called HOPX with the priority-based encoding by hybridizing the characteristics of the two most performent operators, the Order Crossover (OX) and Positionbased crossover (PX). Numerical results are presented and discussed for several instances showing the performance of the developed approach to obtain optimal solution in reduced time in comparison to GAs with other crossover operators.
Algorithm Finding Maximum Concurrent Multicommodity Linear Flow with Limited ...IJCNCJournal
Graphs and extended networks are is powerful mathematical tools applied in many fields as transportation,
communication, informatics, economy, … Algorithms to find Maximum Concurrent Multicommodity Flow
with Limited Cost on extended traffic networks are introduced in the works we did. However, with those
algorithms, capacities of two-sided lines are shared fully for two directions. This work studies the more
general and practical case, where flows are limited to use two-sided lines with a single parameter called
regulating coefficient. The algorithm is presented in the programming language Java. The algorithm is
coded in programming language Java with extended network database in database management system
MySQL and offers exact results.
MULTIPROCESSOR SCHEDULING AND PERFORMANCE EVALUATION USING ELITIST NON DOMINA...ijcsa
Task scheduling plays an important part in the improvement of parallel and distributed systems. The problem of task scheduling has been shown to be NP hard. The time consuming is more to solve the problem in deterministic techniques. There are algorithms developed to schedule tasks for distributed environment, which focus on single objective. The problem becomes more complex, while considering biobjective.This paper presents bi-objective independent task scheduling algorithm using elitist Nondominated
sorting genetic algorithm (NSGA-II) to minimize the makespan and flowtime. This algorithm generates pareto global optimal solutions for this bi-objective task scheduling problem. NSGA-II is implemented by using the set of benchmark instances. The experimental result shows NSGA-II generates efficient optimal schedules.
Fast Algorithm for Computing the Discrete Hartley Transform of Type-IIijeei-iaes
The generalized discrete Hartley transforms (GDHTs) have proved to be an efficient alternative to the generalized discrete Fourier transforms (GDFTs) for real-valued data applications. In this paper, the development of direct computation of radix-2 decimation-in-time (DIT) algorithm for the fast calculation of the GDHT of type-II (DHT-II) is presented. The mathematical analysis and the implementation of the developed algorithm are derived, showing that this algorithm possesses a regular structure and can be implemented in-place for efficient memory utilization.The performance of the proposed algorithm is analyzed and the computational complexity is calculated for different transform lengths. A comparison between this algorithm and existing DHT-II algorithms shows that it can be considered as a good compromise between the structural and computational complexities.
Scaling Multinomial Logistic Regression via Hybrid ParallelismParameswaran Raman
Distributed algorithms in machine learning follow two main paradigms: data parallel, where the data is distributed across multiple workers and model parallel, where the model parameters are partitioned across multiple workers. The main limitation of the first approach is that the model parameters need to be replicated on every machine. This is problematic when the number of parameters is very large, and hence cannot fit in a single machine. The drawback of the latter approach is that the data needs to be replicated on each machine. Such replications limit the scalability of machine learning algorithms, since in several real-world tasks it is observed that the data and model sizes typically grow hand in hand. In this talk, I will present Hybrid-Parallelism, a new paradigm that partitions both, the data as well as the model parameters simultaneously in a completely de-centralized manner. As a result, each worker only needs access to a subset of the data and a subset of the parameters while performing parameter updates. Next, I will present a case-study showing how to apply these ideas to reformulate Multinomial Logistic Regression to achieve Hybrid Parallelism (DSMLR: Doubly-Separable Multinomial Logistic Regression). Finally, I will demonstrate the versatility of DS-MLR under various scenarios in data and model parallelism, through an empirical study consisting of real-world datasets.
A new transformation into State Transition Algorithm for finding the global m...Michael_Chou
To promote the global search ability of the original state transition algorithm, a new operator called axesion is suggested, which aims to search along the axes and strengthen single dimensional search. Several benchmark minimization
problems are used to illustrate the advantages of the improved algorithm over other random search methods. The results of
numerical experiments show that the new transformation can enhance the performance of the state transition algorithm and the new strategy is effective and reliable.
Direct split-radix algorithm for fast computation of type-II discrete Hartley...TELKOMNIKA JOURNAL
In this paper, a novel split-radix algorithm for fast calculation the discrete Hartley transform of type-II (DHT-II) is intoduced. The algorithm is established through the decimation in time (DIT) approach, and implementedby splitting a length N of DHT-II into one DHT-II of length N/2 for even-indexed samples and two DHTs-II of length N/4 for odd-indexed samples. The proposed algorithm possesses the desired properties such as regularity, inplace calculation and it is represented by simple closed form decomposition sleading to considerable reductions in the arithmetic complexity compared to the existing DHT-II algorithms. Additionally, the validity of the proposed algorithm has been confirmed through analysing the arithmetic complexityby calculating the number of real additions and multiplications and associating it with the existing DHT-II algorithms.
