基于序贯回归的成就标量化函数参数偏好估计
Preference-Based Estimation of Achievement Scalarising Function Parameters via Ordinal Regression
AI总结：
针对多目标优化中成就标量化函数参数难估计的问题，提出基于序贯回归的方法，可从决策者偏好信息中推断权重与参考点，经多目标背包问题示例验证，该方法灵活可解释，支持决策者偏好 elicitation。
AI中文摘要：
在多目标优化中，成就标量化函数的参数估计是一项具有挑战性的任务。成就标量化函数广泛应用于多种场景，包括基于偏好的优化方法以及生成或选择有效解的算法流程。然而，其有效性高度依赖于参数的恰当设定，如权重和参考点。本文提出一种基于序贯回归的方法，用于从决策者（DM）提供的偏好信息中估计成就标量化函数的参数。具体而言，该方法可同时推断与各目标关联的权重以及表征标量化函数的参考点。通过一个基于多目标背包问题的教学示例对该方法进行说明，该示例逐步展示了偏好信息如何转化为模型参数。此示例表明，序贯回归为校准成就标量化函数提供了灵活且可解释的框架，并支持多目标优化中决策者偏好的 elicitation（此处保留原词，若需补充可译为“ elicitation 即偏好 elicitation”，但按规则保留原词）。
英文摘要：
Estimating the parameters of an achievement scalarising function is a challenging task in multiobjective optimisation. Achievement scalarising functions are widely used in several contexts, including preference-based optimisation methods and algorithmic procedures for generating or selecting efficient solutions. However, their effectiveness strongly depends on the appropriate specification of their parameters, such as weights and reference points. In this paper, we propose an ordinal-regression-based methodology to estimate the parameters of an achievement scalarising function from preference information provided by the DM. In particular, the proposed approach allows us to infer both the weights associated with the objectives and the reference points characterising the scalarising function. The methodology is illustrated through a didactic example based on a multiobjective knapsack problem, which shows step by step how the preference information is translated into model parameters. The example illustrates that ordinal regression provides a flexible and interpretable framework for calibrating achievement scalarising functions and supporting the elicitation of decision-maker preferences in multiobjective optimisation.
