In many real-world scenarios, agents are involved in optimization problems. Since most of these scenarios are over-constrained, optimal solutions do not always satisfy all agents. Some agents might be unhappy and ask questions of the form ``Why does solution $S$ not satisfy property $P$?''. We propose CMAoE, a domain-independent approach to obtain contrastive explanations by: (i) generating a new solution $S^\prime$ where property $P$ is enforced, while also minimizing the differences between $S$ and $S^\prime$; and (ii) highlighting the differences between the two solutions, with respect to the features of the objective function of the multi-agent system. Such explanations aim to help agents understanding why the initial solution is better in the context of the multi-agent system than what they expected. We have carried out a computational evaluation that shows that CMAoE can generate contrastive explanations for large multi-agent optimization problems. We have also performed an extensive user study in four different domains that shows that: (i) after being presented with these explanations, humans' satisfaction with the original solution increases; and (ii) the constrastive explanations generated by CMAoE are preferred or equally preferred by humans over the ones generated by state of the art approaches.

翻译：在许多现实场景中，智能体参与优化问题。由于大多数场景是过约束的，最优解并不总能满足所有智能体。部分智能体可能产生不满，并提出诸如“为什么解$S$不满足性质$P$？”的疑问。我们提出CMAoE，一种领域无关的对比解释生成方法，其实现方式为：(i) 生成满足性质$P$的新解$S^\prime$，同时最小化$S$与$S^\prime$之间的差异；(ii) 突出两个解之间关于多智能体系统目标函数特征的差异。此类解释旨在帮助智能体理解为何初始解在多智能体系统背景下优于其预期。我们进行了计算评估，证明CMAoE能够为大规模多智能体优化问题生成对比解释。同时，我们在四个不同领域开展了广泛用户研究，结果表明：(i) 在接触这些解释后，人类对原始解的满意度有所提升；(ii) 与现有最优方法生成的对比解释相比，人类更偏好或同等偏好CMAoE所生成的对比解释。