Stochastic differential equations (SDE) represent dynamic systems subject to stochastic influences. This paper introduces particle swarm optimization programming (PSOP) as an innovative approach to solving SDE systems. The optimal solutions are reached by sending simulated particle to navigate in the search graph, and particle tours are saved and evaluated using a fitness function (FF). The PSOP has been developed as a programming algorithm in several directions, starting with construct the graph as a solution search space. The vision function is defined that depends on the simulated particle velocity in the swarm and the node position in the research graph, where the digital particle navigating in the research graph from the node to another according to the vision function. Finally, a fitness function is constructed to evaluate the expressions that represent possible solutions. The most important conclusion lies in obtaining symbolic solutions for the SDE systems studied. The PSOP method has been validated through simulations on multi-dimensional SDE systems, showing promising applications in stochastic processes, modeling, automatic programming, and artificial intelligence.

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Solving Stochastic Differential Equation Systems by Particle Swarm Optimization Programming

  • Ali Sami Rashid,
  • Salah H. Abid,
  • Sadiq A. Mehdi

摘要

Stochastic differential equations (SDE) represent dynamic systems subject to stochastic influences. This paper introduces particle swarm optimization programming (PSOP) as an innovative approach to solving SDE systems. The optimal solutions are reached by sending simulated particle to navigate in the search graph, and particle tours are saved and evaluated using a fitness function (FF). The PSOP has been developed as a programming algorithm in several directions, starting with construct the graph as a solution search space. The vision function is defined that depends on the simulated particle velocity in the swarm and the node position in the research graph, where the digital particle navigating in the research graph from the node to another according to the vision function. Finally, a fitness function is constructed to evaluate the expressions that represent possible solutions. The most important conclusion lies in obtaining symbolic solutions for the SDE systems studied. The PSOP method has been validated through simulations on multi-dimensional SDE systems, showing promising applications in stochastic processes, modeling, automatic programming, and artificial intelligence.