Solution to the 0-1 Multidimensional Knapsack Problem Based on DNA Computation

We proposed a two-layer scheme of Deoxyribonucleic acid (DNA) based computation, DNA-01MKP, to solve the typical NP-hard combinatorial optimization problem, 0-1 multidimensional knapsack problem (0-1 MKP). DNA-01MKP consists of two layers of procedures: (1) translation of the problem equations to strands and (2) solution of problems. For layer 1, we designed flexible well-formatted strands to represent the problem equations; for layer 2, we constructed the DNA algorithms to solve the 0-1 MKP. Our results revealed that this molecular computation scheme is able to solve the complicated operational problem with a reasonable time complexity of O(n×k), though it needs further experimental verification in the future. By adjusting the DNA-based procedures, the scheme may be used to resolve different NP-hard problems.

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A Review and Comparison of Genetic Algorithms for the 0-1 Multidimensional Knapsack Problem

International Journal of Operations Research and Information Systems ◽

10.4018/ijoris.2015040102 ◽

2015 ◽

Vol 6 (2) ◽

pp. 21-31 ◽

Cited By ~ 4

Author(s):

Bernhard Lienland ◽

Li Zeng

Keyword(s):

Genetic Algorithm ◽

Genetic Algorithms ◽

Combinatorial Optimization ◽

Knapsack Problem ◽

Optimization Problem ◽

Real Life ◽

Combinatorial Optimization Problem ◽

Multidimensional Knapsack Problem ◽

Multidimensional Knapsack ◽

Problem Types

The 0-1 multidimensional knapsack problem (MKP) is a well-known combinatorial optimization problem with several real-life applications, for example, in project selection. Genetic algorithms (GA) are effective heuristics for solving the 0-1 MKP. Multiple individual GAs with specific characteristics have been proposed in literature. However, so far, these approaches have only been partially compared in multiple studies with unequal conditions. Therefore, to identify the “best” genetic algorithm, this article reviews and compares 11 existing GAs. The authors' tests provide detailed information on the GAs themselves as well as their performance. The authors validated fitness values and required computation times in varying problem types and environments. Results demonstrate the superiority of one GA.

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A Novel Evolutionary Algorithm for Multidimensional Knapsack Problem

International Journal of Operations Research and Information Systems ◽

10.4018/ijoris.2015040101 ◽

2015 ◽

Vol 6 (2) ◽

pp. 1-20 ◽

Cited By ~ 1

Author(s):

Sara Sabba ◽

Salim Chikhi

Keyword(s):

Knapsack Problem ◽

Optimization Problems ◽

Population Based ◽

Multidimensional Knapsack Problem ◽

Great Tendency ◽

Binary Optimization ◽

Local Optima ◽

Multidimensional Knapsack ◽

Hard Problems ◽

Complex Optimization

Binary optimization problems are in the most case the NP-hard problems that call to satisfy an objective function with or without constraints. Various optimization problems can be formulated in binary expression whither they can be resolved in easier way. Optimization literature supplies a large number of approaches to find solutions to binary hard problems. However, most population-based algorithms have a great tendency to be trapped in local optima particularly when solving complex optimization problems. In this paper, the authors introduce a new efficient population-based technique for binary optimization problems (that we called EABOP). The proposed algorithm can provide an effective search through a new proposed binary mutation operator. The performance of our approach was tested on hard instances of the multidimensional knapsack problem. The obtained results show that the new algorithm is able of quickly obtaining high-quality solutions for most hard instances of the problem.

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Optimization Method to Address Psychosocial Risks through Adaptation of the Multidimensional Knapsack Problem

Mathematics ◽

10.3390/math9101126 ◽

2021 ◽

Vol 9 (10) ◽

pp. 1126

Author(s):

Marta Lilia Eraña-Díaz ◽

Marco Antonio Cruz-Chávez ◽

Fredy Juárez-Pérez ◽

Juana Enriquez-Urbano ◽

Rafael Rivera-López ◽

...

Keyword(s):

Risk Factors ◽

Simulated Annealing ◽

Knapsack Problem ◽

Simulated Annealing Algorithm ◽

Psychosocial Risk Factors ◽

Psychosocial Risk ◽

Multidimensional Knapsack Problem ◽

Optimal Subset ◽

Multidimensional Knapsack ◽

A Company

This paper presents a methodological scheme to obtain the maximum benefit in occupational health by attending to psychosocial risk factors in a company. This scheme is based on selecting an optimal subset of psychosocial risk factors, considering the departments’ budget in a company as problem constraints. This methodology can be summarized in three steps: First, psychosocial risk factors in the company are identified and weighted, applying several instruments recommended by business regulations. Next, a mathematical model is built using the identified psychosocial risk factors information and the company budget for risk factors attention. This model represents the psychosocial risk optimization problem as a Multidimensional Knapsack Problem (MKP). Finally, since Multidimensional Knapsack Problem is NP-hard, one simulated annealing algorithm is applied to find a near-optimal subset of factors maximizing the psychosocial risk care level. This subset is according to the budgets assigned for each of the company’s departments. The proposed methodology is detailed using a case of study, and thirty instances of the Multidimensional Knapsack Problem are tested, and the results are interpreted under psychosocial risk problems to evaluate the simulated annealing algorithm’s performance (efficiency and efficacy) in solving these optimization problems. This evaluation shows that the proposed methodology can be used for the attention of psychosocial risk factors in real companies’ cases.

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