Stochastic fractal search based method for economic load dispatchTELKOMNIKA JOURNAL
This paper presents a nature-inspired meta-heuristic, called a stochastic fractal search based
method (SFS) for coping with complex economic load dispatch (ELD) problem. Two SFS methods are
introduced in the paper by employing two different random walk generators for diffusion process in which
SFS with Gaussian random walk is called SFS-Gauss and SFS with Levy Flight random walk is called
SFS-Levy. The performance of the two applied methods is investigated comparing results obtained from
three test system. These systems with 6, 10, and 20 units with different objective function forms and
different constraints are inspected. Numerical result comparison can confirm that the applied approach has
better solution quality and fast convergence time when compared with some recently published standard,
modified, and hybrid methods. This elucidates that the two SFS methods are very favorable for solving
the ELD problem.
Bi-objective Optimization Apply to Environment a land Economic Dispatch Probl...ijceronline
International Journal of Computational Engineering Research (IJCER) is dedicated to protecting personal information and will make every reasonable effort to handle collected information appropriately. All information collected, as well as related requests, will be handled as carefully and efficiently as possible in accordance with IJCER standards for integrity and objectivity.
Biogeography Based Optimization (BBO) is a new evolutionary algorithm for global optimization that was introduced in
2008. BBO is an application of biogeography to evolutionary algorithms. Biogeography is the study of the distribution of biodiversity
over space and time. It aims to analyze where organisms live, and in what abundance. BBO has certain features in common with other population-based optimization methods. Like GA and PSO, BBO can share information between solutions. This makes BBO applicable to many of the same types of problems that GA and PSO are used for, including unimodal, multimodal and deceptive functions. This paper explains the methodology of application of BBO algorithm for the constrained task scheduling problems.
A New Method to Solving Generalized Fuzzy Transportation Problem-Harmonic Mea...AI Publications
Transportation Problem is one of the models in the Linear Programming problem. The objective of this paper is to transport the item from the origin to the destination such that the transport cost should be minimized, and we should minimize the time of transportation. To achieve this, a new approach using harmonic mean method is proposed in this paper. In this proposed method transportation costs are represented by generalized trapezoidal fuzzy numbers. Further comparative studies of the new technique with other existing algorithms are established by means of sample problems.
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.
In conventional transportation problem (TP), all the parameters are always certain. But, many of the real life situations in industry or organization, the parameters (supply, demand and cost) of the TP are not precise which are imprecise in nature in different factors like the market condition, variations in rates of diesel, traffic jams, weather in hilly areas, capacity of men and machine, long power cut, labourer’s over time work, unexpected failures in machine, seasonal changesandmanymore. Tocountertheseproblems,dependingonthenatureoftheparameters, theTPisclassifiedintotwocategoriesnamelytype-2andtype-4fuzzytransportationproblems (FTPs) under uncertain environment and formulates the problem and utilizes the trapezoidal fuzzy number (TrFN) to solve the TP. The existing ranking procedure of Liou and Wang (1992)isusedtotransformthetype-2andtype-4FTPsintoacrisponesothattheconventional method may be applied to solve the TP. Moreover, the solution procedure differs from TP to type-2 and type-4 FTPs in allocation step only. Therefore a simple and efficient method denoted by PSK (P. Senthil Kumar) method is proposed to obtain an optimal solution in terms of TrFNs. From this fuzzy solution, the decision maker (DM) can decide the level of acceptance for the transportation cost or profit. Thus, the major applications of fuzzy set theory are widely used in areas such as inventory control, communication network, aggregate planning, employment scheduling, and personnel assignment and so on.
