Optimal Coalition Structure Generation (CSG) is a significant research problem in multi-agent systems that remains difficult to solve. This problem has many important applications in transportation, eCommerce, distributed sensor networks and others. The CSG problem is NP-complete and finding the optimal result for n agents needs to check $$O (n^n)$$ O ( n n ) possible partitions. The ODP–IP algorithm (Michalak et al. in Artif Intell 230:14–50, 2016) achieves the current lowest worst-case time complexity of $$O (3^n)$$ O ( 3 n ) . In the light of its high computational time complexity, we devise an Imperfect Dynamic Programming (ImDP) algorithm for the CSG problem with runtime $$O (n2^n)$$ O ( n 2 n ) given n agents. Imperfect algorithm means that there are some contrived inputs for which the algorithm fails to give the optimal result. We benchmarked ImDP against ODP–IP and proved its efficiency. Experimental results confirmed that ImDP algorithm performance is better for several data distributions, and for some it improves dramatically ODP–IP. For example, given 27 agents, with ImDP for agent-based uniform distribution time gain is 91% (i.e. 49 min).

中文翻译：

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用不完善的算法改进联盟结构搜索：分析和评估结果

最优联盟结构生成 (CSG) 是多智能体系统中一个仍然难以解决的重要研究问题。这个问题在交通运输、电子商务、分布式传感器网络等领域有许多重要的应用。CSG 问题是 NP 完全问题，找到 n 个代理的最佳结果需要检查 $$O (n^n)$$O (nn) 个可能的分区。ODP-IP 算法（Michalak et al. in Artif Intell 230:14–50, 2016）实现了当前最低的最坏情况时间复杂度 $$O (3^n)$$O (3 n )。鉴于其计算时间复杂度高，我们为 CSG 问题设计了一种不完美动态规划 (ImDP) 算法，运行时间为 $$O (n2^n)$$O (n 2 n ) 给定 n 个代理。不完美的算法意味着有一些人为的输入，算法无法给出最佳结果。我们将 ImDP 与 ODP-IP 进行了基准测试，并证明了其效率。实验结果证实，ImDP 算法的性能对于多个数据分布更好，对于某些数据分布，它显着提高了 ODP-IP。例如，给定 27 个代理，ImDP 用于基于代理的均匀分布时间增益为 91%（即 49 分钟）。