Adaptive Reference Vector Generation for Inverse Model Based Evolutionary Multiobjective Optimization with Degenerate and Disconnected Pareto Fronts

Inverse model based multiobjective evolutionary algorithm aims to sample candidate solutions directly in the objective space, which makes it easier to control the diversity of non-dominated solutions in multiobjective optimization. To facilitate the process of inverse modeling, the objective space is partitioned into several subregions by predefining a set of reference vectors. In the previous work, the reference vectors are uniformly distributed in the objective space. Uniformly distributed reference vectors, however, may not be efficient for problems that have nonuniform or disconnected Pareto fronts. To address this issue, an adaptive reference vector generation strategy is proposed in this work. The basic idea of the proposed strategy is to adaptively adjust the reference vectors according to the distribution of the candidate solutions in the objective space. The proposed strategy consists of two phases in the search procedure. In the first phase, the adaptive strategy promotes the population diversity for better exploration, while in the second phase, the strategy focused on convergence for better exploitation. To assess the performance of the proposed strategy, empirical simulations are carried out on two DTLZ benchmark problems, namely, DTLZ5 and DTLZ7, which have a degenerate and a disconnected Pareto front, respectively. Our results show that the proposed adaptive reference vector strategy is promising in tacking multiobjective optimization problems whose Pareto front is disconnected.