Heptagonal Fuzzy Numbers by Max Min MethodYogeshIJTSRD
In this paper, we propose another methodology for the arrangement of fuzzy transportation problem under a fuzzy environment in which transportation costs are taken as fuzzy Heptagonal numbers. The fuzzy numbers and fuzzy values are predominantly used in various fields. Here, we are converting fuzzy Heptagonal numbers into crisp value by using range technique and then solved by the MAX MIN method for the transportation problem. M. Revathi | K. Nithya "Heptagonal Fuzzy Numbers by Max-Min Method" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-5 | Issue-3 , April 2021, URL: https://www.ijtsrd.com/papers/ijtsrd38280.pdf Paper URL: https://www.ijtsrd.com/mathemetics/applied-mathamatics/38280/heptagonal-fuzzy-numbers-by-maxmin-method/m-revathi
Phenomenological Decomposition Heuristics for Process Design Synthesis of Oil...Alkis Vazacopoulos
The processing of a raw material is a phenomenon that varies its quantity and quality along a specific network and logics and logistics to transform it into final products. To capture the production framework in a mathematical programming model, a full space formulation integrating discrete design variables and quantity-quality relations gives rise to large scale non-convex mixed-integer nonlinear models, which are often difficult to solve. In order to overcome this problem, we propose a phenomenological decomposition heuristic to solve separately in a first stage the quantity and logic variables in a mixed-integer linear model, and in a second stage the quantity and quality variables in a nonlinear programming formulation. By considering different fuel demand scenarios, the problem becomes a two-stage stochastic programming model, where nonlinear models for each demand scenario are iteratively restricted by the process design results. Two examples demonstrate the tailor-made decomposition scheme to construct the complex oil-refinery process design in a quantitative manner.
HOPX Crossover Operator for the Fixed Charge Logistic Model with Priority Bas...IJECEIAES
In this paper, we are interested to an important Logistic problem modelised us optimization problem. It is the fixed charge transportation problem (FCTP) where the aim is to find the optimal solution which minimizes the objective function containig two costs, variable costs proportional to the amount shipped and fixed cost regardless of the quantity transported. To solve this kind of problem, metaheuristics and evolutionary methods should be applied. Genetic algorithms (GAs) seem to be one of such hopeful approaches which is based both on probability operators (Crossover and mutation) responsible for widen the solution space. The different characteristics of those operators influence on the performance and the quality of the genetic algorithm. In order to improve the performance of the GA to solve the FCTP, we propose a new adapted crossover operator called HOPX with the priority-based encoding by hybridizing the characteristics of the two most performent operators, the Order Crossover (OX) and Positionbased crossover (PX). Numerical results are presented and discussed for several instances showing the performance of the developed approach to obtain optimal solution in reduced time in comparison to GAs with other crossover operators.
Algorithm Finding Maximum Concurrent Multicommodity Linear Flow with Limited ...IJCNCJournal
Graphs and extended networks are is powerful mathematical tools applied in many fields as transportation,
communication, informatics, economy, … Algorithms to find Maximum Concurrent Multicommodity Flow
with Limited Cost on extended traffic networks are introduced in the works we did. However, with those
algorithms, capacities of two-sided lines are shared fully for two directions. This work studies the more
general and practical case, where flows are limited to use two-sided lines with a single parameter called
regulating coefficient. The algorithm is presented in the programming language Java. The algorithm is
coded in programming language Java with extended network database in database management system
MySQL and offers exact results.
MULTIPROCESSOR SCHEDULING AND PERFORMANCE EVALUATION USING ELITIST NON DOMINA...ijcsa
Task scheduling plays an important part in the improvement of parallel and distributed systems. The problem of task scheduling has been shown to be NP hard. The time consuming is more to solve the problem in deterministic techniques. There are algorithms developed to schedule tasks for distributed environment, which focus on single objective. The problem becomes more complex, while considering biobjective.This paper presents bi-objective independent task scheduling algorithm using elitist Nondominated
sorting genetic algorithm (NSGA-II) to minimize the makespan and flowtime. This algorithm generates pareto global optimal solutions for this bi-objective task scheduling problem. NSGA-II is implemented by using the set of benchmark instances. The experimental result shows NSGA-II generates efficient optimal schedules.
Fast Algorithm for Computing the Discrete Hartley Transform of Type-IIijeei-iaes
The generalized discrete Hartley transforms (GDHTs) have proved to be an efficient alternative to the generalized discrete Fourier transforms (GDFTs) for real-valued data applications. In this paper, the development of direct computation of radix-2 decimation-in-time (DIT) algorithm for the fast calculation of the GDHT of type-II (DHT-II) is presented. The mathematical analysis and the implementation of the developed algorithm are derived, showing that this algorithm possesses a regular structure and can be implemented in-place for efficient memory utilization.The performance of the proposed algorithm is analyzed and the computational complexity is calculated for different transform lengths. A comparison between this algorithm and existing DHT-II algorithms shows that it can be considered as a good compromise between the structural and computational complexities.
