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arXiv 2007.14778cs.AI
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多目标组合优化的贝叶斯偏好获取

Bayesian preference elicitation for multiobjective combinatorial optimization

Sorbonne Université(索邦大学);CNRS(法国国家科学研究中心);LIP6(巴黎第六大学计算机实验室)

Nadjet Bourdache, Patrice Perny, Olivier Spanjaard

摘要:

我们引入了一个新的增量式偏好诱导过程,能够处理噪声的决策者(DM)的反应。独创性的贡献是提出一个贝叶斯方法来确定一个优选的解决方案,在多目标决策问题涉及一组组合的替代品。我们假设DM的偏好由参数未知的聚集函数表示,并且关于它们的不确定性由参数空间上的密度函数表示。成对比较查询用于减少这种不确定性(通过贝叶斯修正)。查询选择策略是基于一个混合整数线性规划的解决方案与一组组合的变量和约束,这需要使用列和约束生成方法。数值试验表明,该方法的实用性。

英文摘要:

We introduce a new incremental preference elicitation procedure able to deal with noisy responses of a Decision Maker (DM). The originality of the contribution is to propose a Bayesian approach for determining a preferred solution in a multiobjective decision problem involving a combinatorial set of alternatives. We assume that the preferences of the DM are represented by an aggregation function whose parameters are unknown and that the uncertainty about them is represented by a density function on the parameter space. Pairwise comparison queries are used to reduce this uncertainty (by Bayesian revision). The query selection strategy is based on the solution of a mixed integer linear program with a combinatorial set of variables and constraints, which requires to use columns and constraints generation methods. Numerical tests are provided to show the practicability of the approach.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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