Multi-Objective Evolutionary Algorithms (MOEAs) are methods which are strongly recommended to approximate the Pareto frontier whenever the characteristics of objective functions and constraints make it difficult for mathematical programming (cf. Coello, 1999). These approaches construct a solution set formed by non-dominated solutions.
Alternatively, an MOEA can approximate toward the set of best compromise solutions, i.e. the Region of Interest or RoI, through the incorporation of information about the preference of a decision maker (DM). According to (Branke, Salvatore, Greco, Slowiński & Zielniewicz, 2016), the DM preference information within an MOEA search process can be motivated by the necessity of sampling of the Pareto frontier, or the reduction of the DM’s cognitive effort to handle only the RoI, or because the DM’s preference information reinforces the necessary selective pressure. Let us observe that the incorporation of preferences is a method that offers support to the limited capacity of the human mind to handle several conflicting objectives at the same time (Miller, 1956); so, this method has become a very powerful tool that aids in the solution of many-objective problems.
However, most of the time the behavior of a complex system often depends on parameters whose values are unknown in advance (Ling, 2010). Such is the case of MOEAs based on outranking approaches. The outranking approaches are methods that construct outranking relations among potential actions or decision alternatives and exploit such relations to find solutions to decision problems. These approaches have found application in approximating the RoI in Multi-objective Optimization Problems (MOPs) because they allow computational models of preferences of DM’s that can be used to guide the search in MOEAs toward solutions that are closely related to his/her interests.
Ideally, the parameter values of an outranking approach should be defined by the DM; however, given the cognitive effort required from the DM, this task can be extremely difficult and time-consuming, and hence prohibited to be handled directly. This situation is aggravated in cases when a DM is not capable of providing a clear explanation of his/her decisions. These situations prevent from the use of a direct assessment of the parameter values required by a complex system. Instead, the most convenient strategy to overcome such problems lies in the use of preference disaggregation methods.
A preference disaggregation method (PDM) is an indirect elicitation approach that can indirectly infer the values of a predefined set of parameters from a set of examples provided by the DM. In these approaches, the provision of preference information is far simpler for a DM because it can be done based on decisions taken in the past or formulated recently by means of manageable examples. So far, PDMs have been implemented using evolutionary metaheuristics, and they have shown their effectiveness on the parameter elicitation for outranking approaches used in the solution of the Portfolio Selection Problem (PSP). However, the success in the parameter elicitation does not depend only on the quality of the provided set examples but also on the performance of the used algorithms; in this aspect, it has been observed in other problems that the achievement of good solutions in a wider range of instances might require the use of several metaheuristics combined. Recently, hyperheuristics gain more attention because of their capacity to integrate characterization models of problem instances with a set of metaheuristics in order to improve the construction of solution in an optimization problem. Based on the fact that parameter elicitation has been modeled previously by optimization problems, this work proposes the study of the impact on the parameter elicitation of outranking approaches for PSP due to the implementation of a hyperheuristic that selects adequately the best metaheuristics given the instance of the problem and the state of the search process.
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