Scaling Multinomial Logistic Regression via Hybrid ParallelismParameswaran Raman
Distributed algorithms in machine learning follow two main paradigms: data parallel, where the data is distributed across multiple workers and model parallel, where the model parameters are partitioned across multiple workers. The main limitation of the first approach is that the model parameters need to be replicated on every machine. This is problematic when the number of parameters is very large, and hence cannot fit in a single machine. The drawback of the latter approach is that the data needs to be replicated on each machine. Such replications limit the scalability of machine learning algorithms, since in several real-world tasks it is observed that the data and model sizes typically grow hand in hand. In this talk, I will present Hybrid-Parallelism, a new paradigm that partitions both, the data as well as the model parameters simultaneously in a completely de-centralized manner. As a result, each worker only needs access to a subset of the data and a subset of the parameters while performing parameter updates. Next, I will present a case-study showing how to apply these ideas to reformulate Multinomial Logistic Regression to achieve Hybrid Parallelism (DSMLR: Doubly-Separable Multinomial Logistic Regression). Finally, I will demonstrate the versatility of DS-MLR under various scenarios in data and model parallelism, through an empirical study consisting of real-world datasets.
A new transformation into State Transition Algorithm for finding the global m...Michael_Chou
To promote the global search ability of the original state transition algorithm, a new operator called axesion is suggested, which aims to search along the axes and strengthen single dimensional search. Several benchmark minimization
problems are used to illustrate the advantages of the improved algorithm over other random search methods. The results of
numerical experiments show that the new transformation can enhance the performance of the state transition algorithm and the new strategy is effective and reliable.
Direct split-radix algorithm for fast computation of type-II discrete Hartley...TELKOMNIKA JOURNAL
In this paper, a novel split-radix algorithm for fast calculation the discrete Hartley transform of type-II (DHT-II) is intoduced. The algorithm is established through the decimation in time (DIT) approach, and implementedby splitting a length N of DHT-II into one DHT-II of length N/2 for even-indexed samples and two DHTs-II of length N/4 for odd-indexed samples. The proposed algorithm possesses the desired properties such as regularity, inplace calculation and it is represented by simple closed form decomposition sleading to considerable reductions in the arithmetic complexity compared to the existing DHT-II algorithms. Additionally, the validity of the proposed algorithm has been confirmed through analysing the arithmetic complexityby calculating the number of real additions and multiplications and associating it with the existing DHT-II algorithms.
Stochastic fractal search based method for economic load dispatchTELKOMNIKA JOURNAL
This paper presents a nature-inspired meta-heuristic, called a stochastic fractal search based
method (SFS) for coping with complex economic load dispatch (ELD) problem. Two SFS methods are
introduced in the paper by employing two different random walk generators for diffusion process in which
SFS with Gaussian random walk is called SFS-Gauss and SFS with Levy Flight random walk is called
SFS-Levy. The performance of the two applied methods is investigated comparing results obtained from
three test system. These systems with 6, 10, and 20 units with different objective function forms and
different constraints are inspected. Numerical result comparison can confirm that the applied approach has
better solution quality and fast convergence time when compared with some recently published standard,
modified, and hybrid methods. This elucidates that the two SFS methods are very favorable for solving
the ELD problem.
Bi-objective Optimization Apply to Environment a land Economic Dispatch Probl...ijceronline
International Journal of Computational Engineering Research (IJCER) is dedicated to protecting personal information and will make every reasonable effort to handle collected information appropriately. All information collected, as well as related requests, will be handled as carefully and efficiently as possible in accordance with IJCER standards for integrity and objectivity.
Non-convex constrained economic power dispatch with prohibited operating zone...IJECEIAES
This paper is focused on the solution of the non-convex economic power dispatch problem with piecewise quadratic cost functions and practical operation constraints of generation units. The constraints of the economic dispatch problem are power balance constraint, generation limits constraint, prohibited operating zones and transmission power losses. To solve this problem, a meta-heuristic optimization algorithm named crow search algorithm is proposed. A constraint handling technique is also implemented to satisfy the constraints effectively. For the verification of the effectiveness and the superiority of the proposed algorithm, it is tested on 6-unit, 10-unit and 15-unit test systems. The simulation results and statistical analysis show the efficiency of the proposed algorithm. Also, the results confirm the superiority and the high-quality solutions of the proposed algorithm when compared to the other reported algorithms.
Dynamic Economic Dispatch Assessment Using Particle Swarm Optimization TechniquejournalBEEI
This paper presents the application of particle swarm optimization (PSO) technique for solving the dynamic economic dispatch (DED) problem. The DED is one of the main functions in power system planning in order to obtain optimum power system operation and control. It determines the optimal operation of generating units at every predicted load demands over a certain period of time. The optimum operation of generating units is obtained by referring to the minimum total generation cost while the system is operating within its limits. The DED based PSO technique is tested on a 9-bus system containing of three generator bus, six load bus and twelve transmission lines.
