scholarly journals A Faster FPTAS for Knapsack Problem with Cardinality Constraint

2021 ◽  
pp. 16-29
Author(s):  
Wenxin Li ◽  
Joohyun Lee ◽  
Ness Shroff
Keyword(s):  
Knapsack Problem ◽  
Cardinality Constraint

scholarly journals On the rectangular knapsack problem: approximation of a specific quadratic knapsack problem

2020 ◽  
Vol 92 (1) ◽  
pp. 107-132 ◽  
Author(s):  
Britta Schulze ◽  
Michael Stiglmayr ◽  
Luís Paquete ◽  
Carlos M. Fonseca ◽  
David Willems ◽  
...  
Keyword(s):  
Knapsack Problem ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Approximation Ratio ◽  
Experimental Results ◽  
Cardinality Constraint ◽  
Quadratic Knapsack Problem ◽  
Problem Instances ◽  
Quadratic Knapsack ◽  
Special Case

Abstract In this article, we introduce the rectangular knapsack problem as a special case of the quadratic knapsack problem consisting in the maximization of the product of two separate knapsack profits subject to a cardinality constraint. We propose a polynomial time algorithm for this problem that provides a constant approximation ratio of 4.5. Our experimental results on a large number of artificially generated problem instances show that the average ratio is far from theoretical guarantee. In addition, we suggest refined versions of this approximation algorithm with the same time complexity and approximation ratio that lead to even better experimental results.

A core approach to the 0 –1 equality knapsack problem

1998 ◽  
Vol 49 (1) ◽  
pp. 86-92
Author(s):  
A Volgenant ◽  
S Marsman
Keyword(s):  
Knapsack Problem

Recycling Lethal Chromosomes Based on Immune Operation in Genetic Algorithm for Multi-Knapsack Problem

2014 ◽  
Vol 1 ◽  
pp. 219-222
Author(s):  
Jing Guo ◽  
Jousuke Kuroiwa ◽  
Hisakazu Ogura ◽  
Izumi Suwa ◽  
Haruhiko Shirai ◽  
...  
Keyword(s):  
Genetic Algorithm ◽  
Knapsack Problem

An enhanced binary slime mould algorithm for solving the 0–1 knapsack problem

2021 ◽  
Author(s):  
Benyamin Abdollahzadeh ◽  
Saeid Barshandeh ◽  
Hatef Javadi ◽  
Nicola Epicoco
Keyword(s):  
Knapsack Problem ◽  
Slime Mould

scholarly journals ACO with Intuitionistic Fuzzy Pheromone Updating Applied on Multiple-Constraint Knapsack Problem

Mathematics ◽  
2021 ◽  
Vol 9 (13) ◽  
pp. 1456
Author(s):  
Stefka Fidanova ◽  
Krassimir Todorov Atanassov
Keyword(s):  
Decision Making ◽  
Knapsack Problem ◽  
Propositional Logic ◽  
Optimization Problems ◽  
Real Life ◽  
Combinatorial Optimization Problems ◽  
Intuitionistic Fuzzy ◽  
Life Problems ◽  
Multiple Constraint

Some of industrial and real life problems are difficult to be solved by traditional methods, because they need exponential number of calculations. As an example, we can mention decision-making problems. They can be defined as optimization problems. Ant Colony Optimization (ACO) is between the best methods, that solves combinatorial optimization problems. The method mimics behavior of the ants in the nature, when they look for a food. One of the algorithm parameters is called pheromone, and it is updated every iteration according quality of the achieved solutions. The intuitionistic fuzzy (propositional) logic was introduced as an extension of Zadeh’s fuzzy logic. In it, each proposition is estimated by two values: degree of validity and degree of non-validity. In this paper, we propose two variants of intuitionistic fuzzy pheromone updating. We apply our ideas on Multiple-Constraint Knapsack Problem (MKP) and compare achieved results with traditional ACO.

A Polynomial-Time Algorithm for the Knapsack Problem with Two Variables

1976 ◽  
Vol 23 (1) ◽  
pp. 147-154 ◽  
Author(s):  
D. S. Hirschberg ◽  
C. K. Wong
Keyword(s):  
Polynomial Time ◽  
Knapsack Problem ◽  
Polynomial Time Algorithm ◽  
Time Algorithm
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