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In the algorithm proposed here, each feasible solution is demonstrated by the mode string.
Furthermore, if the conditions of Theorem 4.1 hold for all feasible solutions of (MFP) and each feasible solution ((u',z',v',mu',lambda',w',p'=0, q'=0, r'=0, s'=0)) of (MFD), then ((bar{u},bar{z},bar{v},bar{mu},bar{lambda},bar {w},bar{p}=0, bar{q}=0, bar{r}=0, bar{s}=0)) is an efficient solution of (MFD).
Each feasible solution yielding the same optimum as the original was considered for further variance analysis.
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(ii) Methods from mathematical programming guarantee the quality of solutions, i.e. each new feasible solution comes with a maximal distance to an optimal solution.
While the conversion of fluxes 10 and 9 into FAF during backtracking each produced a feasible solution, only the conversion of flux 1 into FAF led to EFM4.
In the MAOA, multiple agents work in a grouped environment where each agent represents a feasible solution.
For each chromosome, the best feasible solution obtained by these neighborhood searches is a member of the initial population.
In genetic algorithms, each chromosome represents a feasible solution in the search space and is formed by a fixed number of genes.
Geometrically, for a given feasible solution, each source component is a segment of length |s j | in the direction of the corresponding a j and, by concatenation, their sum defines a path from the origin to x [i].
A separate genetic algorithm (GA) is allocated at each epipolar to search the feasible solution space.
The clustering procedure increases the likelihood that the solution will converge to an optimal value, between-route operations (relocate, 2-opt* exchange, and swap move) in the heuristic algorithm will improve the initial solution, and the within-route (dynamic programming) procedure will calculate a good feasible solution for each vehicle route.
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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