Optimization of Corridor Observation Method to Solve Environmental and Econom...ijceronline
This paper presents an optimization of corridor observation method (COM) which is an applicable optimization algorithm based on the evolutionary algorithm to solve an environmental and economic Dispatch (EED) problem. This problem is seen like a bi-objective optimization problem where fuel cost and gas emission are objectives. In this method, the optimal Pareto front is found using the concept of corridor observation and the best compromised solution is obtained by fuzzy logic. The optimization of this method consists to find best parameters (number of corridor, number of initial population and number of generation) which improve solution and reduce a computational time. The simulated results using power system with different numbers of generation units showed that the new parameters ameliorate the solution keep her stability and reduce considerably the CPU time (time is minimum divide by 4) comparatively at parameterization with originals parameters.
This paper evokes the vehicle routing problem (VRP) which aims to determine the minimum total cost
pathways for a fleet of heterogeneous vehicles to deliver a set of customers' orders. The inability of
optimization algorithms alone to fully satisfy the needs of logistic managers become obvious in
transportation field due to the spatial nature of such problems. In this context, we couple a geographical
information system (GIS) with a metaheuristic to handle the VRP efficiently then generate a geographical
solution instead of the numerical solution. A real-case instance in a Tunisian region is studied in order to
test the proposed approach.
INTEGRATION OF GIS AND OPTIMIZATION ROUTINES FOR THE VEHICLE ROUTING PROBLEMijccmsjournal
This paper evokes the vehicle routing problem (VRP) which aims to determine the minimum total cost pathways for a fleet of heterogeneous vehicles to deliver a set of customers' orders. The inability of optimization algorithms alone to fully satisfy the needs of logistic managers become obvious in transportation field due to the spatial nature of such problems. In this context, we couple a geographical information system (GIS) with a metaheuristic to handle the VRP efficiently then generate a geographical solution instead of the numerical solution. A real-case instance in a Tunisian region is studied in order to
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ANALYSINBG THE MIGRATION PERIOD PARAMETER IN PARALLEL MULTI-SWARM PARTICLE SW...ijcsit
In recent years, there has been an increasing interest in parallel computing. In parallel computing, multiple
computing resources are used simultaneously in solving a problem. There are multiple processors that will
work concurrently and the program is divided into different tasks to be simultaneously solved. Recently, a
considerable literature has grown up around the theme of metaheuristic algorithms. Particle swarm
optimization (PSO) algorithm is a popular metaheuristic algorithm. The parallel comprehensive learning
particle swarm optimization (PCLPSO) algorithm based on PSO has multiple swarms based on the masterslave
paradigm and works cooperatively and concurrently. The migration period is an important parameter
in PCLPSO and affects the efficiency of the algorithm. We used the well-known benchmark functions in the
experiments and analysed the performance of PCLPSO using different migration periods.
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In this paper hybrid method, Modified Nondominated Sorted Genetic Algorithm (MNSGA-II) and Modified Population Variant Differential Evolution(MPVDE) have been placed in effect in achieving the best optimal solution of Multiobjective economic emission load dispatch optimization problem. In this technique latter, one is used to enforce the assigned percent of the population and the remaining with the former one. To overcome the premature convergence in an optimization problem diversity preserving operator is employed, from the tradeoff curve the best optimal solution is predicted using fuzzy set theory. This methodology validated on IEEE 30 bus test system with six generators, IEEE 118 bus test system with fourteen generators and with a forty generators test system. The solutions are dissimilitude with the existing metaheuristic methods like Strength Pareto Evolutionary Algorithm-II, Multiobjective differential evolution, Multiobjective Particle Swarm optimization, Fuzzy clustering particle swarm optimization, Nondominated sorting genetic algorithm-II.
EFFECTS OF THE DIFFERENT MIGRATION PERIODS ON PARALLEL MULTI-SWARM PSOcscpconf
In recent years, there has been an increasing interest in parallel computing. In parallel computing, multiple computing resources are used simultaneously in solving a problem. There are multiple processors that will work concurrently and the program is divided into different tasks to be simultaneously solved. Recently, a considerable literature has grown up around the theme of metaheuristic algorithms. Particle swarm optimization (PSO) algorithm is a popular metaheuristic algorithm. The parallel comprehensive learning particle swarm optimization (PCLPSO) algorithm based on PSO has multiple swarms based on the master-slave paradigm and works cooperatively and concurrently. The migration period is an important parameter in PCLPSO and affects the efficiency of the algorithm. We used the well-known benchmark functions in the experiments and analysed the performance of PCLPSO using different migration periods.
