scholarly journals Minimum-Energy Wireless Real-Time Multicast by Joint Network Coding and Scheduling Optimization

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Guoping Tan ◽  
Yandan Zhu ◽  
Yueheng Li ◽  
Lili Zhang ◽  
Jing Xu
Keyword(s):  
Linear Programming ◽  
Network Coding ◽  
Programming Problem ◽  
Real Time ◽  
Linear Programming Problem ◽  
Minimum Energy ◽  
Conflict Graph ◽  
Subgradient Optimization ◽  
Primal Dual ◽  
Multicast Services

For real-time multicast services over wireless multihop networks, to minimize the energy of transmissions with satisfying the requirements of a fixed data rate and high reliabilities, we construct a conflict graph based framework by joint optimizing network coding and scheduling. Then, we propose a primal-dual subgradient optimization algorithm by random samplingKmaximal stable sets in a given conflict graph. This method transforms the NP-hard scheduling subproblem into a normal linear programming problem to obtain an approximate solution. The proposed algorithm only needs to adopt centralized technique for solving the linear programming problem while all of the other computations can be distributed. The simulation results show that, comparing with the existing algorithm, this algorithm can not only achieve about 20% performance gain, but also have better performance in terms of convergence and robustness.

scholarly journals UNBELIEVABLE O(L^1.5) WORST CASE COMPUTATIONAL COMPLEXITY ACHIEVED BY spdspds ALGORITHM FOR LINEAR PROGRAMMING PROBLEM

2021 ◽  
Author(s):  
KESHAVA PRASAD HALEMANE
Keyword(s):  
Linear Programming ◽  
Computational Complexity ◽  
Programming Problem ◽  
Linear Programming Problem ◽  
Decision Strategy ◽  
Worst Case ◽  
Wide Range ◽  
Primal Dual ◽  
Pivot Selection ◽  
Optimum Solution

The Symmetric Primal-Dual Symplex Pivot Decision Strategy (spdspds) is a novel iterative algorithm to solve linear programming problems. Here, a symplex pivoting operation is considered simply as an exchange between a basic (dependent) variable and a non-basic (independent) variable, in the Tucker's Compact Symmetric Tableau (CST) which is a unique symmetric representation common to both the primal as well as the dual of a linear programming problem in its standard canonical form. From this viewpoint, the classical simplex pivoting operation of Dantzig may be considered as a restricted special case. The infeasibility index associated with a symplex tableau is defined as the sum of the number of primal variables and the number of dual variables, which are infeasible. A measure of goodness as a global effectiveness measure of a pivot selection is defined/determined as/by the decrease in the infeasibility index associated with such a pivot selection. At each iteration the selection of the symplex pivot element is governed by the anticipated decrease in the infeasibility index - seeking the best possible decrease in the infeasibility index - from among a wide range of candidate choices with non-zero values - limited only by considerations of potential numerical instability. The algorithm terminates when further reduction in the infeasibility index is not possible; then the tableau is checked for the terminal tableau type to facilitate the problem classification - a termination with an infeasibility index of zero indicates optimum solution. The worst case computational complexity of spdspds is shown to be O(L^1.5).

scholarly journals A comparative study on interval arithmetic operations with intuitionistic fuzzy numbers for solving an intuitionistic fuzzy multi–objective linear programming problem

2017 ◽  
Vol 27 (3) ◽  
pp. 563-573 ◽  
Author(s):  
Rajendran Vidhya ◽  
Rajkumar Irene Hepzibah
Keyword(s):  
Linear Programming ◽  
Programming Problem ◽  
Linear Programming Problem ◽  
Fuzzy Numbers ◽  
Optimization Method ◽  
Arithmetic Operations ◽  
Intuitionistic Fuzzy Numbers ◽  
Multi Objective ◽  
Intuitionistic Fuzzy ◽  
Interval Valued

AbstractIn a real world situation, whenever ambiguity exists in the modeling of intuitionistic fuzzy numbers (IFNs), interval valued intuitionistic fuzzy numbers (IVIFNs) are often used in order to represent a range of IFNs unstable from the most pessimistic evaluation to the most optimistic one. IVIFNs are a construction which helps us to avoid such a prohibitive complexity. This paper is focused on two types of arithmetic operations on interval valued intuitionistic fuzzy numbers (IVIFNs) to solve the interval valued intuitionistic fuzzy multi-objective linear programming problem with pentagonal intuitionistic fuzzy numbers (PIFNs) by assuming differentαandβcut values in a comparative manner. The objective functions involved in the problem are ranked by the ratio ranking method and the problem is solved by the preemptive optimization method. An illustrative example with MATLAB outputs is presented in order to clarify the potential approach.

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