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The four papers in this special issue focus on preference-based multiobjective evolutionary algorithms.

The centrality of the decision maker (DM) is widely recognized in the multiple criteria decision-making community. This translates into emphasis on seamless human-computer interaction, and adaptation of the solution technique to the knowledge which is progressively acquired from the DM. This paper adopts the methodology of reactive search optimization (RSO) for evolutionary interactive multiobjective optimization. RSO follows to the paradigm of “learning while optimizing,” through the use of online machine learning techniques as an integral part of a self-tuning optimization scheme. User judgments of couples of solutions are used to build robust incremental models of the user utility function, with the objective to reduce the cognitive burden required from the DM to identify a satisficing solution. The technique of support vector ranking is used together with a k-fold cross-validation procedure to select the best kernel for the problem at hand, during the utility function training procedure. Experimental results are presented for a series of benchmark problems.

In this paper, a concept for efficiently approximating the practically relevant regions of the Pareto front (PF) is introduced. Instead of the original objectives, desirability functions (DFs) of the objectives are optimized, which express the preferences of the decision maker. The original problem formulation and the optimization algorithm do not have to be modified. DFs map an objective to the domain [0, 1] and nonlinearly increase with better objective quality. By means of this mapping, values of different objectives and units become comparable. A biased distribution of the solutions in the PF approximation based on different scalings of the objectives is prevented. Thus, we propose the integration of DFs into the S-metric selection evolutionary multiobjective algorithm. The transformation ensures the meaning of the hypervolumes internally computed. Furthermore, it is shown that the reference point for the hypervolume calculation can be set intuitively. The approach is analyzed using standard test problems. Moreover, a practical validation by means of the optimization of a turning process is performed.

Maximizing the lifetime of a sensor network by scheduling operations of sensors is an effective way to construct energy efficient wireless sensor networks. After the random deployment of sensors in the target area, the problem of finding the largest number of disjoint sets of sensors, with every set being able to completely cover the target area, is nondeterministic polynomial-complete. This paper proposes a hybrid approach of combining a genetic algorithm with schedule transition operations, termed STHGA, to address this problem. Different from other methods in the literature, STHGA adopts a forward encoding scheme for chromosomes in the population and uses some effective genetic and sensor schedule transition operations. The novelty of the forward encoding scheme is that the maximum gene value of each chromosome is increased consistently with the solution quality, which relates to the number of disjoint complete cover sets. By exerting the restriction on chromosomes, the forward encoding scheme reflects the structural features of feasible schedules of sensors and provides guidance for further advancement. Complying with the encoding requirements, genetic operations and schedule transition operations in STHGA cooperate to change the incomplete cover set into a complete one, while the other sets still maintain complete coverage through the schedule of redundant sensors in the sets. Applications for sensing a number of target points, termed point-coverage, and for the whole area, termed area-coverage, have been used for evaluating the effectiveness of STHGA. Besides the number of sensors and sensors’ sensing ranges, the influence of sensors’ redundancy on the performance of STHGA has also been analyzed. Results show that the proposed algorithm is promising and outperforms the other existing approaches by both optimization speed and solution quality.