A Survey of Multiobjective Evolutionary Algorithms Based on Decomposition: Variants, Challenges and Future Directions <s> 3) METHODS BASED ON USER PREFERENCES <s> The resulting set of solutions obtained by MOEA/D depends on the weights used in the decomposition. In this work, we use this feature to incorporate user preferences into the search. We use co-evolutionary approach to change the weights adaptively during the run of the algorithm. After the user specifies their preferences by assigning binary preference values to the individuals, the co-evolutionary step improves the distribution of weights by creating new (offspring) weights and selecting those that better match the user preferences. The algorithm is tested on a set of benchmark functions with a set of different user preferences. <s> BIB001 </s> A Survey of Multiobjective Evolutionary Algorithms Based on Decomposition: Variants, Challenges and Future Directions <s> 3) METHODS BASED ON USER PREFERENCES <s> Related to the safety of public lives and property in the lower area of reservoirs, flood control is a priority for most large reservoirs. Considering both dam safety and downstream flood control, reservoir flood control is a multi-objective problem (MOP). To meet the needs of irrigation and generating electricity after the flood, the decision maker usually has his/her preferred final scheduling water level. To deal with this kind of MOP with user-preference information, we incorporate user-preference information into the framework of MOEA/D (multi-objective evolutionary algorithm-based decomposition). The widely used preference information is mainly composed of reference points and preference directions. Compared with the Pareto dominance-based multi-objective evolutionary algorithms (MOEAs), MOEA/D can naturally include two kinds of preference information since MOEA/D is directly based on the reference point and the preference direction. The weight vector of a subproblem in MOEA/D is just its preference. Aiming to obtain uniformly distributed solutions on the objective space, one of innovation points in this paper is using modified Tchebycheff decomposition instead of Tchebycheff decomposition as the decomposition method. To focus the search on the interesting regions of decision maker, the other innovation point in this paper is to integrate biased subproblem (weight vector) adjustment into the framework of MOEA/D. The distribution of subproblems (weight vectors) are adjusted periodically so that the subproblems are re-distributed adaptively to search the interesting regions. Some subproblems, which are far away from the preference regions, are deleted. And then some new subproblems, which are expected to search the preference regions, are added into the current evolutionary population. The efficiency and the effectiveness of the proposed algorithm are assessed through multi-objective reservoir flood control problem and two- to ten-objective test problems. <s> BIB002
The algorithm of this category uses the mechanism that is dependent on user preferences to objectives. Pilát and Neruda BIB001 presented an MOEA/D with the co-evolution of weights (cwMOEA/D), which introduces the CE method to adaptively adjust weights in terms of user preferences during an evolution. DMs specify their preferences by assigning the binary preference values to the individuals in a form of function. After every iteration, the weight vectors are adjusted adaptively by the CE method. The update process generates new weights by the Gaussian mutation with different standard deviations, refines the user preferences function, assigns individuals with both the parent weights and the offspring weights, compares the preferences of the assigned individuals, and selects the weight that corresponds to the individual with a lower preference. The experiments showed that the cwMOEA/D is able to find well-spread solutions in the preference regions specified by DMs, thus effectively utilizing the computational resources. Ma et al. BIB002 proposed an MOEA/D with the biased weight vector (pMOEA/D), which adjusts the distribution of weight vectors based on the geometric analysis of a modified TCH decomposition method for handling the MOPs with preference information. This pMOEA/D attempts to maintain a set of nondominated solutions in the DM's ROI, rather than all solutions of a PS. Particularly, some subproblems whose solutions remain far away from the preference regions are removed while some new subproblems that may help search the preference regions are added into the current evolutionary population. The capability of pMOEA/D to solve practical engineering problems was investigated by testing two multiobjective reservoir flood control problems.