Haitham Seada

Most evolutionary many-objective optimization (EMaO) algorithms start with a description of a number of predefined set of reference points on a unit simplex. So far, most studies have used the Das and Dennis’s structured approach for generating well-spaced reference points. Due to the highly structured nature of the procedure, this method cannot produce an arbitrary number of points, which is desired in an EMaO application. Although a layer-wise implementation has been suggested, EMO researchers always felt the need for a more generic approach. Motivated by earlier studies, we introduce a metric for defining well-spaced points on a unit simplex and propose a number of viable methods for generating such a set. We compare the proposed methods on a variety of performance metrics such as hypervolume, deviation in triangularized simplices, distance of the closest point pair, and variance of the geometric means to nearest neighbors in up to 15-dimensional spaces. We show that an iterative improvement based on Riesz s-Energy is able to effectively find an arbitrary number of wellspaced points even in higher-dimensional spaces. Reference points created using the proposed Riesz s-Energy method for a number of standard combinations of objectives and reference points as well as a source code written in Python are available publicly at https://www.egr.msu.edu/coinlab/blankjul/uniform.

In multiobjective optimization, defining a good solution is a multi-factored process. Most existing evolutionary multi-or many-objective optimization (EMO) algorithms have utilized two factors: domination and crowding levels of each solution. Although these two coarse-grained factors are found to be adequate in many EMO algorithms, their relative importance in an algorithm has been a matter of great concern to many current studies. We argue that beside these issues, other more fine-grained factors are of importance. For example, since extreme objective-wise solutions are important in establishing a noise-free and stable normalization process, reaching extreme solutions is more crucial than finding other solutions. In this paper, we propose an integrated algorithm, B-NSGA-III, that produces much better convergence and diversity preservation. For this purpose, in addition to emphasizing extreme objective-wise solutions, B-NSGA-III tries to find solutions near intermediate undiscovered regions of the front. B-NSGA-III addresses critical algorithmic issues of convergence and diversity-preservation directly through recent progresses in literature and integrates all these critical fine-grained factors seamlessly in an alternating phases scheme. The proposed algorithm is shown to perform better than a number of commonly used existing methods.