Challenge: sum of squares. Let's break 299

01242018, 10:29 PM
(This post was last modified: 01242018 10:32 PM by Allen.)
Post: #34




RE: Challenge: sum of squares. Let's break 299
Thomas,
Thank you for verifying those solutions! It's always nice to have a second set of eyes. I have an important event in less than an hour, but generally speaking, I think the hamiltonian approach is good for randomwalk kind of graphs, but these "square" graphs have some interesting properties we can exploit. Namely, there are bottlenecks in the graph. For N=71 ( and numbers around there) the bottleneck is 50. There is only 1 or 2 ways to include 50 in the string. By sorting the nodes of the graph according to how many outgoing edges there are, one can write a penalty/reward scoring to promote those strings that contain the most bottlenecks. Make a population of possible strings, and sort them according to their score, decimating to only keeping a portion of the resulting population. I'm still trying to find the optimal settings for decimation, and growth rates to ensure the population does not collapse, while still finishing reasonably quickly. Will post more as soon as I'm able. 17bii  32s  32sii  41c  41cv  41cx  42s  48g  48g+  48gx  50g  30b 

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