T.G. Artyushina - Ph. D. (Eng.), Associate Professor, Russian Economic University named after G.V. Plekhanov. E-mail: t.g.art@yandex.ru

In this article we shall study the problems that arise from describing the multilevel and multifunctional systems, and analyze all the existing solutions for this problem. To simplify the analysis we will focus on one particular system - the vessel. The container ship with its own cargo handling gear was picked as the type of vessel that will be simulated. Text description of the mathematical model that corresponds to this type of vessel is represented in the table. This model can be used in early stages of vessel design and it represents a solid mathematical base for selecting optimal vessel characteristics. Algorithms that describe the vessel-s systems are in essence the enumeration algorithms; hence the conflict occurs between the detalization level and the computational power requirements. This conflict can be solved by using multilevel optimization: subsystems are optimized locally first and then local solutions are merged and adjusted within the global framework of vessel-s design. However this method requires selecting the right algorithm that will describe the vessel. In this article most of the existing methods are analyzed and their shortcomings are revealed. Furthermore, the new algorithm of random search is introduced. It scans the area of limitation functions - definitions and effectiveness criteria by pseudorandom selection of random points (see picture 1). This algorithm is a simplified version of a random search by P. Mandel and L. Reuve, improved by A.I. Gaikovitch. Adjusting and combining the results of local optimization is done by applying fuzzy set theory, especially when local subsystems have common variables. Therefore, this mathematical framework is factually a new tool for the theory of vessel design. Moreover, we developed a universal algorithm for solving conflicts between subsystems and the system as a whole (see pic 3). Our algorithm coordinates the goals of vessel-s local subsystems and the global goal of the whole system. Thus no matter what kind of solution with different parameters for upper level system we get; all the lower level systems must demonstrate the solutions that are the best for the upper level system. Among the advantages of the algorithm is not only its applicability to the conflict situations, but also its applicability to compatible solutions. For example, there may be a non-empty set of possible solutions and solutions for the upper-level system could fall into the same non-empty set. It-s also important to mention that our fuzzy set algorithm allows to work with discrete sets in the same manner as with regular functions. Moreover, this algorithm was primary developed for discrete compounding - perpetual functions are transformed into sets of discrete values by the method of set pace digitalizing. In summary, switching to mathematical models described above allows us to raise the bar in terms of detalization of the vessel-s design by using optimal vessel-s systems; thus improving the quality of design solutions.

 

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