Hetero-Dimensional Multitask Neuroevolution for Chaotic Time Series Prediction

Abstract

Chaotic time series prediction has important research and application value, and neural network-based prediction methods have problems such as low accuracy and difficulty in determining the number of nodes in the hidden layer. In recent years, as a representative of evolutionary multitask optimization algorithms(EMTO), multifactorial evolutionary algorithms (MFEA) have achieved excellent results in Multitask Optimization (MTO) problems, but it does not work well in solving hetero-dimensional multitask problem. We analyzed this phenomenon and proposed the concept of harmful transfer. Then to solve these problems, in this paper, we propose the hetero-dimensional multitask neuroevolution algorithms (HD-MFEA neuroevolution) for chaotic time series prediction. First, we propose hetero-dimensional assortative mating algorithm and self-adaption elite replacement algorithm, so that the hetero-dimensional multitask evolutionary algorithm (HD-MFEA) can overcome the problems caused by harmful transfer on hetero-dimensional multitask problem. Second, in order to adapt to the hierarchical characteristics of neural networks, we propose the neural level segmental coding strategy. Third, we consider the optimization of neural networks with different hidden layer nodes as hetero-dimensional multitask problem and use the HD-MFEA neuroevolution to solve this problem. We verify the effectiveness of the HD-MFEA on six heterodimensional multitask benchmark problems. The Mackey-Glass, Lorenz and Sunspot time series are used to demonstrate the performance of the HD-MFEA neuroevolution. Experimental results have showed that the HD-MFEA neuroevolution performs well in predicting the chaotic time series problems.

Multi-Task Optimization and Multi-Task Evolutionary Computation in the Past Five Years: A Brief Review

“…Zhang and Jiang [145] systematically analyzed the defects of MFEA in dealing with heterogeneous MTO problems, and proposed the concepts of harmful transfer and defective parents. Then hetero-dimensional assortative mating and self-adaption elite replacements were proposed to overcome these issues.…”

“…None [114], AT-MFEA [116], EBS-CMAES [122], EBSFA-CMAES [123], SREMTO [125], MTO-DRA [127], AMA [129], GMFEA [130], mMTDE [131], MTDE [132], TLTLA [133], MFEA [137], MaTDE [141], None [142], MFEA-VT [143,144], HD-MFEA [145], MFEA-FuR [146,147] Vehicle routing problem (VRP)…”

“…Island-EMT [167] Examination timetabling problem EMHH [78] Graph coloring problem EMHH [78] Minimum inter-cluster routing cost clustered tree problem (InterCluMRCT) CC-MFEA [65] Clustered shortest path tree problem (CluSTP) None [62], None [64], CC-MFEA [65], N-MFEA [68], N-MFEA [70] Real-world problem Machine learning Time series prediction problem MFGP [61] Performance prediction problem None [168] Gene regulatory network (GRN) reconstruction MMMA-FCM [169] Community detection MUMI [73] Chaotic time series prediction problem HD-MFEA neuroevolution [145] Training deep neural networks (DNN) problem AMTO [170], None [171] Fuzzy cognitive map (FCM) learning MMMA-FCM [169] Symbolic regression problem (SRP) MFGP [61] Multi-classification problem mXOF [138], EMC-GEP [172] Binary classification problem MFGP [59] Automatic hyperparameter tuning of machine learning models TEMO-MPS [109] Fuzzy system optimization problem MTGFS [72] Association mining problem MFEA [76] Classification problem DMSPSO [89], PSO-EMT [173], MMT-ELM [174] Table 3. Cont.…”

Expanded Neo-Fuzzy Adaptive Decayed Brain Emotional Learning Network for Online Time Series Predication

“…The Mackey-Glass system is presented as a model of white blood cell production [12]. Let us first predict the time series data generated from a time-delayed Mackey-Glass nonlinear differential equation, which has been used as a benchmark by the researchers for validating their prediction algorithms [13], [14]. The series can be defined as mentioned in [2].…”