Using Choquet integral as preference model in interactive evolutionary multiobjective optimization

We propose an interactive multiobjective evolutionary algorithm that attempts to discover the most preferred part of the Pareto-optimal set. Preference information is elicited by asking the user to compare some solutions pairwise. This information is then used to curb the set of compatible user's value functions, and the multiobjective evolutionary algorithm is run to simultaneously search for all solutions that could potentially be the most preferred. Compared to previous similar approaches, we implement a much more efficient way of determining potentially preferred solutions, that is, solutions that are best for at least one value function compatible with the preference information provided by the decision maker. For the first time in the context of evolutionary computation, we apply the Choquet integral as a user's preference model, allowing us to capture interactions between objectives. As there is a trade-off between the flexibility of the value function model and the complexity of learning a faithful model of user's preferences, we propose to start the interactive process with a simple linear model but then to switch to the Choquet integral as soon as the preference information can no longer be represented using the linear model. An experimental analysis demonstrates the effectiveness of the approach.