We study the adjustment and use of the Max-sum algorithm for solving Asymmetric Distributed Constraint Optimization Problems (ADCOPs). First, we formalize asymmetric factor-graphs and apply the different versions of Max-sum to them. Apparently, in contrast to local search algorithms, most Max-sum versions perform similarly when solving symmetric and asymmetric problems and some even perform better on asymmetric problems. Second, we prove that the convergence properties of Max-sum_ADVP (an algorithm that was previously found to outperform standard Max-sum and Bounded Max-sum) and the quality of the solutions it produces, are dependent on the order between nodes involved in each constraint, i.e., the inner constraint order (ICO). A standard ICO allows to reproduce the properties achieved for symmetric problems. Third, we demonstrate that a non-standard ICO can be used to balance exploration and exploitation. Our results indicate that Max-sum_ADVP with non-standard ICO and Damped Max-sum, when solving asymmetric problems, both outperform other versions of Max-sum, as well as local search algorithms specifically designed for solving ADCOPs.

中文翻译：

---

将最大和应用于非对称分布约束优化问题

我们研究最大和算法的调整和使用来解决非对称分布式约束优化问题（ADCOP）。首先，我们将不对称因子图形式化，并将Max-sum的不同版本应用于它们。显然，与局部搜索算法相比，大多数Max-sum版本在解决对称和非对称问题时的性能相似，有些甚至在非对称问题上的性能更好。其次，我们证明Max-sum_ADVP（先前发现其性能优于标准Max-sum和Bounded Max-sum的算法）的收敛性及其产生的解决方案的质量取决于每个节点所涉及的节点之间的顺序。约束，即内部约束顺序（ICO）。标准ICO可以重现对称问题所获得的特性。第三，我们证明了可以使用非标准ICO来平衡勘探和开发。我们的结果表明，在解决非对称问题时，具有非标准ICO和Damped Max-sum的Max-sum_ADVP均胜过其他版本的Max-sum和专门设计用于解决ADCOP的本地搜索算法。