Molecular solution to the 0–1 knapsack problem based on DNA computing

Darehmiraki, Majid; Nehi, Hassan Mishmast

doi:10.1016/j.amc.2006.09.020

Cited by 35 publications

(9 citation statements)

References 3 publications

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“…et al [5] described an algorithm which generated an optimal solution for the 0-1 integer knapsack problem based on DNA computing. Hsieh et al [6] presented DNA-based algorithms to solve the graph isomorphism problem using a polynomial number of basic biological operations.…”

Section: Introductionmentioning

confidence: 99%

A DNA sticker algorithm for bit-substitution in a block cipher

Geng¹,

Pan²,

Xu³

2008

Journal of Parallel and Distributed Computing

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Section: Introductionmentioning

confidence: 99%

A DNA sticker algorithm for bit-substitution in a block cipher

Geng¹,

Pan²,

Xu³

2008

Journal of Parallel and Distributed Computing

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“…Previous researchers have attempted to address the BKP with exact and approximate algorithms [3], [2], [4], [5], [6], [7]. Also, in order to facilitate the study of new algorithmic proposals, a classification study was developed to encompass multiple problem situations with different profit/weight relations [2].…”

Section: Introductionmentioning

confidence: 99%

Automatic generation of algorithms for the binary knapsack problem

Parada

Sepúlveda

Herrera

et al. 2013

2013 IEEE Congress on Evolutionary Computation

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Because it is classified as NP-hard, the binary knapsack problem is a good example of a combinatorial optimization problem that still presents increased difficulty when attempting to determine the optimal solution for any instance. Although exact and heuristic methods have been developed in an attempt to solve the problem, such methods have been unable to solve even small instances of the problem. In this paper, new algorithms for this problem are automatically generated by means of genetic programming from sets of training instances of different sizes and are then evaluated against other larger sized sets of instances, thereby detecting the robustness of the algorithms for larger instances. Overall, the produced algorithms are able to identify up to 52% of the optimal solutions for the biggest instances used.

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“…In the last years, numerous works on solving hard computational problems via DNA computing were published: Travelling salesman problem [3], Maximal clique [4] [5], Maximal weight clique [6], [7] SAT [2] [8], k-SAT [9], Knapsack [10][11] ... etc. To the best of our knowledge, there is no published study dealing with MAX-W-SAT problem and we think this present work is the first one that addresses this problem and adapts it to MAX-SAT problem.…”

Section: Introductionmentioning

confidence: 99%

DNA based algorithms for solving both MAX-SAT and MAX-W-SAT problems

Sadeg

Drias

Aid

et al. 2010

2010 IEEE Fifth International Conference on Bio-Inspired Computing: Theories and Applications (BIC-TA)

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In this paper, we propose three DNA algorithms for the weighted maximum satisfiability problem (MAX-W-SAT for short). The first one is an extension of Lipton's algorithm for SAT. The space solution is represented by a graph and the weights are encoded in form of pieces which are appended to the double strands representing the solutions. The second algorithm proposes a different encoding of information (clauses and weights) aiming at reducing the quantity of DNA required, and the last one proposes to represent all the weights by fixed length DNA sequences and using molecular beacons to access them. The designed algorithms solve MAX-SAT problem by assuming all the clauses having the same weight.

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Molecular solution to the 0–1 knapsack problem based on DNA computing

Cited by 35 publications

References 3 publications

A DNA sticker algorithm for bit-substitution in a block cipher

A DNA sticker algorithm for bit-substitution in a block cipher

Automatic generation of algorithms for the binary knapsack problem

DNA based algorithms for solving both MAX-SAT and MAX-W-SAT problems

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