Effects of The Different Migration Periods on Parallel Multi-Swarm PSO csandit
In recent years, there has been an increasing inter
est in parallel computing. In parallel
computing, multiple computing resources are used si
multaneously in solving a problem. There
are multiple processors that will work concurrently
and the program is divided into different
tasks to be simultaneously solved. Recently, a cons
iderable literature has grown up around the
theme of metaheuristic algorithms. Particle swarm o
ptimization (PSO) algorithm is a popular
metaheuristic algorithm. The parallel comprehensive
learning particle swarm optimization
(PCLPSO) algorithm based on PSO has multiple swarms
based on the master-slave paradigm
and works cooperatively and concurrently. The migra
tion period is an important parameter in
PCLPSO and affects the efficiency of the algorithm.
We used the well-known benchmark
functions in the experiments and analysed the perfo
rmance of PCLPSO using different
migration periods.
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NO1 Uk best vashikaran specialist in delhi vashikaran baba near me online vas...Amil Baba Dawood bangali
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Author: Robbie Edward Sayers
Collaborators and co editors: Charlie Sims and Connor Healey.
(C) 2024 Robbie E. Sayers
Multi-Index Bi-Criterion Transportation Problem: A Fuzzy Approach
1. International Journal of Advanced Engineering, Management and Science (IJAEMS) [Vol-4, Issue-7, Jul- 2018]
https://dx.doi.org/10.22161/ijaems.4.7.8 ISSN: 2454-1311
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Multi-Index Bi-Criterion Transportation
Problem: A Fuzzy Approach
Dr. Samiran Senapati
Department of Mathematics, Nabadwip Vidyasagar College, Nadia, West Bengal, India
samiransenapati@yahoo.co.in
Abstract—This paper represents a non linear bi-criterion
generalized multi-index transportation problem (BGMTP)
is considered. The generalized transportation problem
(GTP) arises in many real-life applications. It has the form
of a classical transportation problem, with the additional
assumption that the quantities of goods change during the
transportation process. Here the fuzzy constraints are used
in the demand and in the budget. An efficient new solution
procedure is developed keeping the budget as the first
priority. All efficient time-cost trade-off pairs are obtained.
D1-distance is calculated to each trade-off pair from the
ideal solution.Finally optimum solution isreached by using
D1-distance.
Keywords— Time-cost trade-off pair, D1-distance, ideal
solution, membership function,
priority.
I. INTRODUCTION
The cost minimizing classical multi-index transportation
problems play important rule in practical problems. The
cost minimizing classical multi-index transportation
problems have been studied by several authors [14, 15, 16,
17] etc. Some times there may exist emergency situation eg
police services, time services, hospital management etc.
where time of transportation is of greater importance than
cost of transportation. In this situation, it is to be noted that
the cost as well as time play prominent roles to obtain the
best decision. Here the two aspects (ie cost and time) are
conflicting in nature. In general one can not simultaneously
minimize both of them. Bi-criterion transportation problem
have been studied by several authors [3, 4, 8, 17, 11] etc.
There are many business problems, industrial
problems, machine assignment problems, routing problems,
etc. that have the characteristic in common with generalized
transportation problem that have been studied by several
authors [1, 2, 4, 5, 9, 10, 14 ] etc.
In real world situation, most of the intimations are
imprecise in nature involving vagueness or to say fuzziness.
Precise mathematical model are not enough to tackle all
practical problems. Fuzzy set theory was developed for
solving the imprecise problems in the field of artificial
intelligence. To tackle this situation fuzzy set theory are
used. In this field area pioneer work came from Bellman
and Zadeh [6]. Fuzzy transportation problem have been
studied by several authors [12, 18, 19, 20, 21, 23, 24] etc.
The importance of fuzzy generalized multi-index
transportation problem is increasing in a great deal but the
method for finding time-cost trade-off pair in a bi-
criterion fuzzy generalized multi-index transportation
problem has been paid less attention. In this paper, we have
developed a new algorithm to find time-cost trade-off pair
of bi-criterion fuzzy generalized multi-index transportation
problem. Thereafter an optimum time-cost trade-off pair has
been obtained.
Problem Formulation:
Let there be m-origins, n-destinations and q-
products in a bi-criterion generalized multi-index fuzzy
transportation problem.
Let,
xijk = the amount of the k-th type of product
transported from the i-th origin to the j-th
destination,
tijk = the time of transporting the k-th type of
product from the i-th origin to the j-th
destination which is independent of
amount of commodity transported so long
as xijk > 0,
rijk = the cost involved in transporting per unit
of the k-th type of product from the i-th
origin to the j-th destination,
ai = number of units available at origin i,
bj = number of units required at the
destination j,
ck = requirements of the number of units of the
k-th type of product and
2
ijk
1
ijk d,d
= positive constants ratherthan unity,due to
2. International Journal of Advanced Engineering, Management and Science (IJAEMS) [Vol-4, Issue-7, Jul- 2018]
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generalized multi-index transportation
problem (GMTP).
