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The phrase "search for solution" is correct and usable in written English.
You can use it whenever you want to express the action of looking for a solution to a problem. For example, "I spent the entire afternoon searching for a solution to the problem."
Exact(6)
They have held joint events with youth groups in a cross-generational attempt to raise awareness, pass on knowledge and jointly search for solution.
A problem-specific local refinement procedure is developed to search for solution space that is unexplored by the honey bees.
This spatial information is compressed and utilized to generate conformational space estimations throughout the algorithm, which expedites the search for solution graphs.
Periprosthetic infection in total hip replacement that results in extensive removal of necrotic tissue has prompted the search for solution to salvage limbs.
Instead, search for solution(s) to the conflict rather than wasting your time and energy determining who is at fault.
One automatic regularization procedure found in literature to this problem is to the search for solution of equation of form Σ x = b (which involves a formal inversion of matrix Σ), which can be achieved by slightly incrementing all diagonal elements in Σ by a constant factor (Tikhonov regularization, [22]).
Similar(54)
See educators as partners in a search for solutions.
His search for solutions is Socratic, not quixotic.
An American-organized peace conference, with constructive help from Egypt and Saudi Arabia, can renew the search for solutions.
It's the Tories who are proving to be most innovative in the search for solutions.
I believe that's where the search for solutions takes a wrong turn.
More suggestions(2)
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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