Our maintenance optimization problem, like many other multi-objective optimization problems, can lead to a large objective space. However, finding a well-distributed set of solutions on the Pareto front requests a large population size and computational effort. Therefore, instead of spreading a limited size of individuals across the entire Pareto front, we want to only focus on a part of the Pareto front. In other words, the search for solutions can only be guided towards the preference region which is determined by the decision maker (DM).
A target region based multiobjective evolutionary algorithm framework has been proposed to incorporate preference into the optimization process . The target region is the preferred region and it can be different shapes based on the way that the DM provides it. For example, if the lower bound and upper bound of the objective space are provided by the DM, the target region is rectangular; if the DM specifies the center point and radius of a sphere, the target region can be a sphere.
Three algorithms have been proposed based on the target region based multiobjective evolutionary algorithm framework, which are T-SMS-EMOA, T-R2-EMOA and T-NSGA-II (where T stands for target region). Instead of the original two ranking criteria in SMS-EMOA , R2-EMOA  and NSGA-II , our target region based algorithms add one extra ranking criterion as the third criterion, which is the Chebyshev distance. To be specific, for example, three ranking criteria are used in T-NSGA-II. The first one is non-dominated sorting, the second one is the crowding distance and the third one is the Chebyshev distance to the center of the target region.
These algorithms have been tested on several bi- and tri-objective benchmark problems, which include both discrete and continuous problems. The following figure shows the example when a sphere is assigned as the target region on DTLZ1 problem. The transparent sphere depicts the target region, the blue points show the entire Pareto front and red points are solutions obtained by T-SMS-EMOA.
It can be seen that our proposed algorithm can find a more fine-grained resolution of a target region without exploring the whole set of Pareto optimal solutions. It can guide the search towards the regions on the Pareto Front which are of real interest to the decision maker.
By: Yali Wang
 Wang, Yali, Longmei Li, Kaifeng Yang, and Michael TM Emmerich. “A new approach to target region based multiobjective evolutionary algorithms.” In 2017 IEEE Congress on Evolutionary Computation (CEC), pp. 1757-1764. IEEE, 2017.
 Beume, Nicola, Boris Naujoks, and Michael Emmerich. “SMS-EMOA: Multiobjective selection based on dominated hypervolume.” European Journal of Operational Research181, no. 3 (2007): 1653-1669.
 Trautmann, Heike, Tobias Wagner, and Dimo Brockhoff. “R2-EMOA: Focused multiobjective search using R2-indicator-based selection.” In International Conference on Learning and Intelligent Optimization, pp. 70-74. Springer, Berlin, Heidelberg, 2013.
 Deb, Kalyanmoy, Amrit Pratap, Sameer Agarwal, and T. A. M. T. Meyarivan. “A fast and elitist multiobjective genetic algorithm: NSGA-II.” IEEE transactions on evolutionary computation 6, no. 2 (2002): 182-197.