Minimal and efficient graph representations are key to store, communicate, and sample the search space of graphs and networks while meeting user-defined criteria. In this paper, we investigate the feasibility of gradient-free optimization heuristics based on Differential Evolution to search for minimal integer representations of undirected graphs. The class of Differential Evolution algorithms are population-based gradient-free optimization heuristics having found a relevant attention in the nonconvex and nonlinear optimization communities. Our computational experiments using eight classes of Differential Evolution schemes and graph instances with varying degrees of sparsity have shown the merit of attaining minimal numbers for graph encoding/representation rendered by exploration-oriented strategies within few function evaluations. Our results have the potential to elucidate new number-based encoding and sample-based algorithms for graph representation, network design and optimization.

翻译：最小且高效的图表示是存储、通信和采样满足用户定义标准的图与网络搜索空间的关键。本文研究了基于差分进化的无梯度优化启发式方法在搜索无向图最小整数表示中的可行性。差分进化算法是一类基于种群的、无需梯度计算的优化启发式方法，在非凸和非线性优化领域受到广泛关注。我们利用八类差分进化方案以及不同稀疏程度的图实例进行了计算实验，结果表明，采用面向探索的策略能够在少量函数评估内实现图编码/表示的最小整数化。我们的研究结果有望为图表示、网络设计与优化中的新型数值编码和基于采样的算法提供启示。