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A novel hybrid model based on multi-objective Harris hawks optimization algorithm for daily PM2.5 and PM10 forecasting
Pei Du, Jianzhou Wang, Yan Hao, Tong Niu, Wendong Yang
TL;DR
Air-pollution forecasting matters for health and public warnings, but prior models have limitations in preprocessing, stability, and initialization. The paper combines ICEEMDAN, MOHHO, and ELM for PM2.5 and PM10 forecasting, and reports higher accuracy and greater stability than five comparison models.
Problem
Prior air-pollutant forecasting studies have used simple preprocessing, neglected predictive stability, or had poor initial parameters, despite the need for accurate and reliable forecasts.
Source: §1.2 · p. 3, §6 · p. 19Method
The study decomposes pollutant series with ICEEMDAN and uses MOHHO to optimize ELM for forecasting PM2.5 and PM10 in three Chinese cities.
Source: §3 · p. 3Results
The authors report higher prediction accuracy and more stable results than the five comparison models considered.
Source: §6 · p. 19Takeaways & Limitations
The authors say the model’s prediction ability may help develop air-pollutant emission plans and prevent health problems caused by air pollution.
Source: §6 · p. 19
Abstract
from arXiv · showhide
High levels of air pollution may seriously affect people's living environment and even endanger their lives. In order to reduce air pollution concentrations, and warn the public before the occurrence of hazardous air pollutants, it is urgent to design an accurate and reliable air pollutant forecasting model. However, most previous research have many deficiencies, such as ignoring the importance of predictive stability, and poor initial parameters and so on, which have significantly effect on the performance of air pollution prediction. Therefore, to address these issues, a novel hybrid model is proposed in this study. Specifically, a powerful data preprocessing techniques is applied to decompose the original time series into different modes from low- frequency to high- frequency. Next, a new multi-objective algorithm called MOHHO is first developed in this study, which are introduced to tune the parameters of ELM model with high forecasting accuracy and stability for air pollution series prediction, simultaneously. And the optimized ELM model is used to perform the time series prediction. Finally, a scientific and robust evaluation system including several error criteria, benchmark models, and several experiments using six air pollutant concentrations time series from three cities in China is designed to perform a compressive assessment for the presented hybrid forecasting model. Experimental results indicate that the proposed hybrid model can guarantee a more stable and higher predictive performance compared to others, whose superior prediction ability may help to develop effective plans for air pollutant emissions and prevent health problems caused by air pollution.
1 Introduction
Air pollution threatens health and creates a need for accurate forecasts that can inform public warnings and air-quality management. The introduction reviews forecasting approaches and identifies limitations in preprocessing, predictive stability, and model initialization.
1.1 Background
- Outdoor air pollution is linked to serious health impacts, and estimates cited for China attribute 350,000–500,000 premature deaths annually to it.The introduction says forecasting can help inform emissions measures, daily activities, and public warnings.Source: §1.1 · p. 2
1.2 Literature overview
- CTMs may not perform well amid complex atmospheric processes, while linear statistical models can miss relationships that nonlinear models are designed to capture.The review names ANNs and LSSVM among nonlinear forecasting approaches.Source: §1.2 · p. 2
- Hybrid forecasts combine forecasting models, optimization algorithms, and data decomposition, but prior studies still use simple preprocessing, overlook stability, or rely on poor initial parameters.The introduction presents these shortcomings as reasons to seek more precise and stable air-pollutant prediction.Source: §1.2 · p. 3
3. Aims and innovations
The study proposes an ICEEMDAN–MOHHO–ELM forecasting model and evaluates it on PM2.5 and PM10 data from three Chinese cities. Its stated innovations include multi-objective optimization and a systematic assessment of accuracy and stability.
3. Aims and innovations
- The proposed ICEEMDAN–MOHHO–ELM model is tested on PM2.5 and PM10 datasets from Jinan, Nanjing, and Chongqing.The study presents it as an approach to improve air-pollutant forecasting performance.Source: §3 · p. 3
- The authors identify ICEEMDAN decomposition, MOHHO optimization, and simultaneous accuracy-and-stability forecasting as core innovations.They report that MOHHO outperforms MOGOA, MOPSO, and MSSA in most cases and offers an option for multi-objective optimization.Source: §3 · p. 3
- The evaluation combines several experiments, seven performance metrics, and a Diebold–Mariano test across air-pollution time series.The authors say the model may support air-quality regulation, daily guidance, and public warnings.Source: §3 · p. 4
1.4. The remainder structure of this paper
- The paper proceeds from methodology and data/evaluation criteria to forecasting experiments, discussion, and conclusions.The experiments and forecasting results are presented in Section 4; Section 5 discusses the model and MOHHO.Source: §1.4 · p. 4
2 Methodology formulation
The methodology decomposes pollutant series into modes, forecasts each mode with an MOHHO-optimized ELM, and combines the mode forecasts. It also describes ICEEMDAN, HHO/MOHHO, and ELM components used in the pipeline.
