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Lecture Notes in Computer Science 3472

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fitness<br />

13 Real-Time and Hybrid Systems Test<strong>in</strong>g 383<br />

y<br />

fitness<br />

x x<br />

(a) unimodal function (b) multimodal function<br />

Fig. 13.15. Examples of fitness functions with different difficulty<br />

the population for a new cycle of the evolutionary algorithm. This proceed<strong>in</strong>g is<br />

expla<strong>in</strong>ed <strong>in</strong> more detail by Goldberg [Gol89].<br />

Initial Population<br />

Insert new<br />

Population<br />

Fitness<br />

Evaluation<br />

Generation by Variation<br />

Exit<br />

Test<br />

Selection<br />

F<strong>in</strong>al Solution<br />

Fig. 13.16. Operational cycle of evolutionary algorithms<br />

With respect to test<strong>in</strong>g, the test case generator must be able to derive test<br />

cases. Furthermore, it has to be able to evaluate the fitness of each <strong>in</strong>dividual<br />

and to perform exit tests. This may require to collect and merge values of several<br />

observations <strong>in</strong>to one fitness value.<br />

Test<strong>in</strong>g the Worst-Case Execution Time: To demonstrate the application of<br />

evolutionary test<strong>in</strong>g, we describe its application to measurement-based tim<strong>in</strong>g<br />

analysis of real-time systems. Test<strong>in</strong>g real-time systems means ensur<strong>in</strong>g the correctness<br />

<strong>in</strong> the value and time doma<strong>in</strong>. In contrast to other methods that test<br />

both properties <strong>in</strong> comb<strong>in</strong>ation, the aim of the test method described <strong>in</strong> this section<br />

[PN98, Weg01, AHP99, GW98] is test<strong>in</strong>g only the time doma<strong>in</strong>. The value<br />

doma<strong>in</strong> can be tested separately by other test methods. The property p1 of the<br />

end state of a real-time system we are <strong>in</strong>terested <strong>in</strong> is the tuple 〈BCET, WCET〉<br />

where the BCET means the best-case execution time and WCET the<br />

worst-case execution time. In the follow<strong>in</strong>g we will just describe test case<br />

generation for WCET as BCET can be handled similar. The application of evo-<br />

y

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