Abstract: For a class of multi-attribute group decision making problems, the concept of optimal clutch points is introduced according to the principle of least squares. The combining algorithm of Plant Growth Simulation Algorithm and Accelerating Genetic Algorithm （PGSA-RAGA） is used to obtain the optimal clutch points, and then the projection pursuit model is used with the matrix of the optimal clutch points to get the final projection value and the sorting results. This method solves the problem, which is usually inadequate to use the average number embodying the integrated willingness of the group decision making, in order to get the best sorting results on condition that the property of evaluation features is completely unknown. Through comparative analysis, the feasibility of this method is verified, and it is more simple and easier to operate, which effectively solves many multi-attribute group decision making problems.

Key words: Plant Growth Simulation Algorithm and Accelerating Genetic Algorithm（PGSA-RAGA） combination algorithm, interval number, group decision making, optimal clutch point, projection pursuit

摘要： 针对一类多指标群决策问题，根据最小二乘原理提出了最优离合点的概念。运用模拟植物生长算法与加速遗传算法组合算法（PGSA-RAGA），求解得出最优离合点，并且根据投影寻踪模型利用最优离合点所组成的矩阵，得出最终投影值与排序结果。该方法解决了以往以平均数体现群决策的综合意愿所出现的不足的问题，在指标的属性权重完全未知的情况下，得到最优的排序结果，经过对比分析，该方法的可行性得到验证，更加简便易操作，并且有效地推广到大规模多指标群决策问题。

关键词: 模拟植物生长算法与加速遗传算法（PGSA-RAGA）组合算法, 区间数, 群决策, 最优离合点, 投影寻踪