The value of cost function for theDEoptimization of the system of loads may be calcu-lated as the absolute value of the sum of differences between the outputs of the simulations based on the assumption about the maximal loads and the values of loads which are as-sumed to be transported by the company. The parameter that effects the loads generation in this case is the value ofλin exponential distribution. Thus, this value has to be consid-ered as the parameter of the cost function. Moreover, as it was concluded in the section 5.4, the parameterλhas to be different for various areas. Thus, the cost function has seven parametersλ1, λ2, λ3, λ4, λ5, λ6, λ7 each of which corresponds to the relevant field. The system of loads is also stochastic, that makes difficult accurate differentiation of optimal parameters. As in the previous case, it is possible to define confidential intervals for each of the parameters. They are presented in the following table:
Table 7.Optimized parameters for the system of loads λi bottom bound upper bound
i= 1 31.55 34.99
Figure 18.Results of the simulations of the systems of loads after optimization
The results of the simulation of the system, based on the assumption about maximum loads generated with averaged optimal parameters, which are represented by the first and second columns for each of the regions, are fairly close to those originally suggested by the company (the last red columns). Thus, we can conclude that the optimization was successfully carried out.
7 CONCLUSIONS
In this paper, the analysis of existing simulation technologies for solving the problems of transport logistics has been carried out. The analysis included the study of existing simu-lation methods and their application for the simusimu-lation of the Finnish company processes.
The classification proposed by Taniguchi in [9] was used in the paper. He divided the methods into the three groups, such as multi-agent systems, system dynamics and traffic simulation. The application of the last two was illustrated by the development of simu-lation models for the presumably not optimal processes of the Finnish company, related to the traffic simulation and the system dynamics of the loads. The information about the classification is presented in Chapter 2. Based on the simulation results and comparing them with the existing real statistical data we can conclude that, despite the variability in the results, they approximate well the company processes. The models as well as the re-sults of their simulations are presented in the Chapters 4 and 5. The variability in outputs is caused by the stochasticity of the models, which, is in its turn, caused by the lack of information and requirement of the assumptions and consideration of different possible conditions.
However, despite the proved reliability of simulation methods, the results of the simu-lations confirmed the non-optimality of the processes. For the solution of this problem, it was decided to analyze and define the parameters, initial values of which caused the non-optimality. After their differentiation, the differential evolution optimization was performed. The realization of the optimization is presented in the Chapter 6. Due to the properties of this algorithm, the values of the objective function were determined as the output of the simulations. Thus, the possibility of the effective processes optimization based on simulation methods was illustrated as well.
Based on the above information, we can conclude that the application of simulation tech-nologies for description the processes is a quite new and promising way. The model formulated in this way is flexible enough and allows describing any, even the most in-significant details of the process, which in turn makes it as close to real conditions. The results of the simulations can also be considered as values of the target function, which in turn allows you to optimize the system. In this paper, all steps such as the construc-tion of the simulaconstruc-tion model, the evaluaconstruc-tion of simulaconstruc-tion results and the implementaconstruc-tion of optimization were done for the processes of the Finnish company and they prove the correctness of the above statements.
7.1 Future Work
All the processes in this paper were described by models optimized in the absence of a large amount of initial information. This phenomenon led to the need for constructing hypotheses and considering various scenarios. For this reason, each model has several random parameters. This fact does not allow to make a more precise evaluation of the optimal parameters for the system than the confidence interval. Therefore, one of the options for future work may be to conduct the same research for the company, whose sys-tem of work is sufficiently predefined and evaluate the results of optimization within such conditions. Otherwise, another possible future direction is to study and apply methods of robust statistics for the models described in the paper.
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