# What is a heuristic algorithm

## Heuristic solution methods

The heuristic solution methods are used wherever the analytical methods in solving complex planning problems cause a disproportionately high amount of computing and time expenditure, which is no longer economically justifiable with regard to an optimal result. In the case of many optimization problems, the analytical methods even fail, so that heuristic methods have been developed. In contrast to the analytical methods, they do not have a formal algorithm that inevitably leads to the optimum. In many cases, however, a result that is as close as possible to the optimum is sufficient. In the heuristic solution method, a distinction is made between approximation rules and priority rules. The calculation process can be greatly shortened by the approximation rules, which is useful with regard to the objective and the problem structure (e.g. branch and bound). However, there is a risk that the optimal solution will not be selected from the multitude of alternative solutions, since not all possible solutions are calculated individually. When applying the priority rules, which are also referred to as "rules of thumb", priorities are assigned to individual alternatives. In practice, a large number of priority rules, e.g. for planning the production process, are known. The examination of the most important rules for their effectiveness is generally done with the help of simulation.

are processes with which new ideas are to be developed in the most spontaneous and creative way possible. In the context of planning, they are mainly used in the search for alternatives. Heuristic processes are particularly important when planning new products. The main processes are: brainstorming (technique to stimulate creative thinking in groups); Synectics (is a further development of brainstorming with alienation of a problem with the formation of analogies; a moderator controls the session of the participants); Morphological method (a complex problem is systematically broken down into sub-problems using criteria, with the sub-problems being solved separately and an overall solution being put together step by step, which takes all interdependencies into account as far as possible); Scenario technique (starting from a given situation, a possible future situation of events in a certain period of time is developed step by step as a logical sequence; after each partial step, alternatives are accepted and the developments are shown) Delphi method (a multi-stage expert survey, whereby the forecasts of the individual experts are collected separately and made available to all experts anonymously; a possible repetition of the process leads to plausible predictions). All of these procedures are essential auxiliary instruments in the context of strategic controlling.

Type of decision tree method of combinatorial optimization, belonging to the class of incomplete enumeration. Heuristic methods can be used to quickly generate good solutions for most combinatorial optimization problems, even if no optimal guarantee can be given for these solutions. Heuristic methods are used above all when the decision tree methods of the implicit full enumeration type appear too complex. The decision trees created with heuristic procedures usually only contain a single branch sequence (see example on Branch and Bound). Since not only branches that are clearly recognized as hopeless, but also branches that are presumed to be hopeless are aborted, the abort decision (decision tree procedure) is of particular importance in the heuristic procedures. Heuristic methods are to be assessed on the one hand according to the solution quality (average and worst case) and on the other hand according to the computing time. The tendency of the two assessment criteria is opposite to one another. Simulation methods are often used to measure the values ​​of both criteria. A distinction is often made between two classes of heuristic procedures: those that lead to an initial solution to a problem and those that can be used to improve solutions. In many heuristic methods, the selection between different branches is made according to priority rules. An important area of ​​application of priority control procedures is in machine occupancy planning. Literature: Witte, Th., Heuristic Planen, Wiesbaden 1979. Müller-Merbach, H., Heuristics and their Design: A Survey, in: European Journal of Operational Research, Vol. 8 (1981), No. 1, p. Lff. Pearl, /., Heuristics, Reading, Mass. 1984.

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