[HN Gopher] Chess and solution pool with linear programming (2018)
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       Chess and solution pool with linear programming (2018)
        
       Author : cpp_frog
       Score  : 66 points
       Date   : 2023-10-02 13:50 UTC (9 hours ago)
        
 (HTM) web link (yetanothermathprogrammingconsultant.blogspot.com)
 (TXT) w3m dump (yetanothermathprogrammingconsultant.blogspot.com)
        
       | brosco wrote:
       | More specifically, using mixed integer linear programming.
       | 
       | I've never seen an MILP used this way, to characterize the entire
       | feasible set (or "solution pool"). Is this one of the fastest
       | ways to do so? The usual branch-and-bound type methods won't
       | apply, since the solver has to enumerate every feasible solution.
       | 
       | The CPLEX docs
       | (https://www.ibm.com/docs/en/icos/22.1.1?topic=solutions-how-...)
       | mention the potential slowness and also the numerical issues the
       | author faces in the article.
        
         | whatever1 wrote:
         | Everything happens in the branch and bound tree. Instead of
         | discarding feasible solutions that have worse value than your
         | best one you keep them in a pool.
         | 
         | The author is losing solutions because cplex does smart
         | branching. He can change the branching option to strong
         | branching and he will get the missing solutions. Or he can
         | implement a custom branching callback to ensure that all nodes
         | are visited, even non promising ones.
        
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