There are some real-world problems in which multiple objectives conflict with each other and the objectives change with time. These problems require an optimization algorithm to track the moving Pareto front or Pareto set over time. In this paper, we propose a predictive strategy based on special points (SPPS) which consists of three mechanisms. The first one is that the non-dominated set is predicted directly by feed-forward center points, which can eliminate many useless individuals predicted by traditional prediction using feed-forward center points. The second one is that a special point set(such as boundary point, knee point, etc.) is introduced into the predicted population which can track Pareto front or Pareto set more accurately. The third one is the adaptive diversity maintenance mechanism based on boundary points and center points. The mechanism can introduce diverse individuals of the corresponding number according to the degree of difficulty of the problem to keep the diversity of the population. The number of these diverse individuals is strongly related to the center points. Then, they are generated evenly throughout the decision space between the boundary points. The proposed strategy is
Maintaining a balance between convergence and diversity of the population in the objective space has been widely recognized as the main challenge when solving problems with two or more conflicting objectives.
Aiming at the difficulty in evaluating preferencebased evolutionary multiobjective optimization, this paper proposes a new performance indicator. The main idea is to project the preferred solutions onto a constructed hyperplane which is perpendicular to the vector from the reference (aspiration) point to the origin. And then the distance from preferred solutions to the origin and the standard deviation of distance from each mapping point to the nearest point will be calculated. The former is used to measure the convergence of the obtained solutions. The latter is utilized to assess the diversity of preferred solutions in the region of interest. The indicator is conducted to assess different algorithms on a series of benchmark problems with various features. The results show that the proposed indicator is able to properly evaluate the performance of preference-based multiobjective evolutionary algorithms.
The challenge of solving dynamic multi-objective optimization problems is to effectively and efficiently trace the varying Pareto optimal front and/or Pareto optimal set. To this end, this paper proposes a multi-direction search strategy, aimed at finding the dynamic Pareto optimal front and/or Pareto optimal set as quickly and accurately as possible before the next environmental change occurs.
It is well known that maintaining a good balance between convergence and diversity is crucial to the performance of multiobjective optimization algorithms (MOEAs). However, the Pareto front (PF) of multiobjective optimization problems (MOPs) affects the performance of MOEAs, especially reference point-based ones.This paper proposes a reference-point-based adaptive method to study the PF of MOPs according to the candidate solutions of the population. In addition, the proportion and angle function presented selects elites during environmental selection. Compared with five state-of-the-art MOEAs, the proposed algorithm shows highly competitive effectiveness on MOPs with six complex characteristics.
Classical multi-objective evolutionary algorithms (MOEAs) have been proven to be inefficient for solving multiobjective optimizations problems when the number of objectives increases due to the lack of sufficient selection pressure towards the Pareto front (PF). This poses a great challenge to the design of MOEAs. To cope with this problem, researchers have developed reference-point based methods, where some welldistributed points are produced to assist in maintaining good diversity in the optimization process. However, the convergence speed of the population may be severely affected during the searching procedure. This paper proposes a proportion-based selection scheme (denoted as PSS) to strengthen the convergence to the PF as well as maintain a good diversity of the population. Computational experiments have demonstrated that PSS is significantly better than three peer MOEAs on most test problems in terms of diversity and convergence.
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