Abstract
Most evolutionary multi-objective algorithms perform poorly in many objective problems. They normally do not make selective pressure towards the Region of Interest (RoI), the privileged zone in the Pareto frontier that contains solutions important to a DM. Several works have proved that a priori incorporation of preferences improves convergence towards the RoI. The work of (E. Fernandez, E. Lopez, F. Lopez & C.A. Coello Coello, 2011) uses a binary fuzzy outranking relational system to map many-objective problems into a tri-objective optimization problem that searches the RoI; however, it requires the elicitation of many preference parameters, a very hard task. The use of an indirect elicitation approach overcomes such situation by allowing the parameter inference from a battery of examples. Even though the relational system of Fernandez et al. (2011) is based on binary relations, it is more convenient to elicit its parameters from assignment examples. In this sense, this paper proposes an evolutionary-based indirect parameter elicitation method that uses preference information embedded in assignment examples, and it offers an analysis of their impact in a priori incorporation of DM’s preferences. Results show, through an extensive computer experiment over random test sets, that the method estimates properly the model parameter’s values.
Highlights
A consequence of the multi-objective conflicting nature of optimization problems is the difficulty to reach the ideal solution
The second subsection summarizes the results from the statistical evaluation; according to these data, the method reveals that the strategy using a change over the range of ±10% from the expected values of the parameters has the best performance, showing significant difference in contrast with the other two strategies; this reveals the importance for a Decision Maker (DM) to invest a bit of time trying to figure out proper ranges of values to estimate parameters of a preference model
Let us note that the performance of all the indicators m*perf in the set S42,3 was of 0 inconsistences, i.e. the preference model with the estimated parameter values given by the optimization approach reflects the preferences of the DM
Summary
A consequence of the multi-objective conflicting nature of optimization problems is the difficulty to reach the ideal solution (cf, Deb, 2001; Coello, Lamont, & Van Veldhuizen, 2007; Zhu & Luo, 2016). The research shows experimental evidence that the PDA method estimates properly the parameter values for the preference model considered, according to the reference set and by reducing the inconsistencies to zero. It shows that the capacity of prediction on new decisions using the parameters identified results in a low level of inconsistencies. In comparison to the rational paradigm in which the value function methods are based, the outranking approach is more flexible and capable to model ill-shaped preferences of real decision makers and consumers In this sense, new methods able to make robust and cognitive less-demanding elicitation of preference model parameters are welcome. The Section Conclusions shows the final remarks derived from the research
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