2.1 The framework of proposed model
- ICEEMDAN decomposes the original series into modes; MOHHO tunes ELM parameters, each mode is forecast, and the mode forecasts are integrated.The evaluation uses error criteria, benchmark models, and experiments on six pollutant time series from China.Source: §2.1 · p. 4
2.2 ICEEMDAN
- ICEEMDAN is an EMD-family decomposition method used on pollutant series; the paper describes it as an improvement intended to produce components with less noise and more physical meaning.The EMD family is described as designed for nonlinear and nonstationary datasets.Source: §2.2 · pp. 5–6
2.3 Multi-objective Harris hawks optimization algorithm (MOHHO)
- HHO is inspired by Harris’ hawks’ cooperative pursuit and is described in three phases: prey exploration, surprise pounce, and attacking strategies.The paper introduces MOHHO as a multi-objective version of HHO.Source: §2.3 · p. 6, Phase III: Exploitation phase · p. 8
Phase I: Exploration phase
- HHO uses the rabbit’s escaping energy to switch between exploration and exploitation; the text defines hawk locations and population size for its position updates.The exploration description also refers to the rabbit’s position, randomly selected hawks, and the average hawk position.Source: Phase I: Exploration phase · pp. 6–7
Phase III: Exploitation phase
- During exploitation, HHO selects among four attack strategies according to the prey’s remaining energy and chance of escape.The strategies are soft or hard besiege, with or without progressive rapid dives.Source: Phase III: Exploitation phase · p. 7
- MOHHO archives non-dominated Pareto solutions, updates the archive each iteration, and uses removal probability for crowded neighborhoods when capacity is reached.A roulette-wheel method is also introduced to improve the distribution of archived solutions.Source: Phase III: Exploitation phase · p. 8
2.4 Extreme Learning Machine
- ELM is described as fast to learn, with random input weights and hidden biases; its output weights use the hidden-layer output matrix’s generalized inverse.The paper also frames ELM as a way to address least-squares problems with less time.Source: §2.4 · p. 9
3 Data description and model evaluation criteria
The study evaluates daily PM2.5 and PM10 forecasting using six series from Jinan, Nanjing, and Chongqing, and assesses models with seven error and agreement criteria.
3 Data description and model evaluation criteria
- The section introduces the data description and model evaluation criteria as its two parts.Source: §3 · p. 9
3.1 Study area and data description
- Six daily PM2.5 and PM10 series from Jinan, Nanjing, and Chongqing, each with 338 observations from November 1, 2017 to November 23, 2018, form the study dataset.The passage says the first 338 samples are used for training and the remaining data for verification.Source: §3.1 · p. 9
3.2 Model evaluation criteria
- The evaluation uses MAE, RMSE, MAPE, U1, and U2, where smaller values indicate better performance, plus IA and r, where larger values indicate better performance.The passage identifies IA as the index of agreement and r as Pearson's correlation coefficient.Source: §3.2 · p. 10
4 Experiments and analysis
The experiments compare ICEEMDAN-MOHHO-ELM with five benchmark models for daily PM2.5 and PM10 forecasting in three Chinese cities. The proposed model reports the best values across the stated evaluation criteria for both pollutants.
