A model for organizing cargo transportation between two node stations connected by a railway line which contains a certain number of intermediate stations is considered. The movement of cargo is in one direction. Such a situation may occur, for example, if one of the node stations is located in a region which produce raw material for manufacturing industry located in another region, and there is another node station. The organization of freight traffi c is performed by means of a number of technologies. These technologies determine the rules for taking on cargo at the initial node station, the rules of interaction between neighboring stations, as well as the rule of distribution of cargo to the fi nal node stations. The process of cargo transportation is followed by the set rule of control. For such a model, one must determine possible modes of cargo transportation and describe their properties. This model is described by a fi nite-dimensional system of diff erential equations with nonlocal linear restrictions. The class of the solution satisfying nonlocal linear restrictions is extremely narrow. It results in the need for the "correct" extension of solutions of a system of diff erential equations to a class of quasisolutions having the distinctive feature of gaps in a countable number of points. It was possible numerically using the Runge-Kutta method of the fourth order to build these quasi-solutions and determine their rate of growth. Let us note that in the technical plan the main complexity consisted in obtaining quasisolutions satisfying the nonlocal linear restrictions. Furthermore, we investigated the dependence of quasi-solutions and, in particular, sizes of gaps (jumps) of solutions on a number of parameters of the model characterizing a rule of control, technologies for transportation of cargo and intensity of giving of cargo on a node station.Key words: organizing cargo transportation, dynamic model, differential equations, solution of the traveling wave type, numerical realization.
we investigate the dependence of the error in the performance of nonlocal restrictions on model parameters, which are the characteristics of the technologies used to carry out the cargo fl ow.
This paper presents a new real-coded genetic algorithm with Fuzzy control for the Real-Coded Genetic Algorithm (F-RCGA) aggregated with System Dynamics models (SD-models). The main feature of the genetic algorithm presented herein is the application of fuzzy control to its parameters, such as the probability of a mutation, type of crossover operator, size of the parent population, etc. The control rules for the Real-Coded Genetic Algorithm (RCGA) were suggested based on the estimation of the values of the performance metrics, such as rate of convergence, processing time and remoteness from a potential extremum. Results of optimisation experiments demonstrate the greater time-efficiency of F-RCGA in comparison with other RCGAs, as well as the Monte-Carlo method. F-RCGA was validated by using well-known test instances and applied for the optimisation of characteristics of some system dynamics models.
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