scholarly journals Approximation schemes for knapsack problems with shelf divisions

2006 ◽  
Vol 352 (1-3) ◽  
pp. 71-84 ◽  
Author(s):  
E.C. Xavier ◽  
F.K. Miyazawa
Keyword(s):  
Knapsack Problems ◽  
Approximation Schemes

Parallel approximation schemes for Subset Sum and Knapsack problems

1987 ◽  
Vol 24 (4) ◽  
pp. 417-432 ◽  
Author(s):  
Joseph G. Peters ◽  
Larry Rudolph
Keyword(s):  
Knapsack Problems ◽  
Approximation Schemes ◽  
Subset Sum ◽  
Parallel Approximation

A Note on Approximation Schemes for Multidimensional Knapsack Problems

1984 ◽  
Vol 9 (2) ◽  
pp. 244-247 ◽  
Author(s):  
Michael J. Magazine ◽  
Maw-Sheng Chern
Keyword(s):  
Knapsack Problems ◽  
Approximation Schemes ◽  
Multidimensional Knapsack

Approximation schemes for r-weighted Minimization Knapsack problems

2018 ◽  
Vol 279 (1-2) ◽  
pp. 367-386
Author(s):  
Khaled Elbassioni ◽  
Areg Karapetyan ◽  
Trung Thanh Nguyen
Keyword(s):  
Knapsack Problems ◽  
Approximation Schemes

scholarly journals Approximation Schemes for Two Non-Linear Knapsack Problems and Their Applications in Alternating Current Electric Systems

2017 ◽  
Vol 33 (2) ◽  
pp. 165-179
Author(s):  
Thanh Nguyen
Keyword(s):  
Objective Function ◽  
Polynomial Time ◽  
Alternating Current ◽  
Knapsack Problems ◽  
Approximation Schemes ◽  
Programming Approach ◽  
Approximation Factor ◽  
Electrical Systems ◽  
Non Linear ◽  
Efficient Approximation

The purpose of this paper is to study the approximability of two non-linear Knapsack problems, which are motivated by important applications in alternating current electrical systems. The first problem is to maximize a nonnegative linear objective function subject to a quadratic constraint, whilst the second problem is a dual version of the first one, where an objective function is minimized. Both problems are $\np$-hard since they generalize the unbounded Knapsack problem, and it is unlikely to obtain polynomial-time algorithms for them, unless $\p=\np$. It is therefore of great interest to know whether or not there exist efficient approximation algorithms which can return an approximate solution in polynomial time with a reasonable approximation factor. Our contribution of this paper is to present polynomial-time approximation schemes (PTASs) and this is the best possible result one can hope for the studied problems. Our technique is based on the linear-programming approach which seems to be more simple and efficient than the previous one.

Modified adaptive genetic algorithms for solving 0/1 knapsack problems

2013 ◽  
Vol 32 (6) ◽  
pp. 1682-1684
Author(s):  
Na WANG ◽  
Feng-hong XIANG ◽  
Jian-lin MAO
Keyword(s):  
Genetic Algorithms ◽  
Knapsack Problems ◽  
Adaptive Genetic Algorithms

scholarly journals Solving knapsack problems using a binary gaining sharing knowledge-based optimization algorithm

2021 ◽  
Author(s):  
Prachi Agrawal ◽  
Talari Ganesh ◽  
Ali Wagdy Mohamed
Keyword(s):  
Life Span ◽  
Population Size ◽  
Linear Function ◽  
Optimization Algorithm ◽  
Optimization Problems ◽  
Search Space ◽  
Knapsack Problems ◽  
Local Optima ◽  
Knowledge Based ◽  
Two Stages

AbstractThis article proposes a novel binary version of recently developed Gaining Sharing knowledge-based optimization algorithm (GSK) to solve binary optimization problems. GSK algorithm is based on the concept of how humans acquire and share knowledge during their life span. A binary version of GSK named novel binary Gaining Sharing knowledge-based optimization algorithm (NBGSK) depends on mainly two binary stages: binary junior gaining sharing stage and binary senior gaining sharing stage with knowledge factor 1. These two stages enable NBGSK for exploring and exploitation of the search space efficiently and effectively to solve problems in binary space. Moreover, to enhance the performance of NBGSK and prevent the solutions from trapping into local optima, NBGSK with population size reduction (PR-NBGSK) is introduced. It decreases the population size gradually with a linear function. The proposed NBGSK and PR-NBGSK applied to set of knapsack instances with small and large dimensions, which shows that NBGSK and PR-NBGSK are more efficient and effective in terms of convergence, robustness, and accuracy.

scholarly journals Improvement Dependability of Offshore Horizontal-Axis Wind Turbines by Applying New Mathematical Methods for Calculation the Excess Speed in Case of Wind Gusts

Energies ◽  
2021 ◽  
Vol 14 (11) ◽  
pp. 3085
Author(s):  
Konstantin Osintsev ◽  
Seregei Aliukov ◽  
Alexander Shishkov
Keyword(s):  
Computer Simulation ◽  
Wind Turbines ◽  
Experimental Studies ◽  
Offshore Wind ◽  
Approximation Schemes ◽  
Calculation Error ◽  
Strong Wind ◽  
Mathematical Methods ◽  
Wind Gusts ◽  
Gas Dynamic

The problem of increasing the reliability of wind turbines exists in the development of new offshore oil and natural gas fields. Reducing emergency situations is necessary due to the autonomous operation of drilling rigs and bulk seaports in the subarctic and Arctic climate. The relevance of the topic is linked with the development of a methodology for theoretical and practical studies of gas dynamics when gas flows in a pipe, based on a mathematical model using new mathematical methods for calculation of excess speeds in case of wind gusts. Problems in the operation of offshore wind turbines arise with storm gusts of wind, which is comparable to the wave movement of the gas flow. Thus, the scientific problem of increasing the reliability of wind turbines in conditions of strong wind gusts is solved. The authors indicate a gross error in the calculations when approximating through the use of the Fourier series. The obtained results will allow us to solve one of the essential problems of modeling at this stage of its development, namely: to reduce the calculation time and the adequacy of the model built for similar installations and devices. Experimental studies of gas-dynamic flows are carried out on the example of a physical model of a wind turbine. In addition, a computer simulation of the gas-dynamic flow process was carried out. The use of new approximation schemes in processing the results of experiments and computer simulation can reduce the calculation error by 1.2 percent.

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