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"the optimum solution" is correct and is widely used in written English.
It is often used to refer to the best solution or the best approach to a given problem. For example: "After much deliberation, the team decided that the optimum solution was to outsource the production process to a third party."
Exact(60)
"They always take the optimum solution.
To me, it didn't look like the optimum solution, I'll admit.
It is not wrong to use paper if the water is present, he intoned, but the optimum solution would be to employ both.
When the ball was in the back of the net, it was clear it had been the optimum solution after all".
The engineering solution is the optimum solution, the end result that, taking many factors into account, is most desirable.
The optimum solution is cross checked twice.
The optimum solution however remains unaffected.
Thus, the optimum solution of problem (15) is also the optimum solution of problem (14).
Afterward, the best result is selected as the optimum solution.
We use method 2 to calculate the optimum solution.
If the optimum solution of the relaxed problem is integer, this corresponds to the optimum solution of the original problem.
More suggestions(15)
the perfect solution
the good solution
the optimised solution
the ultimate solution
the ideal solution
the optimum approach
the optimum resolving
the maximum solution
the best case solution
the optimize solution
the greater solution
the optimization solution
the optimum alternative
the better solution
the best solution
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com