High generalization performance structured self-attention model for knapsack problem

Abstract

The end-to-end learning approaches possess the advantages of high efficiency, rapidity and superior solving precision for combinatorial optimization problems, while exploring generalization to instances different from training scale is an open question. In this paper, we focus on the knapsack problem (KP) and employ an end-to-end data-driven approach based on attention model incorporated with different forms of baseline of policy gradient algorithm to solve KP. We first investigate the generalization performance of the proposed approach for KP on various problem scales with different capacities. The experimental results show that the end-to-end model possesses certain learning and generalization abilities to discover the intrinsic characteristics between instances, then guides to solve other instances of different scales.