Model of Multi-Parameter Optimization of the Characteristics of a Cable Car in a Solid Waste Transportation System
Authors: Marchenko Yu. V. , Deryushev V. V. , Popov S. I. , Marchenko E. V. 
Published: December 2023

Introduction. Modern scientific and applied literature examines the problems of cable cars functioning quite thoroughly. First of all, it concerns ensuring the reliability and safety of traffic, both during operation and during project development. In addition, the paper considers the relationship of cable cars with the environment and the level of environmental load from this type of transport. A good solution could be the use of mathematical models that can take into account a set of parameters and criteria that characterize the cable car as a system. The same approach would be useful for optimizingtechnical characteristics of the object. However, there is no description of such a solution in the literature. This gap is partially filled by the presented work.

   The study aims to create a model of multivariable optimization of cable car technical characteristics for the transportation of municipal solid waste (MSW).

   Material and Methods. To clarify the theoretical basis, the literature describing the problems of cable cars and their solutions in general has been studied.  Mathematical calculations were justified by a volume of equations that proved their adequacy in determining the useful transport work, load, adjustment of time and speed of cargo movement and other significant parameters of the system under study. When forming the model, we proceeded from the principles of L. S. Pontryagin (needle variation) and Hamilton — Ostrogradsky (kinematics of a certain road segment). Text data about the features of the system elements and their interaction were summarized in tables. The main calculations results were visualized in the form of graphs.

   Results. The solution to the problem of optimal control of the cable car on which solid waste was moved was presented. The motion control vector was shown as a vector of optimized technical parameters of the system: speed of movement, rope tension, number and weight of containers. The well-known solution to the optimization problem was reproduced in a general form, which involved determination of a control vector function and its corresponding trajectory with the achievement of a minimum of the target functional. The weak point of the system of differential equations for the realization of the goals of this scientific work was noted. In this regard, it was proposed to consider the investigated section of the cable car as a dynamic system with distributed parameters. The formulation of the multi-criteria optimization problem was described in detail. The advantages of reducing the number of criteria taken into account were listed and the use of the reduction method, which was based on the hierarchical structuring of the system of partial optimality criteria, was justified. Four main elements of the municipal solid waste (MSW) transportation system were considered in interrelation. This was a cable car, a transport and logistics point, a transport and logistics terminal and an environment that generated solid waste. Within the framework of this work, we considered an urbanized environment. The sub-elements of the named elements were listed and 12 directions of their interactions were shown. In detail, within the framework of a three-level hierarchy, four main complex indicators of the complexity of the system under study were described: environment, road, point and terminal. The solution of a multi-criteria optimization problem was shown, calculations were performed for the optimized parameters — the characteristic of the complexity of the road and the characteristic of the terrain. The results of calculations were presented in the form of graphs. Thus, the dependences of the optimized parameters on the weight of the loaded container, the length and speed of the cable car were illustrated.

   Conclusions. The main result of the study is an idea of the possibility of a mathematical solution of a multivariable and multi-criteria problem of optimizing two characteristics of a cable car (complexity and terrain feature). The proposed approach allows you to change the hierarchy in the complex of indicators. The results of this scientific work can be used, if necessary, to integrate the road project with neural network models, to work with fuzzy linguistic indicators, to solve applied problems.