Singular optimal control for stochastic linear quadratic singular system using ant colony programming

Kumaresan, N.; Balasubramaniam, P.

doi:10.1080/00207160903026634

Cited by 6 publications

(4 citation statements)

References 17 publications

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“…The ant colony programming (ACP) is a stochastic approach which is implemented on a space graph [13]. This consists of the variables, functions and constants which is represented by the nodes.…”

Section: Ant Colony Programmingmentioning

confidence: 99%

“…The inclusion of this two new properties are vital in order to differentiate with the use of multiplication symbol '*'. In the work reported by Kumaresan and co-workers [13], the '*' symbol is used not only for representing multiply operations but also for showing the implementations of bracket in the expressions. For example, the tour of an ant which generated an expression: e * t + 1 * + 5 is actually representing an equation e(t+1)+5.…”

Section: Tours Of Antsmentioning

confidence: 99%

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Solving differential equations with ant colony programming

Kamali

Kumaresan

Ratnavelu

2015

Applied Mathematical Modelling

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Differential equations are widely used to model physical phenomena in the real world. In the present work, a nontraditional modified ant colony programming (ACP) method is implemented. The modified ACP algorithm is unique as it does not use the criteria of distance. It utilizes the probability function which related to the quantity of the pheromone level in the ACP.The motivation in this present work is to describe the consistency and the applicability of the nontraditional ant colony programming (ACP) method in solving various ordinary differential equations (ODE's) and partial differential equations (PDE's) problems. Comparatively, similar and exact solution is achieved by using the ACP approach. Illustrative numerical example as well as tables are presented for comparison purpose.

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Section: Ant Colony Programmingmentioning

confidence: 99%

Section: Tours Of Antsmentioning

confidence: 99%

Solving differential equations with ant colony programming

Kamali

Kumaresan

Ratnavelu

2015

Applied Mathematical Modelling

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“…Kumaresan applied the ACP expression approach to optimal control and modeling. 14,56,57,58 To obtain optimal control, AP is in charge of solving differential algebraic equations to compute the matrix Ricatti differential equation, which is the central issue in optimal control theory. The solution obtained by using the proposed method was very close to the exact solution of the problem.…”

Section: Ant Programmingmentioning

confidence: 99%

Swarm‐based metaheuristics in automatic programming: a survey

Olmo

Romero

Ventura

2014

WIREs Data Min & Knowl

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On the one hand, swarm intelligence (SI) is an emerging field of artificial intelligence that takes inspiration in the collective and social behavior of different groups of simple agents. On the other hand, the automatic evolution of programs is an active research area that has attracted a lot of interest and has been mostly promoted by the genetic programming paradigm. The main objective is to find computer programs from a high‐level problem statement of what needs to be done, without needing to know the structure of the solution beforehand. This paper looks at the intersection between SI and automatic programming, providing a survey on the state‐of‐the‐art of the automatic programming algorithms that use an SI metaheuristic as the search technique. The expression of swarm programming (SP) has been coined to cover swarm‐based automatic programming proposals, since they have been published to date in a disorganized manner. Open issues for future research are listed. Although it is a very recent area, we hope that this work will stimulate the interest of the research community in the development of new SP metaheuristics, algorithms, and applications. WIREs Data Mining Knowl Discov 2014, 4:445–469. doi: 10.1002/widm.1138 This article is categorized under: Algorithmic Development > Association Rules Technologies > Classification Technologies > Computational Intelligence

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“…ACP algorithm was developed by Boryczka and Czech and has been used to solve approximation problems [13], [14]. Kumaresan and Balasubramaniam developed the ACP to solve a stochastic linear singular system [15], Kamali modified the ACP to solve differential equations [16].…”

Section: Introductionmentioning

confidence: 99%

Application of Ant Colony Programming Approach for Solving Systems of Stochastic Differential Equations

Rashid,

Abid,

Mehdi

2024

Int. J. Anal. Appl.

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Stochastic differential equations (SDE) have wide applications in natural phenomena, engineering, finance, and biological models. Obtaining analytic solutions for an SDE is often complex, and the complexity increases for an SDE system. The paper introduces ant colony programming (ACP) as a novel approach for solving SDE system. Ant colony programming was developed in two directions, the first is to add the Wiener process as a variable to the terminals and functions, and the second is to construct the appropriate fitness function . ACP constructs mathematical expressions and evaluates them using the fitness function . The ACP proposed effectiveness has been demonstrated by applying to 2,3 and 4-dimensional SDE systems. The most important finding of this work is that ACP generates symbolic stochastic processes that represent solutions for SDE system. Methods for solving SDE systems are important tools for study phenomena that involve noise or randomness.

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Singular optimal control for stochastic linear quadratic singular system using ant colony programming

Cited by 6 publications

References 17 publications

Solving differential equations with ant colony programming

Solving differential equations with ant colony programming

Swarm‐based metaheuristics in automatic programming: a survey

Application of Ant Colony Programming Approach for Solving Systems of Stochastic Differential Equations

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