Multiobjective differential evolution enhanced with principle component analysis for constrained optimization

Abstract

Multiobjective evolutionary algorithms (MOEAs) have been successfully applied to a number of constrained optimization problems. Many of them adopt mutation and crossover operators from differential evolution. However, these operators do not explicitly utilise features of fitness landscapes. To improve the performance of algorithms, this paper aims at designing a search operator adapting to fitness landscapes. Through an observation, we find that principle component analysis (PCA) can be used to characterise fitness landscapes. Based on this finding, a new search operator, called PCA-projection, is proposed. In order to verify the effectiveness of PCA-projection, we design two algorithms enhanced with PCA-projection for solving constrained optimization problems, called PMODE and HECO-PDE, respectively. Experiments have been conducted on the IEEE CEC 2017 competition benchmark suite in constrained optimisation. PMODE and HECO-PDE are compared with the algorithms from the IEEE CEC 2018 competition and another recent MOEA for constrained optimisation. Experimental results show that an algorithm enhanced with PCA-projection performs better than its corresponding opponent without this operator. Furthermore, HECO-PDE is ranked first on all dimensions according to the competition rules. This study reveals that decomposition-based MOEAs, such as HECO-PDE, are competitive with best single-objective and multiobjective evolutionary algorithms for constrained optimisation, but MOEAs based on non-dominance, such as PMODE, may not.

A novel electronic nose for the detection and classification of pesticide residue on apples

“…This unsupervised exploratory technique is usually applied prior to any other prediction method. 47–49 In an electronic nose, PCA is applied to extract the principal components from the odor fingerprint information database detected by the MOS sensor for reduction, and the visual data analysis graph is displayed on the interface after training and transformation.…”

“…This unsupervised exploratory technique is usually applied prior to any other prediction method. [47][48][49] In an electronic nose, PCA is applied to extract the principal components from the odor ngerprint information database detected by the MOS sensor for reduction, and the visual data analysis graph is displayed on the interface aer training and transformation. The classication of samples without pesticide and with the maximum pesticide residue of the national standard revealed signicant differences between the various apple samples.…”

Nutritional quality and volatile flavor substances of “laba” garlic products produced by either soaking or fumigating with acetic acid

“…PCA is a mathematical tool based on factor analysis that aims to represent the variation present in the dataset using a small number of factors (Huang et al., 2019). To better observe the volatile differences and the correlations between samples and their volatile compositions, PCA of volatile compounds in three garlic samples identified by GC‐MS were performed.…”

Development of volatile compounds fingerprints by headspace‐gas chromatography‐ion mobility spectrometry in concentrated tomato paste and distillate during evaporation processing

“…Principal component analysis is a multivariate statistical analysis method for dimension reduction, in which several principal factors displaying linear relationships are extracted to reflect the main information of the original variables (Huang et al ., 2019). It was performed here to analyse the similarities of volatile profiles in the fresh pulp, concentrated tomato pastes and distillates.…”