Multi-criteria decision analysis presumes trade-off between different criteria. As a result, the optimal solution is not unique and can be represented by the Pareto frontier in the objective space. Each Pareto solution is a compromise between different objectives. Despite a limited number of Pareto optimal solutions, the decision-maker eventually has to choose only one option. Such a choice has to be made with the use of additional preferences not included in the original formulation of the optimization problem. The paper represents a new approach to an automatic ranking that can help the decision-maker. In contrast to the other methodologies, the proposed method is based on the minimization of trade-off between different Pareto solutions. To be realized, the approach presumes the existence of a well-distributed Pareto set representing the entire Pareto frontier. In the paper, such a set is generated with the use of the directed search domain algorithm. The method is applied to a number of test cases and compared against two existing alternative approaches.

中文翻译：

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多标准决策分析的折衷排序方法

多标准决策分析假定了不同标准之间的权衡。结果，最优解不是唯一的，并且可以由客观空间中的帕累托边界表示。每个Pareto解决方案都是不同目标之间的折衷方案。尽管Pareto最优解决方案数量有限，但决策者最终只能选择一个选项。这种选择必须使用优化问题的原始公式中未包含的其他首选项来进行。本文代表了一种自动排名的新方法，可以为决策者提供帮助。与其他方法相比，所提出的方法基于最小化不同Pareto解决方案之间的权衡取舍。要实现，该方法假定存在一个分布良好的Pareto集，代表整个Pareto边界。在本文中，使用有向搜索域算法生成了这样的集合。该方法适用于许多测试案例，并与两种现有替代方法进行了比较。