4 Experiments and analysis
- The experiments assess PM2.5 and PM10 forecasts in three cities against five comparison models, including individual and hybrid-model comparisons for PM2.5.The PM2.5 comparisons include ARIMA, ELM, LSSVM, EMD-MOHHO-ELM, and CEEMD-MOHHO-ELM; the PM10 experiment uses the same five benchmarks.Source: §4.1 · p. 11, §4 · p. 11, §4.2 · p. 13
4.1. Experiment I: PM2.5 forecasting
- For Jinan, single-model ARIMA, ELM, and LSSVM MAPE values all exceed 20%; their reported values are 35.913%, 38.441%, and 38.945%, respectively, and the authors describe performance as limited.Source: §4.1 · pp. 11–12
- Among PM2.5 hybrid variants, Nanjing RMSE values are 23.567% for EMD-MOHHO-ELM, 13.112% for CEEMD-MOHHO-ELM, and 8.718% for ICEEMDAN-MOHHO-ELM.The authors attribute the difference to ICEEMDAN contributing more to the proposed model's performance than EMD and CEEMD.Source: §4.1 · p. 12
- For PM2.5, ICEEMDAN-MOHHO-ELM has lower MAE, RMSE, MAPE, U1, and U2 and higher IA and r than the comparison models.The forecasting errors and improvement percentages are presented in Tables 2 and 3.Source: §4.1 · p. 12, Table 2 · p. 12, Table 3 · p. 13
4.2. Experiment II: PM10 forecasting
- For PM10 in Jinan, Nanjing, and Chongqing, ICEEMDAN-MOHHO-ELM obtains the best MAE, RMSE, MAPE, IA, U1, U2, and r values among the compared models.The PM10 error and improvement comparisons are presented in Tables 4 and 5.Source: §4.2 · p. 13, Table 4 · p. 14, Table 5 · p. 14
5 Discussions
The discussion evaluates the hybrid forecaster’s accuracy and stability and benchmarks MOHHO on standard multi-objective test functions. The authors report advantages for both the forecasting model and MOHHO, with a qualification on ZDT3.
5 Discussions
- The evaluation used DM and variance-ratio tests for forecasting models, and IGD to compare four optimizers across four ZDT functions over 50 runs.MOHHO tests used an archive size of 100, 100 iterations, and 40 search agents; IGD measures distance from true Pareto solutions to the nearest obtained solutions.Source: §5 · p. 14, §5.2 · pp. 15–16
5.1. DM test and stability test
- The hybrid model outperformed five comparison models in predictive ability and had the highest variance-ratio values, indicating greater forecasting stability.The reported DM statistics exceeded the 1% threshold (2.58).Source: §5.1 · pp. 14–15
5.2. Validity of the proposed MOHHO algorithm
- MOHHO significantly outperformed MOPSO, MOGOA, and MSSA on ZDT1, ZDT2, and ZDT1 with a linear front, but was competitive rather than consistently superior on ZDT3.MOHHO and MSSA converged well to the true fronts; MOGOA had the poorest convergence despite good coverage on ZDT1 and the linear-front test, while MOPSO performed best on most ZDT3 results.Source: §5.2 · p. 16, Figure 3 · p. 16, Figure 4 · p. 17
6 Conclusions
The paper presents an ICEEMDAN–MOHHO–ELM hybrid for air-pollutant forecasting and reports higher accuracy and stability than five comparison models. Its evaluation covers six pollutant concentration series from three Chinese cities.
6 Conclusions
- The motivation is that air pollution can endanger lives, creating a need for accurate and reliable forecasts to guide daily activities and warn the public about hazardous pollutants.Source: §6 · p. 19
- The model decomposes pollutant time series into modes, uses MOHHO to tune ELM parameters for accuracy and stability, and evaluates six series from three Chinese cities.The evaluation system includes multiple error criteria, benchmark models, and experiments.Source: §6 · p. 19
- The hybrid forecasting model achieved higher prediction accuracy and more stable results than the five comparison models.The authors say its predictive performance may help develop air-pollutant emission plans and prevent health problems.Source: §6 · p. 19
Appendix A: Concepts of multi-objective optimization
The appendix introduces a minimization formulation and defines Pareto dominance, optimality, the optimal set, and the optimal front.
Appendix A: Concepts of multi-objective optimization
- The appendix presents a multi-objective minimization formulation and identifies the counts of variables, objectives, inequality constraints, and equality constraints, along with variable bounds.Source: Appendix A · pp. 19–20
- Pareto dominance is introduced as a relation for comparing candidate solutions in multi-objective optimization.Source: Appendix A · pp. 19–20
- The appendix defines Pareto optimality for solutions in the feasible set.Source: Appendix A · p. 20
- The Pareto optimal set is named as a set of Pareto-optimal solutions.Source: Appendix A · p. 20
- The Pareto optimal front comprises the objective-function values for solutions in the Pareto optimal set.Source: Appendix A · p. 20
Appendix B. List of abbreviations 63
Appendix B includes a table titled as improvement percentages for criteria.
Appendix B. List of abbreviations 63
- Table B1 is titled as reporting improvement percentages for criteria.Source: Table B1 · p. 20