Then the cost minimizing fuzzy GMTP can be formulated
as follows:
q)k1n,j1m,i(1;0)(x: ijk1 FindP
subject to the constraints,
1
m
1i
n
1j
q
1k
ijk
m
1i
n
1j
k
2
ijk
m
1i
q
1k
jijk
*
i
1 1
1
Zrand
1;cd
n,j1;b~x~
m,i1;a
ijk
ijk
j
n
j
q
k
ijkijk
x
qkx
b
xd
(1)
Some times there may arise emergency situation,
eg, hospital managements, fire services, police services etc.,
where the time of transportation is of greater importance
than that of cost. Then time minimizing transportation
problem arises. The time minimizing transportation problem
can be written as:
0x:tMaxTMin:P ijkijk
qk1
nj1
mi1
1
Subject to the constraints (1).
Combining the problem P1 and P1, the fuzzy BGMTP
appears as:
(1)}sconstraintsatisfiesxand0x:t{MaxFind:P ijkijkijk
qk1
nj1
mi1
subject to the constraints (1).
Difference between Classical Multi-index
Transportation Problem (MTP) and Generalized Multi-
index Transportation Problem (GMTP):
There are several important differences between
classical MTP and GMTP which are given below:
(i) The rank of the co-efficient matrix [xijk]m × n × q is in
general m + n + q rather than m + n + q - 2, ie, all the
constraints are in general independent.
(ii) In GMTP the value of xijk may not be integer, though it
is integer in classical MTP.
(iii) The activity vector in GMTP is
knmijkjmiijkijk edeedP 21
Whereas in classical MTP it is
knmjmiijk eeeP .
(iv) In GMTP it need not be true that cells corresponding to
a basic solution form a tree. Or in other words vectors in the
loop are linearly independent. But in classical MTP vectors
in the loop are linearly dependent.
The problem consists of two parts,
P1 : the problem of solving the fuzzy GMTP
P1 : the problem of minimizing the time.
To solve the problem P, the following technique is used.
The triangular membership function for the fuzzy
demand constraints are
m
1i
q
1k
*
ijk
m
1i
q
1k
*
ijk
1 1
**
j
1 1
*
1 1
**
j
1 1
*
x
andxif;0
;Bif;
)(
;Bif;
)(
)(
jj
jj
m
i
q
k
jjijk
j
m
i
q
k
ijkjj
m
i
q
k
jijkj
j
m
i
q
k
jjijk
j
bB
bB
bBx
b
xbB
Bxb
b
bBx
xD (2)
where
*
jb and bj
3. International Journal of Advanced Engineering, Management and Science (IJAEMS) [Vol-4, Issue-7, Jul- 2018]
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2
*
jj
j
bb
b
,
2
*
* jj
j
bb
B
The linear membership function of the fuzzy budget goal can be written as:
*if;0
,*Zif;
*Z
,rif;1
)(
1 1 1
1 1 1
1
1 1
m
1i
n
1j
q
1k
1ijk
m
i
n
j
q
k
ijkijk
m
i
n
j
q
k
ijkijk
m
i
n
j k
ijkijk
ijk
Zxr
Zxr
Z
xr
Zx
xR (3)
Where Z* is the upper tolerance limit of the budget goal and 1* ZZZ .
II. SOLUTION PROCEDURE
The fuzzy programming model of problem P1 is equivalent to the following linear programming problem as:
Max
subject to the constraints
[0,1]and
R(x)],(x)n,j1min[
R(x),
n,j1;)(
,1;cd
m,i1;a
m
1i
n
1j
k
2
ijk
i
1 1
1
j
j
ijk
n
j
q
k
ijkijk
D
xD
qkx
xd
(4)
After solving the problem the optimum solution
*
1X and the corresponding optimum cost
*
1Z at the first
iteration are obtained. Next the problem P1 is solved for
minimizing the time.
Let
,0: *
1
1
1
1
*
1 XxxtMaxMinT ijkijkijk
qk
nj
mi
subject to the constraints (1)
So, for the first iteration the time-cost trade-off
pair is ),( *
1
*
1 TZ . Using re-optimizing technique and
replacing Zr by Zr+1, (1 -1) where
r;*Z1 rr ZZ - 1. All efficient
time-cost trade-off pairs are obtained as:
),(......,),........,(.........,),........,(),,( *****
2
*
2
*
1
*
1 hhrr TZTZTZTZ
(say)
where
***
2
*
1 .................. hr ZZZZ
and
***
2
*
1 ............... hr TTTT
The pair ),( **
1 hTZ is termed as the ideal solution.
