Multi-objective preference alignment of large language models (LLMs) is critical for developing AI systems that are more configurable, personalizable, helpful, and safe. However, optimizing model outputs to satisfy diverse objectives with variable weights at inference time for truly personalized models presents a significant challenge. Existing approaches are either computationally expensive to train or do not sufficiently steer model behaviors. This paper introduces the Multi-Objective Online DPO (MO-ODPO) algorithm, designed to robustly and efficiently align model behaviors with multiple, potentially conflicting human preferences. Our approach incorporates a prompt conditioning mechanism, allowing us to train a single preference-conditional policy, that can adapt to new preference combinations at inference. Experiments on two popular benchmarks show that MO-ODPO Pareto-dominates existing baselines while providing excellent inference-time steerability between diverse objectives.

At present, most of the prediction studies related to antagonistic event-group competitions focus on the prediction of competition results, and less on the prediction of the competition process, which can not provide real-time feedback of the athletes' state information in the actual competition, and thus can not analyze the changes of the competition situation. In order to solve this problem, this paper proposes a prediction model based on Random Forest for the turning point of the antagonistic event-group. Firstly, the quantitative equation of competitive potential energy is proposed; Secondly, the quantitative value of competitive potential energy is obtained by using the dynamic combination of weights method, and the turning point of the competition situation of the antagonistic event-group is marked according to the quantitative time series graph; Finally, the random forest prediction model based on the optimisation of the KM-SMOTE algorithm and the grid search method is established. The experimental analysis shows that: The quantitative equation of competitive potential energy can effectively reflect the dynamic situation of the competition; The model can effectively predict the turning point of the competition situation of the antagonistic event-group, and the recall rate of the model in the test set is 86.13%; The model has certain significance for the future study of the competition situation of the antagonistic event-group.

The multiple attribute decision-making (MADM) probl ems are of the most interesting problems for many decision-making experts. This problem aris es in various fields of the real life, and constitutes very important content in scientific research such as management science, decision-making theory, system theory, operational research and economics. Now, many effective methods to determine the att ributive weights have been studied for MADM. Those are the subjective weight determining methods such as the feature vector method ( Saaty T.L. 1977), the least square sum method (Chu A Tw, Kala ba R E, Spingarn K, 1979), Delphi and AHP method (Hwang C.L., Lin M, 1987), and the objective weight determining methods such as the entropy method (Hwang C.L., Yoon K, 1981), the principal component analysis (Yan Jian-huo, 1989) and DEA (Data Envelopment Analysis) (Ye Chen, Kevin W. Li, Haiyan Xu and Sifeng Liu, 2009). The final ranking method affects greatly on the dec ision-making process. Hwang and Yoon (1981) proposed a new approach, TOPSIS (Technique for Orde r Preference by Similarity to Ideal Solution) for solving MADM problem. Recently, TOPSIS methods with interval weights (Gao Feng-ji, et al, 2005) and multiple attribute interval number TOPSIS (Chu A Tw, Kalaba R E, Spingarn K, 1979) have been studied. Guo Kai-hong and Mu You-jing (2012) studied the relation between several possibility degree formulas and proposed a possibil ity degree matrices-based method that aimed to objectively determine the weights of criteria in MA DM with intervals. A hybrid approach integrating OWA (Ordered Weighted Averaging) aggreg ation into TOPSIS is proposed to tackle * This work was supported in part by Nanjing Univer sity of Aeronautics and Astronautics, China. 2

This paper proposes a grey interval relation TOPSIS for the decision making in which all of the attribute weights and attribute values are given by the interval grey numbers. The feature of our method different from other grey relation decision-making is that all of the subjective and objective weights are obtained by interval grey number and that decision-making is performed based on the relative approach degree of grey TOPSIS, the relative approach degree of grey incidence and the relative membership degree of grey incidence using 2-dimensional Euclidean distance. The weighted Borda method is used for combining the results of three methods. An example shows the applicability of the proposed approach.