Morphological methods - System theory and system analysis

Morphological methods

The term "morphology" in biology and linguistics defines the doctrine of the internal structure of the systems (organisms, languages) under investigation or the very internal structure of these systems.

Morphological way of thinking goes back to Aristotle and Plato, to the famous medieval model P. Lulliya . The idea of ​​the morphological method was proposed by the Swiss astronomer F. Zwicky [109], and for a long time the morphological approach to the study and design of complex systems was known as the Zwicky method. The history of the development of the morphological approach can be found in the book В. M. Obrina on the morphological analysis of technical systems [64], which systematized and developed methods of morphological analysis of complex problems.

The main idea of ​​the morphological approach is to systematically find the largest number, and in the limit - all possible solutions to the problem posed or the implementation of the system by combining the main (identified by the researcher) structural elements of the system or their attributes. At the same time, the system or problem can be divided into parts in different ways and considered in various aspects.

Starting points of system research F. Zwicky considers: 1) equal interest in all objects of morphological modeling; 2) the elimination of all assessments and limitations until a complete structure of the investigated area is obtained; 3) the most accurate formulation of the problem posed.

In addition to these general provisions, Zwicky proposed a number of separate methods (methods) of morphological modeling: the method of systematic field coverage, the method of negation and construction, the method of the morphological box, the method of extreme situations, the method of comparing the perfect with the defective, generalization method. The most famous were the first three methods.

Method of systematic field coverage. This method assumes that there are a number of strong points knowledge in any area under investigation. These points can be theoretical propositions, empirical facts, currently known components of a complex system, open laws, according to which various processes take place, etc.

Based on a limited number of strong points of knowledge and a sufficient number of principles of thinking (including various proximity measures), MSPP is looking for possible solutions to the problem posed.

The method of negation and construction. The method is based on considerations that F. Zwicky formulated as follows: "On the path of constructive progress lie dogmas, compromise or dictatorial restrictions. Therefore, it makes sense to deny them. However, this alone is not enough. What is obtained from negation, it is necessary to constructively rework the [64]. In accordance with this, the IOC is implemented through three stages:

1) the formation of a number of statements (statements, statements, axioms, etc.) that correspond to the current level of development of the studied area of ​​knowledge;

2) the replacement of one, several or all formulated sentences by the opposite;

3) the construction of all possible consequences arising from such a negation and the verification of the consistency of newly received and unchanged statements.

The IOC can be implemented in the form of one of the methods of "brainstorming" - the ships method.

Morphological box method (MMN). The method is based on the formation and analysis of the morphological matrix, which Zwicky calls the morphological box (MJ). The construction and investigation of the Zwicky morphological box is carried out in five stages:

1) the formulation of the problem posed;

2) definition of parameters (classification characteristics)

, on which the solution of the problem depends (the analysis procedure can be iterative with changing the set in measure refinement of ideas about the object under investigation or in the decision-making process);

3) the division of parameters into their values ​​ (the formation of classifiers according to the selected characteristics ) and their representation in the form of row matrices

(2.26)

a set of values ​​(one of each line) of various parameters is a possible variant of the solution of the simulated problem: for example, the variant ; the total number of variants contained in the morphological box is equal to

where - the number of values ​​of the i -th parameter;

4) evaluation of all options available in the morphological box;

5) choosing the best solution for the problem (y Zwicky - the optimal solution, strictly speaking, is incorrect).

From the mathematical point of view, the idea of ​​a morphological search is based on obtaining placements with repetitions from to by n, whose number is generally counted as shown in step 3, and in the private case with the same number of values ​​for each of the parameters (i.e., ) is determined using the well-known combinatorics theorem

(2.27)

where n is the number of MN lines; k is the number of elements in each line.

To reduce the search, steps 3 and 4 can be combined, and explicitly unacceptable options can be immediately excluded from consideration in step 5.

It should be noted that, strictly speaking, there is no question of optimization. The idea of ​​finding the best variant (variants) of a solution is better to be qualified as a gradual limited search, which from the very beginning is reduced due to the formation of a morphological box (the number of allocations with repetitions is less than the number of combinations). As the volume of the morphological box increases, the gap increases and the restriction of the search results in a greater degree, then the area of ​​choice of the solution is limited by the elimination of clearly unacceptable variants, and further limitation of the range of possible solutions can be organized by introducing and accounting for quantitative, and then (other things being equal) and qualitative criteria in the same way as it is proposed in the examples of the use of MMN in planning with a custom system of production in Ch. 4.

The following ways of choosing solutions from the MJ are possible (Figure 2.17): application of one criterion completely excluding all the solutions except one (Figure 2.17, a ); consistent application of several criteria A, B, C, gradually excluding all options except one (Figure 2.17, b ); The problem is divided into subproblems (or tasks for subtasks) and the consistent application of several criteria for choosing one solution variant for each of the subproblems (subtasks), which together make up the desired solution (Figure 2.17, in ) .

In the latter case, more than one solution composed of sub-problems can be obtained, and several such solutions, and then to reduce these options further narrowing of the domain of feasible solutions can be achieved by introducing additional criteria (usually qualitative ones), as is done , for example, in Ch. 4.

It should also be stipulated that decisions on the subproblems from which the general solution is formed can be interdependent, which is also illustrated in the examples in Ch. 4 (in particular, when placed along assembly lines, the same order can not be placed on different interchangeable assembly lines in the relevant planning period).

Ph. Zwicky and his followers developed and researched MY of various kinds.

For example, we know the variant of constructing MN, in which the values ​​of the same parameter were plotted along both the horizontal and vertical axes of the two-dimensional matrix "boxes", and the solutions of the floor

Fig. 2.17

were at the intersection of different parameter values, i.e. variants of solutions were elements of this matrix.

Morphological boxes can also be not only two-dimensional. Three-dimensional and higher-dimensional MEs are used, for example, to use in the development of forecasts and in the macro-design of variants of new technology.

However, when forming and analyzing multi-dimensional MN, especially when analyzing the problems of organizational management, there are significant difficulties in their presentation to decision-makers in interpreting the results. Therefore, it is more convenient, using the idea of ​​a morphological approach, to develop modeling languages ​​(modeling automation, design automation, etc.) that are used for generation possible situations in the system, possible solutions, and often as an auxiliary tool for the formation of lower levels of the hierarchical structure of goals and functions or organizational structures of management systems. In this case, the term morphological approach is used in a broader sense.

Suggested F. Zwicky methods have found wide application as a means of activating inventive activity. And when modeling design automation tasks, scheduling tasks, for example, the distribution of orders for planned periods, placing them by production lines, assembly lines, etc., MME turned out to be a convenient tool, which will be described in more detail.

Let's pay attention to the fact that during the formation of the morphological table (morphological box) other methods of morphological modeling can be used as auxiliary ones.

In the practice of volume scheduling, it turned out to be convenient, as it were, to turn the 2D ME and combine not elements of rows, but column elements (such tables are more common for workers in planning departments).

The automation of morphological modeling significantly contributes to the expansion of the practical application of MMN. At the same time, it is important to automate not only obtaining solution options, i.e. actually busting, but also obtaining estimates of these options, and even the formation of the ME. Examples of algorithms for automating morphological modeling are given in Ch. 4.

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