scholarly journals A Comprehensive Method for Arriving at Initial Feasible Solution for Optimization Problems in Engineering with Illustrative Examples

2021 ◽  
Vol 12 (5) ◽  
pp. 1189-1205
Author(s):  
Chandrasekhar Putcha, Et. al.
Keyword(s):  
Feasible Solution ◽  
Optimization Problems ◽  
Computer Software ◽  
Optimal Solution ◽  
Simplex Algorithm ◽  
The Other ◽  
Basic Feasible Solution ◽  
Adequate Number ◽  
Comprehensive Method ◽  
Initial Feasible Solution

Two methods have been used extensively for arriving at initial basic feasible solution (IBF). One of them is Northwest corner rule and the other on is Russell method (Hillier & Lieberman, 2005.) Both methods have drawbacks. The IBF obtained is either far from optimal solution or does not have adequate number of entries to initiate transportation simplex algorithm. The Northwest Corner rule gives an initial feasible solution that is far from optimal while the IBF solution obtained using Russell method doesn’t give enough number of entries to start the transportation simplex algorithm. Hence, there is a need for developing a method for arriving at initial basic feasible solution with adequate number of entries needed to initiate transportation simplex algorithm, which can then be used to get an optimal solution. A computer software has been developed based on the new proposed method for this purpose. The proposed new method has been validated through four simple but illustrative examples.

scholarly journals On the Simplex Algorithm Initializing

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
Nebojša V. Stojković ◽  
Predrag S. Stanimirović ◽  
Marko D. Petković ◽  
Danka S. Milojković
Keyword(s):  
Feasible Solution ◽  
Numerical Test ◽  
Optimal Solution ◽  
Simplex Algorithm ◽  
Initial Solution ◽  
Test Problems ◽  
Basic Feasible Solution ◽  
Cpu Time ◽  
Starting Point ◽  
Number Of Iterations

This paper discusses the importance of starting point in the simplex algorithm. Three different methods for finding a basic feasible solution are compared throughout performed numerical test examples. We show that our two methods on theNetlibtest problems have better performances than the classical algorithm for finding initial solution. The comparison of the introduced optimization softwares is based on the number of iterative steps and on the required CPU time. It is pointed out that on average it takes more iterations to determine the starting point than the number of iterations required by the simplex algorithm to find the optimal solution.

scholarly journals A New Technique for Solving Transportation Problems by Using Decomposition-Based Pricing and its Implementation in Real Life

2016 ◽  
Vol 64 (1) ◽  
pp. 45-50
Author(s):  
Sajal Chakroborty ◽  
M Babul Hasan
Keyword(s):  
Feasible Solution ◽  
Real Life ◽  
Optimal Solution ◽  
Computer Code ◽  
The Other ◽  
New Technique ◽  
Business Organization ◽  
Basic Feasible Solution ◽  
Transportation Problems ◽  
A New Technique

In this paper, we develop a new technique for solving transportation problems (TP) and develop a computer code by using mathematical programming language AMPL. There are many existing techniques for solving TP problems in use. By these techniques one has to determine initial basic feasible solution at first then improve this solution to determine optimal solution by another method. But this process is very lengthy and time consuming. By our technique we can determine optimal solution directly without determining initial basic feasible solution and optimal solution separately and we hope that this technique will provide an easier way than that of the other methods. We use the idea of decomposition based pricing (DBP) method to develop our technique. To our knowledge, there is no other paper which used DBP to solve TP. We demonstrate our technique by solving real life models developed by collecting data from a business organization of Bangladesh.Dhaka Univ. J. Sci. 64(1): 45-50, 2016 (January)

scholarly journals A New Method to Obtain an Initial Basic Feasible Solution of Transportation Problem with the Average Opportunity Cost Method

2019 ◽  
Vol 9 (2) ◽  
pp. 206-209
Keyword(s):  
Opportunity Cost ◽  
Transportation Problem ◽  
Feasible Solution ◽  
Optimal Solution ◽  
The Other ◽  
New Method ◽  
Basic Feasible Solution ◽  
Distribution Method

In this preset article, we have explained all new method to get Initial Basic Feasible solution (IBFS) of Transportation Problem (TP) with the Average Opportunity Cost Method (AOCM). It is very simple arithmetical and logical calculation.After finding the IBFS we use Modified Distribution Method (MODI) method to optimize the IBFS. Results obtained by using this method we found that IBFS of most of the transportation problem closer to optimal solution than using the other existing methods. We illustrate the same by suitable examples.

scholarly journals An evolutionary-based optimization algorithm for truss sizing design

