Trade-off ranking method for multi-criteria decision analysis

Abstract

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. KEYWORDSdirected search domain algorithm, multi-criteria decision analysis, multi-objective optimization, Pareto optimal solution, trade-off, ranking INTRODUCTIONIn the real-life design, it is required to improve different objectives simultaneously. A trade-off between the objectives is usually unavoidable because of the constraints. As a result, the optimal solution is not unique and corresponds to a so-called Pareto solution. In the objective space, all Pareto solutions create a Pareto frontier. For a practical decision-making analysis, the Pareto frontier is represented by a Pareto set that contains a finite number of optimal solutions. Eventually, the decision-maker has to choose only one solution. This leads to the problem of ranking because the formal definition of the Pareto solution does not presume any preferences. An additional algorithm is required to introduce the ranking.In the multi-criteria decision analysis, the ranking problem has been developed for the last 20 years. However, there are no universal approaches. Each method stands on its own background and principles.The most natural approach is to introduce individual preferences. One of the basic and simplest multi-criteria decision analysis techniques is the sum of weightage calculation model. In this technique, a weight is assigned to each criterion to denote its importance. Each aggregate function is then calculated as the sum of weightage criteria. A classic work on the weight determination is by Eckenrode (1965). Eckenrode worked with 24 expert judges, who were required to put a weightage on six criteria in a specified experiment related to an air-defence system.Another well-known decision-making method is the analytic hierarchy process (AHP). AHP was proposed by Saaty (1980). The essence of this method is that human judgement is used in performing evaluations. AHP structures a decision problem into a hierarchy with the goal, decision criteria, and alternatives. Then, it uses the pairwise ...

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