๐ค AI Summary
This work proposes a reservoir computingโbased mechanism for cross-task dynamic programming reuse to reduce the overall computational cost of solving multiple combinatorial optimization problems. By encoding intermediate states generated during dynamic programming into feature representations and feeding them into a lightweight linear regression model, the method automatically learns transferable computational patterns across distinct problems, enabling efficient sharing and reuse of intermediate results. As the first approach to leverage machine learning for automatically identifying and exploiting cross-task computational redundancy, this study demonstrates its effectiveness on the Traveling Salesman Problem and the Subset Sum Problem. Experimental results show that, compared to solving each problem independently, the proposed framework significantly improves the accuracy of approximate solutions while substantially reducing computation time, highlighting the potential of this novel computational paradigm.
๐ Abstract
Reusing previously computed results is a long-standing principle for reducing computational cost, but such reuse has largely been confined to a single problem's computation. Sharing computational processes across multiple simultaneously solved problems remains possible in principle, yet designing algorithms that exploit nontrivial cross-task relationships is difficult to do manually. Here, we use machine learning to discover such algorithms automatically. Specifically, based on reservoir computing, we propose a method that uses computation results recorded by dynamic programming for combinatorial optimization problems as features for linear regression, leveraging them to assist other combinatorial optimization computations. We validate the approach on the traveling salesman and subset sum problems. Multiplexing the dynamic programming process improves approximation accuracy over generic features and reduces computation time compared with independent solutions. These results suggest a new form of computation, distinct from conventional computational design, in which multiple processes efficiently share and recycle intermediate results and states.