2016 ◽  
Vol 38 (4) ◽  
pp. 307-317
Author(s):  
Pham Hoang Anh
Keyword(s):  
Local Search ◽  
Objective Function ◽  
Optimization Algorithm ◽  
Optimization Problems ◽  
Optimal Solution ◽  
The Other ◽  
Truss Structures ◽  
Benchmark Problems ◽  
Discrete Variables ◽  
Objective Functions

In this paper, the optimal sizing of truss structures is solved using a novel evolutionary-based optimization algorithm. The efficiency of the proposed method lies in the combination of global search and local search, in which the global move is applied for a set of random solutions whereas the local move is performed on the other solutions in the search population. Three truss sizing benchmark problems with discrete variables are used to examine the performance of the proposed algorithm. Objective functions of the optimization problems are minimum weights of the whole truss structures and constraints are stress in members and displacement at nodes. Here, the constraints and objective function are treated separately so that both function and constraint evaluations can be saved. The results show that the new algorithm can find optimal solution effectively and it is competitive with some recent metaheuristic algorithms in terms of number of structural analyses required.

scholarly journals Multiple infill criterion-assisted hybrid evolutionary optimization for medium-dimensional computationally expensive problems

2021 ◽  
Author(s):  
Shufen Qin ◽  
Chan Li ◽  
Chaoli Sun ◽  
Guochen Zhang ◽  
Xiaobo Li
Keyword(s):  
Evolutionary Algorithms ◽  
Optimization Problems ◽  
Optimal Solution ◽  
Global Search ◽  
Model Management ◽  
The Other ◽  
Local Searches ◽  
Fitness Value ◽  
Expensive Problems ◽  
Computationally Expensive

AbstractSurrogate-assisted evolutionary algorithms have been paid more and more attention to solve computationally expensive problems. However, model management still plays a significant importance in searching for the optimal solution. In this paper, a new method is proposed to measure the approximation uncertainty, in which the differences between the solution and its neighbour samples in the decision space, and the ruggedness of the objective space in its neighborhood are both considered. The proposed approximation uncertainty will be utilized in the surrogate-assisted global search to find a solution for exact objective evaluation to improve the exploration capability of the global search. On the other hand, the approximated fitness value is adopted as the infill criterion for the surrogate-assisted local search, which is utilized to improve the exploitation capability to find a solution close to the real optimal solution as much as possible. The surrogate-assisted global and local searches are conducted in sequence at each generation to balance the exploration and exploitation capabilities of the method. The performance of the proposed method is evaluated on seven benchmark problems with 10, 20, 30 and 50 dimensions, and one real-world application with 30 and 50 dimensions. The experimental results show that the proposed method is efficient for solving the low- and medium-dimensional expensive optimization problems by compared to the other six state-of-the-art surrogate-assisted evolutionary algorithms.

scholarly journals Enhancement of Security and Handling the Inconspicuousness in IoT Using a Simple Size Extensible Blockchain

Energies ◽  
2020 ◽  
Vol 13 (7) ◽  
pp. 1795 ◽  
Author(s):  
B. Saravana Balaji ◽  
P. Vishnu Raja ◽  
Anand Nayyar ◽  
P. Sanjeevikumar ◽  
Sanjeevi Pandiyan
Keyword(s):  
Smart Home ◽  
Feasible Solution ◽  
Optimal Solution ◽  
The Other ◽  
Extraction Operation ◽  
Distributed Environment ◽  
Blockchain Technology ◽  
Shared Time ◽  
Novel Algorithms ◽  
The Internet Of Things

Blockchain technology is increasingly used worldwide to enhance the performance and profit of any environment through its defining characteristics, such as security, auditability, immutability, and inconspicuousness. Owing to these characteristics, the blockchain can be used in various non-financial operations of some domains, such as the Internet of Things (IoT) and distributed computing. However, implementing blockchain technology in IoT is not always a feasible solution because blockchain deployment is costly, it has limited extensibility and provides irregular bandwidth and latency. In this regard, a simple size extensible (SSE) blockchain has been proposed to provide an optimal solution for IoT environments by satisfying the needs of the IoT environment as well as ensuring end-to-end security. The implementation of the proposed blockchain develops an overlay network to obtain a distributed environment where the blockchain is handled by the resources present therein. Two novel algorithms were introduced into the proposed system to minimize the irregularity and latency on one hand, and to maximize the throughput of the system on the other. The shared-time depending agreement algorithm (STD) minimizes the irregularity in the extraction operation and latency. The other, the shared throughput administration algorithm (STA) justifies the overall collection of the transmission load in the network and maintains the performance of the blockchain. The proposed system was applied to smart home IoT appliances to test the performance of the proposed system. The experimental results show that the proposed blockchain system minimizes nearly 70% of the data irregularity, latency, and furthermore, 30% of the blockchain extensibility is maximized as compared to the existing systems.

