Enhance implementation of EGC algorithm

[cb-Hades]

Solve energy generating cycles in a model automatically.

Currently implemented solver:

• GreedyEGCsolver: greedy algorithm, that is based on solving EGCs by using a modifications on ONE reaction to solve (at least) one of the existing cycle

Further ideas:

• LP or DP programming to find all/more complex solutions
  • the paper of Fritzemeier et al. introduced a modified version of the GlobalFit algorithmn in R, but is no longer available there
  • however, the original GlobalFit can still be found on nixpkg here
• ask group of Müller-Hannemann
• while less important, maybe implement a check to check for futile cycles as well
• based on the concept of Bayesian-Gaussian network approach:
  • will be heuristic + highly probable to end in local minima
  • potentially able to solve EGCs connected to more than one modification in the network
  • params like
    • tries: oft often it should be started (from a different starting point)
    • max_variation: maximum of allowed manipulation before abort (to improve runtime/ make sure model is not broken) -> Question: amount-based or score-based?
    • network: the input GEM
    • additionally, growth should be taken into consideration (yes/no or threshold?)
    • maybe add the option to set a seed to allow for reproducible results if needed?
• The following thesis https://digitalcommons.unl.edu/embargotheses/310/ (look maybe for paper?) also covers the topic on how to deal with thermodynamic infeasible cycles - can this be included in refineGEMs/useful for our approach?

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Discussed in #113

^{Originally posted by GwennyGit February 22, 2024}
Possible ideas can be found in the following Wikipedia definitions:

• Knapsack problem
• Change-making problem