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Multiobjective dynamic programming in bipolar multistage method
Annals of Operations Research ( IF 4.4 ) Pub Date : 2021-01-24 , DOI: 10.1007/s10479-020-03911-2
Tadeusz Trzaskalik

The multicriteria Bipolar method can be extended and used to control multicriteria, multistage decision processes. In this extension, at each stage of the given multistage process two sets of reference points are determined, constituting a reference system for the evaluation of stage alternatives. Multistage alternatives, which are compositions of stage alternatives, are assigned to one of six predefined hierarchical classes and then ranked. The aim of this paper is to show the possibility of finding the best multistage alternative, using Bellman’s optimality principle and optimality equations. Of particular importance is a theorem on the non-dominance of the best multistage alternative, proven here. The methodology proposed allows to avoid reviewing each multistage alternative, which is important in large-size problems. The method is illustrated by a numerical example and a brief description of the sustainable regional development problem. The problem can be solved by means of the proposed procedure.



中文翻译:

双极多级法中的多目标动态规划

多准则双极性方法可以扩展并用于控制多准则,多阶段决策过程。在此扩展中,在给定的多阶段过程的每个阶段,确定两组参考点,构成用于评估阶段替代方案的参考系统。多阶段替代方案是阶段替代方案的组成部分,被分配给六个预定义的层次类之一,然后进行排名。本文的目的是展示使用Bellman的最优性原理和最优性方程式找到最佳多级替代方案的可能性。特别重要的是关于最佳多级替代方案的非支配性的定理,在此得到证明。所建议的方法可以避免对每个多阶段替代方案进行审查,这在解决大型问题时很重要。通过数值示例和对区域可持续发展问题的简要说明来说明该方法。该问题可以通过所提出的程序来解决。

更新日期:2021-01-24
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