Discrete Particle Swarm Optimization in the numerical solution of a system of linear Diophantine equations
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| Format: | Artículo científico |
| Language: | en |
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Universidad Nacional de Colombia
2014
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| author | Iván Amaya |
| author_facet | Iván Amaya |
| contents | Discrete Particle Swarm Optimization in the numerical solution of a system of linear Diophantine equations Iván Amaya Luis Gómez Rodrigo Correa Ingeniería optimization particle swarm objective function Linear Diophantine equations This article proposes the use of a discrete version of the well known Particle Swarm Optimization, DPSO, a metaheuristic optimization algorithm for numerically solving a system of linear Diophantine equations. Likewise, the transformation of this type of problem (i.e. solving a system of equations) into an optimization one is also shown. The current algorithm is able to find all the integer roots in a given search domain, at least for the examples shown. Simple problems are used to show its efficacy. Moreover, aspects related to the processing time, as well as to the effect of increasing the population and the search space, are discussed. It was found that the strategy shown herein represents a good approach when dealing with systems that have more unknowns than equations, or when it becomes of considerable size, since a big search domain is required. 2014 artículo científico 0012-7353 https://www.redalyc.org/articulo.oa?id=49631031020 en http://www.redalyc.org/revista.oa?id=496 Dyna application/pdf Universidad Nacional de Colombia Dyna (Colombia) Num.185 Vol.81 |
| format | Artículo científico |
| id | redalyc_49631031020 |
| institution | Redalyc |
| language | en |
| publishDate | 2014 |
| publisher | Universidad Nacional de Colombia |
| spellingShingle | Discrete Particle Swarm Optimization in the numerical solution of a system of linear Diophantine equations Iván Amaya Ingeniería optimization particle swarm objective function Linear Diophantine equations Discrete Particle Swarm Optimization in the numerical solution of a system of linear Diophantine equations Iván Amaya Luis Gómez Rodrigo Correa Ingeniería optimization particle swarm objective function Linear Diophantine equations This article proposes the use of a discrete version of the well known Particle Swarm Optimization, DPSO, a metaheuristic optimization algorithm for numerically solving a system of linear Diophantine equations. Likewise, the transformation of this type of problem (i.e. solving a system of equations) into an optimization one is also shown. The current algorithm is able to find all the integer roots in a given search domain, at least for the examples shown. Simple problems are used to show its efficacy. Moreover, aspects related to the processing time, as well as to the effect of increasing the population and the search space, are discussed. It was found that the strategy shown herein represents a good approach when dealing with systems that have more unknowns than equations, or when it becomes of considerable size, since a big search domain is required. 2014 artículo científico 0012-7353 https://www.redalyc.org/articulo.oa?id=49631031020 en http://www.redalyc.org/revista.oa?id=496 Dyna application/pdf Universidad Nacional de Colombia Dyna (Colombia) Num.185 Vol.81 |
| title | Discrete Particle Swarm Optimization in the numerical solution of a system of linear Diophantine equations |
| topic | Ingeniería optimization particle swarm objective function Linear Diophantine equations |
| url | https://www.redalyc.org/articulo.oa?id=49631031020 |