Автор(-ы):
Ткаченко Ангелина Сергеевна
Кротов Кирилл Викторович
3 апреля 2024
Секция
Информационные технологии
Ключевые слова
Аннотация статьи
When implementing modern information technologies, there is a need to process large volumes of different types of data. Working with large amounts of data is an integral part of professional development; efficient processing of large amounts of data is the foundation for the success of your project. The solution to this problem is realized by creating resources that provide users with services for thematic data processing. Because Data from various sources is accumulated in the reception buffer of the processing center, then the system processes data of different types. Also, the conveyor system does not receive one task for processing, but a set of them (package). Then the data storage buffer simultaneously contains several sets of data of different types. Due to the large volumes of data being processed and the presence of restrictions on the time to obtain results, it is necessary to perform thematic processing as part of high-performance computing systems. In this regard, the task of managing data processing in these systems and developing methods for its implementation is urgent. Optimizing data processing allows us to reduce time costs, improve performance and increase the availability of data processing. Fast and reliable data processing also improves the quality of decisions made and contributes to successful business operations.
Текст статьи
The scheduling of job packages in multi-stage systems is a complex task that often involves various constraints and limitations. In this article, we focus on justifying the implementation of a mixed integer linear programming (MILP) mathematical model for optimizing the schedules of job packages.
Methods
To address the challenges of scheduling job packages, we implemented a MILP mathematical model that takes into account the formation of result sets and the limitation of system functioning time intervals. As the problem of determining job package compositions and groups is NP-hard, we utilized approximate optimization methods. Additionally, we developed a method for constructing initial solutions for optimizing groups of job packages, as well as an algorithm for distributing job package execution results into sets within limited duration time intervals.
Results
The concept of program execution on a conveyor involves dividing it into fragments, each of which is assigned to a corresponding segment of the conveyor. The processing routes for all types of data are identical, strictly fixed, and involve passing through all conveyor segments. Let's introduce the following designations:
Data of the 𝑖-th type (𝑖 = 1, 𝑛) are processed by the corresponding program. The system uses 𝑛 types of programs processing 𝑛 types of data.
To form solutions for data batch compositions, the following notations are introduced:
The solution formed at the top level of the system hierarchy is represented as: [М, А], where:
In accordance with the solution for batch compositions, it is necessary to determine the sequence of their processing on the conveyor segments, the batch processing schedule. The batch processing schedule is denoted as 𝜋, representing a set of sequences 𝜋𝑙 for launching batches for processing on the 𝑙-th conveyor segments .
The schedule 𝜋 is formed assuming that the batch processing sequence is the same on all conveyor segments.
For the formalization of the sequences of 𝜋𝑙, the following is denoted:
Since the batch processing order is the same on all segments, it is sufficient to define a single order matrix 𝑃.
We introduce the matrix 𝑅 – the matrix of the quantities of data of the 𝑖-th types in the batches occupying the 𝑗-th position in the sequences 𝜋𝑙 (𝑟𝑖𝑗 – the quantity of data of the 𝑖-th type in the batch occupying the 𝑗-th position in 𝜋𝑙 sequence).
Then, the solution formed at the lower level in the system hierarchy takes the form [𝑃, 𝑅].
For the formalization of the two-level decision-making model for batch compositions and their processing schedules in a conveyor system, the following notations are introduced:
Then, the time of completion of processing this batch on the 𝐿-th segment and the time of completion of processing all data in the system are determined by the expression:
(1)
Therefore, the two-level model for determining effective batch compositions and their processing schedules takes the form:
1. the first (top) level: min 𝑓1, where:
2. the second (lower) level: min 𝑓2, where:
Thus, we have justified a two-level programming model for forming data batch compositions and their processing schedules in conveyor systems.
Conclusion
The study demonstrates that the proposed method, including the use of local optimization for group compositions, has shown promising results in increasing the number of formed result sets from task package executions in comparison to fixed groups. Furthermore, the dependence of scheduling efficiency on input parameters of the problem has been analyzed, providing valuable insights for optimizing job package schedules in multi-stage systems.
Список литературы
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Ткаченко А. С., Кротов К. В. Justification of the mathematical model of mixed integer programming for optimizing scheduling of job packets // Актуальные исследования. 2024. №14 (196). Ч.I.С. 43-45. URL: https://apni.ru/article/8933-justification-of-the-mathematical-model-of-mi