Hurensohn Heigl
Member
- Nov 8, 2018
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First and foremost, thanks for the props. I have to return them thankfully.I am curious as to what exact particular process you applied get the particular demonstrated example optimum? I ask, since I was heavily inspired by your analysis and borrowed a number of its insights (primarily those concerning constraints), though not your literal actual procedure or algorithm ( I have no direct experience with the specific technical optimization methods you employed ), to try to program my own direct optimization algorithm, and was able to generate a solution that used 104 less XP (425 XP instead of 529 XP) to complete all the rooms, and ultimately had 79 more XP in your sense of the 7th free roam to allocate for work (460 XP instead of 381 XP), with respect to the same simplified floor division calculation of XP from raw points that you also appear to have employed. I bring this up since you mentioned the range of solutions should all be within 20XP within each other. So I am curious as to how to interpret your 20XP range, to see if the solution I found is actually within that range or potentially poses as a genuine counter example of some kind?( I do not have the sufficient know how of your algorithm to make that determination, which is why I programmed my own lol)
To answer your question (as good as I can): The range of 20XP was related to the total XP generation process and not the remainder in turn 7. I see that you have generated a total of 825XP with your allocation plan while my (probably just local) "optimum" generated 840. As I mentioned in the corresponding section, I myself, know how to increase this 840 up to 853.2 (+13.2) as I have not allocated 91XP when I could have. This was for the same reason you are raising this question: I wanted to balance between maximizing XP generation and maximizing the left-over XP in turn 7. Neglecting the last objective, one could even achieve more - but to inferior conditions. Therefore my eductaed guess was 20 which is basically 50% more of what I could have done and am aware of.
In regards to the applied process:
1st subordinate minimization goal: Try to use all of the available XP in one round or get very close to it for the first three rounds. I.e. spend all 60 XP in turn 1. Furthermore, I couldn't further reduce the XP left over in turn 2 without violating the first assumption or not completing one room.
Reasoning: same as above
Limitations: Again, one could argue that spending all XP and leave one room unfinished would be superior, but this would not only be influenced by past decisions but also have to be accounted for in future decisions which is something I can totally not model (and this bothers me........)
2nd subordinate maximization goal: As mentioned in the post, there was this interesting finding that we are able to maximize the total score in turn 6 by clearing 9 rooms in one go. Therefore I artificially limited myself to doing that as it was superior to all previous scenarios.
Reasoning: see fun fact in constraint #2 of my second analysis.
Limitations: Since this assumption affects the previous decision, this is the most fragile one. Even though it maximizes the XP gain in the current turn, one has to account for the XP loss from not maximizing the previous turn with most attention. The solution I presented is maximizing the 5th turn subsequently and the XP loss is lower than the gain, but this only proofs that it is a superior reaction to the decisions made previously. If we change the initial approach (like loosing the restrictions of turn 3), this might look completely different.
However, I have tested multiple scenarios and identified the approach presented in the main post as the most optimal. But comparing ~20 scenarios out of multiple billions of possibilities is certainly not representative by any means.
I hope I could help and I am looking forward to reviving this discussion - to the pain of all other forum members, haha.
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