Your English writing platform
Discover LudwigSuggestions(5)
"the optimal solutions" is a correct and usable phrase in written English
You can use it any time you need to refer to the best possible solutions to a given problem. For example: "After analyzing the data, we determined that the optimal solutions for the project were to reduce costs without sacrificing quality."
Exact(60)
Considering the optimization objective, the optimal solutions of the structural parameters are obtained.
Particle swarm optimization algorithm (PSOA) is employed to search the optimal solutions.
The multiobjective ant colony optimization (MOACO) technique has been utilized to obtain the optimal solutions.
We find the optimal solutions for these problems through formulating them as optimization models.
The optimal solutions obtained by the ACSA are compared with the other global optimizers.
The optimal solutions satisfy (5).
The optimal solutions have been discussed.
In such cases, Structure Hunter cannot find the optimal solutions.
Thus, these methods do not always provide the optimal solutions.
An algorithm to find the optimal solutions is developed.
Most of them commonly fail in finding the optimal solutions.
More suggestions(15)
the optimal decisions
the optimal processes
the appropriate solutions
the maximal solutions
the good solutions
the ideal solutions
the optimal alternatives
the optimal policies
the optimal outcomes
the optimal options
the suitable solutions
the optimised solutions
the optimal option
the best possible solutions
the better solutions
Write better and faster with AI suggestions while staying true to your unique style.
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