Context. An application of the method of searching for schools of fish to construct optimal experiment plans for cost (time) in the study of technological processes and systems that allow the implementation of an active experiment on them is proposed. Object of study. Optimization methods for cost (time) costs of experimental designs, based on the application of a school of fish search algorithm. Objective. To obtain optimization results by optimizing the search for schools of fish for the cost (time) costs of plans for a full factorial experiment. Method. A method is proposed for constructing a cost-effective (time) implementation of an experiment planning matrix using algorithms for searching for schools of fish. At the beginning, the number of factors and the cost of transitions for each factor level are entered. Then, taking into account the entered data, the initial experiment planning matrix is formed. The school of fish search method is based on the rearrangement of the columns of the experiment planning matrix, based on the sum of the costs (times) of transitions between levels for each of the factors. Fish schools are formed according to the following principle: fewer schools of fish where the sum of the costs (times) of transitions between levels of factors is greater. Then, rearrangements of schools of fish located nearby in the experiment planning matrix are performed. Then the gain is calculated in comparison with the initial cost (time) of the experiment. Results. Software has been developed that implements the proposed method, which was used to conduct computational experiments to study the properties of these methods in the study of technological processes and systems that allow the implementation of an active experiment on them. The experimental designs that are optimal in terms of cost (time) are obtained, and the winnings in the optimization results are compared with the initial cost of the experiment. A comparative analysis of optimization methods for the cost (time) costs of plans for a full factorial experiment is carried out. Conclusions. The conducted experiments confirmed the operability of the proposed method and the software that implements it, and also allows us to recommend it for practical use in constructing optimal experiment planning matrices. KEYWORDS: optimal plan, search by school of fish, optimization, experiment planning, cost, win. NOMENCLATURE k-the number of object factors introduced into the study; t-program run time, s; B-winnings; N-the number of experiments in the planning matrix of the experiment and the matrix of costs of transitions between the levels of factors; S total-total cost of the experiment, conv. units; S ij-the cost of the transition from the i-th experience to the j-th, conv. units; X i-the value of the i-th factor of the studied process; С conv-conversion cost matrix; Х-initial plan of the experiment; l-number of iterations of the algorithm; l it-specified number of iterations of the algorithm; a ij-the value of the i-th factor in the j-th experiment; C...
One of the main ways to improve the efficiency of experimental research is the use of methods for planning experiments. At the same time, experiment planning can significantly reduce the amount of experimental research by reducing the number of experiments, as well as improve the accuracy and reliability of the results obtained. It is characteristic that the experiments in terms of experiment are not equivalent, that is, their implementation requires different material and time costs. In this regard, the problem arises of optimizing the plans of multivariate experiments in terms of cost or time costs. This is especially important when studying valuable and long-term processes. To solve the problems of optimizing plans for multifactorial experiments in terms of cost (time) costs, it is necessary to develop effective methods for finding optimal plans and their software. Existing methods for optimizing experimental plans are characterized by such shortcomings as low speed, a limited number of studied object factors, and the exact solution is not always found. This article explores the method of gravitational search for the optimal cost (time) cost plan for multifactorial experiments. The method uses the analogy of the motion of solid bodies due to their gravitational interaction. In this case, the rows of the experiment planning matrix are considered as such solid bodies, which are placed in it depending on the decrease in the cost of transitions between rows (gravity). An algorithm and software have been developed that implement the proposed method. The program is presented in the algorithmic language Python. On a number of examples for the study of technological processes, the efficiency and effectiveness of the method of gravitational search for optimal cost (time) costs of plans for multifactor experiments has been proved. The object of the research: processes of optimization of plans of multifactorial experiments according to cost (time) costs. The subject of the study: the method of gravitational search for the optimal cost (time) plans of multifactorial experiments and the software implementing it.
he planning of the experiment allows us to solve the problem of obtaining a mathematical model with minimal cost and time costs. The cost of implementing an experiment is significantly affected by the order of alternating levels of change in factors. Thus, it is required to find a procedure for the implementation of experiments that provides the minimum cost (time) for conducting a multivariate experiment. This task becomes especially relevant when studying long and expensive processes. The purpose of this article is the further development of the methodology of optimal planning of the experiment in terms of cost (time), which includes a set of methods for optimizing the plans of the experiment and hardware and software for their implementation. Object of study: optimization processes for the cost of three-level plans for multivariate experiments. Subject of research: optimization method for cost and time costs of experimental designs based on the use of the jumping frog method. Experimental research methods are widely used to optimize production processes. One of the main goals of the experiment is to obtain the maximum amount of information about the influence of the studied factors on the production process. Next, a mathematical model of the object under study is built. Moreover, it is necessary to obtain these models at the minimum cost and time costs. The design of the experiment allows you to get mathematical models with minimal cost and time costs. For this, a method and software were developed for optimizing three-level plans using the jumping frog method. Three-level plans are used in the construction of mathematical models of the studied objects and systems. An analysis is made of the known methods for the synthesis of three-level plans that are optimal in cost and time costs. The operability of the algorithm was tested when studying the roughness of the silicon surface during deep plasma-chemical etching of MEMS elements. Its effectiveness is shown in comparison with the following methods: swarm of particles, taboo search, branches and borders. Using the developed method and software for optimizing three-level plans using the jumping frog method, one can achieve high winnings compared to the initial experimental plan, optimal or close to optimal results compared to particle swarm, taboo search, branches and borders methods, and also high speed of solving the optimization problem in comparison with previously developed optimization methods for three-level experimental designs.
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