多目标动态规划问题的非劣矩阵解法

A Method of Noninferior Matrix of Multiobjective Dynamic Programming

  • 摘要: 针对多目标动态规划问题,指出其一般只存在非劣解的性质,提出了多目标阶段收益非劣矩阵、多目标阶段收益非劣合成矩阵和多目标逆向递推矩阵等概念。在此基础上构造出一种新的多目标动态规划解法-非劣矩阵法,该方法不需要事先给出各目标的相应权重,并能保证得到多目标动态规划问题的所有非劣解。文中给出的计算实例验证了这一方法的正确性和实用价值。

     

    Abstract: In this paper,noninferior nature of the solution of multiobjective dynamic programming is discussed.Three concepts are given,which are multiobjective return noninferior matrix,multiobjective return noninferior compound matrix and multiobjective forward recurrence matrix.On the basis of the three concepts,a new method of noninferior matrix of multiobjective dynamic programming is given.In the method,the relative importance of the whole objectives may not be given beforehand,and all the noninferior solutions can be gotten easily.The validity of the method is tested and verified by an example.

     

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