AIA: learn to design greedy algorithm for NP-complete problems using neural networks

Zhenxin Ding, Jingyan Sui, Ruizhi Liu, Shizhe Ding, Liming Xu, Zihao Huang, Chao Wang, Haicang Zhang, Shiwei Sun, Chungong Yu, Dongbo Bu

Abstract: Algorithm design is an art that heavily requires intuition and expertise of the human designers as well as insights into the problems under consideration. In particular, the design of greedy-selection rules, the core of greedy algorithms, is usually a great challenge to designer: it is relatively easy to understand a greedy algorithm while it is always difficult to find out an effective greedy-selection rule. In the study, we present an approach, called AIA, to learn algorithm design with the aid of neural networks. We consider the minimum weighted set cover (SC) problem, one of the NP-hard problems, as an representative example. Initially, we formulate a given weighted SC problem as an 0-1 integer linear program (ILP): each variable $x_i$ has two options, i.e., $x_i=0$, which denotes abandon of the set $s_i$, and $x_i = 1$, which denotes selection of $s_i$. Each option of a variable leads to a sub-problem with respect to the original ILP problem. Next, we design a generic search framework to find the optimal solution to the ILP problem. At each search step, the value of a variable is determined with the aid of neural networks. The key of our neural network is the loss function: the original ILP problem and the sub-problems generated by assigning a variable $x_i$ should satisfy the Bellman-Ford equation, and the dissatisfication of the Bellman-Ford equation is evaluated and used as loss function of our neural network. The trained neural network is used as greedy-selection rule. Experimental results on representative instances suggest that using the NN-based greedy selection rule, we can successfully find the optimal solutions. More importantly, the NN-based greedy-selection rule outperform the outstanding Chavatal greedy algorithm, which was designed by human expert. The basic idea of our approach can be readily extended without significant modification to design greedy algorithm for other NP-hard problems.

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