A NEURAL NETWORK IMPLEMENTATION FOR THE TRAFFIC CONTROL PROBLEM ON CROSSBAR SWITCH NETWORKS

1992 ◽  
Vol 03 (02) ◽  
pp. 209-218 ◽  
Author(s):  
K.T. Sun ◽  
H.C. Fu
Keyword(s):  
Neural Network ◽  
Control Problem ◽  
Energy Function ◽  
Traffic Control ◽  
Feasible Solution ◽  
Optimization Problems ◽  
Stable State ◽  
Optimal Solution ◽  
Neural Network Approach ◽  
Crossbar Switch

In this paper, we propose a neural network for the traffic control problem on crossbar switch networks. First, we represent this problem by an energy function, then apply the proposed neural network to update the state of the energy function until a stable state is reached. Within O(n) iteration steps, where n is the size of an n×n network, the energy function reaches a stable state which corresponds to a feasible solution of the traffic control problem. Also, the simulation results show that our neural network generates either optimal or near optimal solutions. Based on our neural network approach, many problems of applying neural networks to optimization problems are overcome, for example, the unpredictable converging time to reach a stable state, the probability of converging to a local minimum which corresponds to an invalid solution and the selecting of proper parameters of an energy function for obtaining a good (near optimal) solution, etc.

scholarly journals PENYELESAIAN MODEL TRANSPORTASI MENGGUNAKAN METODE ASM

2020 ◽  
Vol 14 (1) ◽  
pp. 40
Author(s):  
Nurul Iftitah ◽  
Pardi Affandi ◽  
Akhmad Yusuf
Keyword(s):  
Transportation Problem ◽  
Feasible Solution ◽  
Direct Method ◽  
Optimal Solution ◽  
Transportation Model ◽  
Initial Feasible Solution ◽  
The Cost

(demand). the method that could be used for solving the transportation problem is to directly find the optimal solution. The direct method that used in this study id the ASM method for solving the balance transportation problem and revised ASM method for solving the unbalance transportation problem. This study aims to construct a transportation model using those methods and it solution. The method on this study is to identify the transportation model, construct the transportation model matrixes, construct an algorithm table using ASM method and to determine the optimal solution of the transportation problem. The obtained result from this study was the model ASM method could determine the optimum value without using initial feasible solution. On solving the unbalance transportation problem, there is an addition of dummy cell or column step. Then reducing the cost of cell and column and change the dummy cost with the biggest cost of reduced cell or column.

scholarly journals Fundamentals of Transportation Problem

2021 ◽  
Vol 10 (5) ◽  
pp. 90-103
Author(s):  
Bhabani Mallia ◽  
Manjula Das ◽  
C. Das
Keyword(s):  
Linear Programming ◽  
Programming Problem ◽  
Linear Programming Problem ◽  
Transportation Problem ◽  
Feasible Solution ◽  
Optimal Solution ◽  
Optimal Solutions ◽  
Basic Feasible Solution ◽  
Distribution Method

Transportation Problem is a linear programming problem. Like LPP, transportation problem has basic feasible solution (BFS) and then from it we obtain the optimal solution. Among these BFS the optimal solution is developed by constructing dual of the TP. By using complimentary slackness conditions the optimal solutions is obtained by the same iterative principle. The method is known as MODI (Modified Distribution) method. In this paper we have discussed all the aspect of transportation problem.

scholarly journals Optimization of Fuzzy Species Pythagorean Transportation Problem under Preserved Uncertainties

2021 ◽  
Vol 6 (6) ◽  
pp. 1629-1645
Author(s):  
Priyanka Nagar ◽  
Pankaj Kumar Srivastava ◽  
Amit Srivastava
Keyword(s):  
Transportation Problem ◽  
Feasible Solution ◽  
Optimal Solution ◽  
Uncertain Parameters ◽  
Optimal Solutions ◽  
Basic Feasible Solution ◽  
Distribution Method ◽  
New Approach ◽  
Work Done ◽  
Cost Of Transportation

The transportation of big species is essential to rescue or relocate them and it requires the optimized cost of transportation. The present study brings out an optimized way to handle a special class of transportation problem called the Pythagorean fuzzy species transportation problem. To deal effectively with uncertain parameters, a new method for finding the initial fuzzy basic feasible solution (IFBFS) has been developed and applied. To test the optimality of the solutions obtained, a new approach named the Pythagorean fuzzy modified distribution method is developed. After reviewing the literature, it has been observed that till now the work done on Pythagorean fuzzy transportation problems is solely based on defuzzification techniques and so the optimal solutions obtained are in crisp form only. However, the proposed study is focused to get the optimal solution in its fuzzy form only. Getting results in the fuzzy form will lead to avoid any kind of loss of information during the defuzzification process. A comparative study with other defuzzification-based methods has been done to validate the proposed approach and it confirms the utility of the proposed methodology.

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