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I currently write my thesis, therefore I develop and later implement a solution for a problem and do a performance & security evaluation afterwards.

The results of the evaluation are quite good in my opinion, because they are just slightly below the solution considered optimal (which can not be applied in the given setup).

But I have problems on finding terms to express that success in the end of the evaluation chapter / conclusion as I can not simply write "This is a success".

Are there any common phrases, or don't I judge my results like this?

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    The answer is in your question: they are just slightly below the solution considered optimal (which can not be applied in the given setup).
    – user9646
    Commented Mar 21, 2018 at 20:54

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You don't need to reserve your conclusion until the end of your Evaluation chapter. Is that separate from the Results section? When you present your "Results", that should be narrowly focused on the test statistics, maybe even numerical comparisons to others' results to put the numbers in context.

The "Discussion" part of your work (not sure if that's all of what your "Evaluation" chapter is or just part of that chapter) is the right place to discuss the interpretation/interpretation of your analysis. You can even have that argument as the thesis for that section. E.g.

As established in [Chapter where you describe the problem], an effective solution to [problem] requires X, Y, and Z. The results in [other section] demonstrate that [this method] is a viable solution.

Then go through and interpret the results to show how the result is suitable. (You should fully acknowledge any drawbacks, but it should be OK to write up this section so that it explains the benefits of your solution.)

The Abstract and Introduction should also clearly say that the approach performs well and securely. You're probably not in a mystery-writing field. :)

Using the word "successful" might be the wrong tone (or it may be OK). Other wordings would be that the approach is "promising" or "proven" or "demonstrated". You might want to look over the wording that published articles in your field use.

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There's nothing wrong with saying something worked. Mostly, I think, you just need to be clear on what your criteria is for success and where the evidence is, e.g.:

"The proposed BAR algorithm appears to successfully mitigate the speed and security problems of the prior FOO method, as demonstrated by these experimental results.

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