Let,
d **
rh
*
1
*
hr
rr
TT
ZZd
(5)
4. International Journal of Advanced Engineering, Management and Science (IJAEMS) [Vol-4, Issue-7, Jul- 2018]
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So,
r1
hr1
opt1 )D(Min)D(
)(
1
rhr
hr
ddMin
shs dd (say)
= (D1)s
Since equal priority to cost as well as time is given, so
),( **
ss TZ attains the optimum trade-off pair.
The Algorithm:
Step - 1: Set b = 1, where b is the number of iteration.
Step - 2: Solve problem P1. Let
*
1Z be the
optimum total cost corresponding to the
optimum solution
*
1X .
Step - 3: Find
*
1T
where,
}Xtoaccording0:{ *
1
1
1
1
*
1
ijkijk
qk
n
mi
xtMaxT
j
Then ),( *
1
*
1 TZ is called time-cost trade-
off pair at the first iteration.
Step - 4: Define
*
ijk
*
ijk1
tif
tif
bijk
bb
ijk
Tr
TM
r
and
m
i
n
j
q
k
ijk
b
ijkb ZxrZ
1 1 1
*1
1
Where Zb+1 > Zb
Where M is a sufficiently large positive
number. Let Pb+1 be the fuzzy GMTP with
the cost values
1b
ijkr , Zb +1 is the aspiration
level of cost and other constraints are
same as in (1).
Step - 5: Find optimum solution of the problemPb +
1. Let
*
1bZ be the total cost of problemPb
+ 1.
Step - 6: If ,*
1 MZb the algorithm terminates
and go to step 8 if b + 1 > 2 otherwise go
to step 10.
Otherwise in (b+1)th iteration the time-
cost trade-off pair is ),( *
1
*
1 bb TZ .
Obviously **
1 bb ZZ
and
**
1 bb TT .
Step - 7: Set b = b + 1 and go to step 4.
Step - 8: Let after the h-th step the algorithm
terminates, ie, MZh
*
1
, then the
complete set of time-cost trade-off pairs,
),(.........,),........,(..,..........),........,(),,( *****
2
*
2
*
1
*
1 hhrr TZTZTZTZ
is identified.
Among the trade-off pairs ),( **
1 hTZ is
recognized as the ideal solution.
Step - 9: Find r
hr
opt DMinD )()( 1
1
1
)(
1
rhr
hr
ddMin
= ds + dh + s (say)
Then ),( **
ss TZ offers the best
compromise solution.
Step - 10: If MZ 2 , ie, if h = 1, then
*
1Z is the
absolute minimum cost and
*
1T is the
absolute minimum time for the optimum
transportation plan.
Numerical Examples:
A manufacturing company produces three types of
products at two factories. They supply their products at four
destinations. The corresponding data are given in Table - 1.
Table – 1
a1 = 1300
a2 = 1200
250*
1 b , b1 = 300
c1 = 500
c2 = 1200
c3 = 1000
600*
2 b , b2 = 700
325*
3 b , b3 = 400
250*
1 b , b4 = 500
The proposed problem is explained by considering
problem, where 342
21
],,[ ijkijkijk rdd values and 342][ ijkt
values are given in Figure - 1 and Figure - 2 respectively.
6. International Journal of Advanced Engineering, Management and Science (IJAEMS) [Vol-4, Issue-7, Jul- 2018]
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Four time-cost trade-off pairs (1250, 70), (1275, 40), (1300, 35), (1310, 30) are obtained. The result shows that the ideal
solution is (1250, 30). The (D1) distance of the trade-off pairs from the ideal solution is presented in the Table - 2.
Table – 2
Trade-off
pairs
Ideal
Solution
Distance (D1)r between ideal
solution and the trade-off pair
(D1 )opt Optimum time-cost
trade-off pair
(1250, 70)
(1250, 30)
40
35 (1275, 40)(1275, 40) 35
(1300, 35) 55
(1310, 30) 60
Time - Cost Graph
So the optimum time-cost trade-off pair is (1275, 40).
REFERENCES
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0
5
10
15
20
25
30
35
40
45
50
55
60
65
70
75
1240 1250 1260 1270 1280 1290 1300 1310 1320
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Cost
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(1275, 40) Optimal Solution
(1300, 35)
(1310, 30)
(1250, 70)
7. International Journal of Advanced Engineering, Management and Science (IJAEMS) [Vol-4, Issue-7, Jul- 2018]
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