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In real word problems, the influence of multiple not perfectly known factors results in using heuristics instead of mathemacial solutions that calculates a perfect value from only precisly defined input data. Consequently, any method that does not supply the mathematical maximum or minimum is not an optimisation but an improvement.

Somehow my opinion on this topic differs from the use of the term optimisation in many papers. Are the people just not precise in their language or is my understanding of the term wrong?

Improvement doesn't sound as facy as optimisation, but is there maybe some facy word that allows people to still be precise?

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    $\begingroup$ This is sort of a linguistic, maybe philosophical, question. Does "optimal" mean "best possible" or "best available"? A more practical answer might be that "optimization" in this context is understood to be subject to some fixed constraints, whether they've been properly defined or not, in which case this is true optimization in the sense you intend. $\endgroup$ – Patrick87 Oct 14 '13 at 15:23
  • $\begingroup$ If one includes time/effort to solution (possibly over several different applications), limited knowledge (of inputs and of algorithms), reliability/accuracy of the solution (e.g., avoiding bad solutions given somewhat inaccurate inputs), flexibility of application (e.g., knowledge changing before solution is used or reuse to reduce later time to solution), and other real-world factors, then such might be considered "true" optimization; but usually the term is used as a synonym for improvement (but with emphasis on the action rather than just describing the effect--not merely being 'fancy'). $\endgroup$ – Paul A. Clayton Oct 14 '13 at 15:54
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Using mathematical nomeclature outside of the well-defined realm of mathematics often yields interesting problems. What for example do you mean by "proof" if you're not talking about logical deduction of a theorem from a set of axioms?

So when I talk about optimization I usually think about some more or less well defined problem, like "Given a set of factories and clients, how do I transport goods to clients using the minimal amount of money. I only have a limited amount of trucks and drivers, so there are some complicated constraints". The tricky part is judging which factors are important to my real world problem and modelling them using well-defined mathematical objects. This transition from real world to mathworld is usually hard and requires several attempts. The result of the process is the optimization problem that we want to solve using mathematical methods. But note that it's only our approximation of the real world and we left out lots of things that we deem irrelevant!

Most real world problems are of course difficult and any model that can give reasonable results is at least NP-hard to solve optimally. So we use heuristics. I still think of this as an optimization process, since I do improve something until I reach some kind of solution. It might not be the global optimum, or even a local optimum, but it's the best I can do. Since my original formalization of the problem already left out lots of things that might or might not have influence on the solution, this additional layer of suboptimality does not matter too much to me.

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