Nonlinear fractional-order modeling and optimal control of crime and its related costs

The purpose of this research is to present a non-linear model of mathematical fractional order for system of crime with its related costs. Both Genetic Algorithm (GA) and Particle Swarm Optimization (PSO) algorithm were used to simulate optimal control. Modeling approach of the type of differential equation machine with fractional order derivatives was used. In the following, it was shown that the presented model has chaos, its order is of fractional order and it needs to be controlled. GA and PSO algorithm were used for simulation and optimal control. It was shown that this model has a chaotic behavior; as a result, optimal control for this behavior was presented. The results of the GA method are excellent. All the results obtained for the PSO method show that this method is also very successful and the results are very close to the GA method. Very low values of MSE and RMSE errors indicate that the simulation is effective and efficient. The comparison of the presented results indicates the superiority of the GA and PSO algorithm models over the traditional linear regression model in the coefficient of determination and MSE. This article is the first article that performs nonlinear modeling of system of crime with its related costs and optimally controls the chaos in the model. This type of modeling and optimal control has not been done so far. Also, software and algorithms have been used that are very fast, accurate and have the lowest possible error.

کلیدواژه ها:

crime ، related costs ، Optimal control ، Modeling ، chaotic system