Game Tree Search in a Robust Multistage Optimization Framework: Exploiting Pruning Mechanisms
Abstract
We investigate pruning in search trees of socalled quantified integer linear programs (QIPs). QIPs consist of a set of linear inequalities and a minimax objective function, where some variables are existentially and others are universally quantified. They can be interpreted as twoperson zerosum games between an existential and a universal player on the one hand, or multistage optimization problems under uncertainty on the other hand. Solutions are socalled winning strategies for the existential player that specify how to react on moves of the universal player  i.e. certain assignments of universally quantified variables  to certainly win the game. QIPs can be solved with the help of game tree search that is enhanced with nonchronological backjumping. We develop and theoretically substantiate pruning techniques based upon (algebraic) properties similar to pruning mechanisms known from linear programming and quantified boolean formulas. The presented Strategic CopyPruning mechanism allows to \textit{implicitly} deduce the existence of a strategy in linear time (by static examination of the QIPmatrix) without explicitly traversing the strategy itself. We show that the implementation of our findings can massively speed up the search process.
 Publication:

arXiv eprints
 Pub Date:
 November 2018
 arXiv:
 arXiv:1811.12146
 Bibcode:
 2018arXiv181112146H
 Keywords:

 Computer Science  Discrete Mathematics;
 Computer Science  Artificial Intelligence