In this paper, we present a link between preference-based and multiobjective sequential decision-making. While transforming a multiobjective problem to a preference-based one is quite natural, the other direction is a bit less obvious. We present how this transformation (from preference-based to multiobjective) can be done under the classic condition that preferences over histories can be represented by additively decomposable utilities and that the decision criterion to evaluate policies in a state is based on expectation. This link yields a new source of multiobjective sequential decision-making problems (i.e., when reward values are unknown) and justifies the use of solving methods developed in one setting in the other one.
A final approach to multiobjective problem assumes an interactive setting where a human expert is present and can provide additional preferential information (i.e., how to trade-off between different objectives). This approach loops between the following two steps until a certain criterion is satisfied (e.g., the expert is satisfied with a proposed solution or there is only one solution left): show potential solutions or ask query to the expert receive a feedback answer from the expert The feedback answer from the expert allows to guide the search for a preferred solution among all Pareto-optimal ones @cite_25 , or elicit unknown parameters of user preference model @cite_12 .
@cite_25 @cite_12
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In many multiobjective optimization problems, the Pareto Fronts and Sets contain a large number of solutions and this makes it difficult for the decision maker to identify the preferred ones. A possible way to alleviate this difficulty is to present to the decision maker a subset of a small number of solutions representatives of the Pareto Front characteristics. In this paper, a two-steps procedure is presented, aimed at identifying a limited number of representative solutions to be presented to the decision maker. Pareto Front solutions are first clustered into "families", which are then synthetically represented by a "head-of-the-family" solution. Level Diagrams are then used to represent, analyse and interpret the Pareto Front reduced to its head-of-the-family solutions. The procedure is applied to a reliability allocation case study of literature, in decision-making contexts both without or with explicit preferences by the decision maker on the objectives to be optimized. While Pareto-based multiobjective optimization algorithms continue to show effectiveness for a wide range of practical problems that involve mostly two or three objectives, their limited application for many-objective problems, due to the increasing proportion of nondominated solutions and the lack of sufficient selection pressure, has also been gradually recognized. In this paper, we revive an early developed and computationally expensive strength Pareto-based evolutionary algorithm by introducing an efficient reference direction-based density estimator, a new fitness assignment scheme, and a new environmental selection strategy, for handling both multiobjective and many-objective problems. The performance of the proposed algorithm is validated and compared with some state-of-the-art algorithms on a number of test problems. Experimental studies demonstrate that the proposed method shows very competitive performance on both multiobjective and many-objective problems considered in this paper. Besides, our extensive investigations and discussions reveal an interesting finding, that is, diversity-first-and-convergence-second selection strategies may have great potential to deal with many-objective optimization.