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"improve the solution" is correct and usable in written English, and can be used when you wish to suggest ways to make a situation better or more effective.
For example, "We need to find ways to improve the solution to this problem before it's too late."
Exact(60)
An iterative improvement procedure is introduced to improve the solution.
Furthermore, we applied tabu search to improve the solution quality.
The GA developed in this paper is hybridized with several heuristics to improve the solution further.
We improve the solution by decreasing the condition number of the random projection matrix.
A random optimization algorithm is used to iteratively improve the solution.
Experiments proved that using this approach can improve the solution and leads to better models.
After the construction of an initial solution, local search is used to improve the solution.
Rollout algorithms are applied to the heuristics to improve the solution quality.
In addition, the objective-oriented local optimization methods are applied to improve the solution quality.
Future work should also incorporate densification of shipborne gravity measurements, which may further improve the solution quality over marine areas.
Including more features like affiliations, topical features extracted from titles, summaries or keyword lists could potentially further improve the solution.
More suggestions(16)
improve the alternative
improve the settlement
implement the solution
enforce the solution
improve the remedy
provide the solution
achieve the solution
improve the resolving
improve the answer
ameliorate the solution
improvement the solution
improve the tackling
improvements the solution
improves the solution
improve the response
improving the 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