This article introduces a new algorithm for computing the set of supported non-dominated points in the objective space and all the corresponding efficient solutions in the decision space for the multi-objective spanning tree (MOST) problem. This algorithm is based on the connectedness property of the set of efficient supported solutions and uses a decomposition of the weight set in the weighting space defined for a parametric version of the MOST problem. This decomposition is performed through a space reduction approach until an indifference region for each supported non-dominated point is obtained. An adjacency relation defined in the decision space is used to compute all the supported efficient spanning trees associated to the same non-dominated supported point as well as to define the indifference region of the next points. An in-depth computational analysis of this approach for different types of networks with three objectives is also presented.

本文介绍了一种新算法，用于计算目标空间中支持的非控制点集以及决策空间中所有目标有效解决方案，以解决多目标生成树（MOST）问题。该算法基于有效支持的解决方案集合的连通性属性，并使用为MOST问题的参数版本定义的加权空间中的加权集合进行分解。通过空间缩减方法执行此分解，直到获得每个支持的非支配点的无差异区域。在决策空间中定义的邻接关系用于计算与同一非支配支持点关联的所有支持的有效生成树，以及定义下一个点的无差异区域。