In this section, we employ transformed data to evaluate the forecast ability in annual GDP and area of agriculture land for our proposed model in the different four data sets, including Malaysia, Mauritius, Sri Lanka, and Madagascar. To prove the superior ability in Xavier weights selection method and GA, this study compares the performances among models named conventional ELM16, OS-ELM19, OS-ELM-GA, and XOS-ELM-GA.
Experimental setting and evaluation
The forecasting performance of the models is critical for accurate sustainability planning, as reliable predictions enable policymakers to design proactive interventions that balance economic growth with environmental protection. The superior performance of XOS-ELM-GA provides a robust foundation for evidence-based sustainable development strategies. Here, we introduce two sets of experiments designed to assess not only the enhancements of our proposed methods but also to demonstrate the superior forecasting capabilities of our model in predicting annual GDP and agricultural land area.
The first experiment using CO\(_\text {2}\) emission and historical annual GDP from four IORA countries to test the amount of annual GDP in the future. The second experiment employs CO\(_\text {2}\) emission and area of agriculture land from four IORA countries to test the area of agriculture land in the future. The national strategy in the short and long term is generally planned by five and ten years. Thus, this study applies ten years historical characteristics to forecast ten years future trend in amount of annual GDP and area of agriculture land for four IORA countries. Following the data transformation approach outlined in Section Methodology, we utilize a decade of CO\(_\text {2}\) emissions and historical annual GDP data as training features, with the subsequent decade’s annual GDP serving as target values. Similarly, we employ a decade of CO\(_\text {2}\) emissions and historical data as training features, with the subsequent decade’s agricultural land area designated as label data. Therefore, the size of prediction window (D) and the number of prediction steps (P) are all defined as ten. The training features and their corresponding target data for both the GDP prediction model and the agriculture land prediction model are transformed by equations (6) and (7) for the former, and equations (10) and (11) for the latter. The Least One Out (LOO) cross-validation is applied to test the models in the experiments.
Furthermore, this study evaluates the forecasting performance of all models using two metrics: Symmetric Mean Absolute Percentage Error (SMAPE) and Mean Square Error (MSE). SMAPE is a measure of prediction accuracy that quantifies the error as a percentage28, and it is defined by the following equation:
$$\begin{aligned} SMAPE = \frac{100 \%}{n}\sum _{t=1}^{T} \frac{\vert \hat{Y_{t}}-Y_{t}\vert }{\left( \vert \hat{Y_{t}} \vert +\vert Y_{t} \vert \right) /2}, \end{aligned}$$
(22)
while MSE calculates the average of the squares of the differences between the actual and predicted values29. It is a measure of the quality of a predictor or estimator. It is defined as the equation (23).
$$\begin{aligned} MSE = \frac{1}{n} \sum _{t=1}^{T}\left( (Y_{t}-\hat{Y_{t}})^{2}\right) , \end{aligned}$$
(23)
where, T is the number of predictions (\(t = 1, 2, \ldots , T\)). \(\hat{Y_{t}}\) is the prediction value in t-th time, and \(Y_{t}\) is the t-th actual target value.
At the same time, to ensure a fair comparison in experiments, this study ensures that the parameters are searched and optimized for all models involved. The conventional ELM uses grid search to identify the optimal parameter (the number of hidden neurons), which sets the within a specified range of 5 to 200 with an interval of 5 to search the best performance by average value of SMAPE. For OS-ELM-based models, the initial training subset was fixed at 60% of the total training samples in order to balance initialization stability and sequential adaptability. A smaller initial proportion may weaken the robustness of the hidden-layer representation and output-weight estimation, whereas a larger proportion may reduce the effective role of sequential updating. Therefore, the current setting was selected as a compromise between these two considerations. We acknowledge that different values of \(\mu\) may affect both the forecasting performance and the GA-optimized number of hidden neurons, and a dedicated sensitivity analysis on this parameter will be included in future work. The number of hidden neurons in the conventional OS-ELM models is determined by a grid search approach, scanning a range from 5 to 200 neurons with an interval of 5. This systematic search allowed us to identify the optimal number of hidden neurons that would yield the best performance for each model. In the case of OS-ELM-GA and XOS-ELM-GA, the optimization of the number of hidden neurons is handled by a Genetic Algorithm, which is known for its ability to efficiently search large and complex spaces. The average SMAPE is selected as the fitness value for the Genetic Algorithm when optimizing parameters, which effectively guides the search towards models that minimize prediction errors.
According to the above settings, eight datasets can be evaluated. Tables 4 and 5 report the forecasting performances in terms of MSE and SMAPE for annual GDP and agricultural land across four countries, respectively.
Table 4 presents a comparative analysis of annual GDP forecasting for five models, namely SVR, ELM, OS-ELM, OS-ELM-GA, and XOS-ELM-GA, across Malaysia, Mauritius, Sri Lanka, and Madagascar under LOO cross-validation. The results are reported at three representative forecast steps (Step 1, Step 5, and Step 10), together with average values of 1-10 step. Overall, XOS-ELM-GA provides the most competitive GDP forecasting performance in terms of average MSE and SMAPE in most cases, although the best results at individual forecast steps are not always produced by the same model.
For Malaysia, XOS-ELM-GA achieves the lowest MSE values at Step 1 (4.48E-04), Step 5 (1.69E-03), Step 10 (8.94E-03), and in the overall average (4.47E-03). It also yields the lowest SMAPE values across all three forecast steps and in the average, namely 4.81%, 7.98%, 11.10%, and 10.13%, respectively. For Mauritius, XOS-ELM-GA again performs best in MSE at all three forecast steps and in the average, with values of 1.46E-03, 1.02E-03, 6.52E-04, and 1.12E-03, respectively. In terms of SMAPE, however, the best Step 1 and Step 5 results are achieved by ELM, while XOS-ELM-GA gives the lowest values at Step 10 (9.50%) and in the overall average (10.48%).
For Sri Lanka, XOS-ELM-GA obtains the lowest MSE values at Step 1 (3.60E-03), Step 5 (1.97E-02), Step 10 (6.57E-02), and in the average (2.98E-02). Regarding SMAPE, XOS-ELM-GA performs best at Step 1 (6.33%), Step 5 (11.60%), Step 10 (16.90%), and in the average (12.13%). For Madagascar, XOS-ELM-GA achieves the lowest MSE at Step 5 (3.32E-03), Step 10 (3.92E-03), and in the average (3.53E-03), while Step 1 shows a tie between OS-ELM and XOS-ELM-GA, both with an MSE of 3.18E-04. For SMAPE, XOS-ELM-GA gives the best values at Step 1 (8.25%), Step 10 (17.53%), and in the overall average (14.21%), whereas ELM performs best at Step 5 (13.30%).
Taken together, these results indicate that XOS-ELM-GA generally provides the strongest GDP forecasting performance, particularly in terms of average accuracy and stability, although several individual forecast steps are better captured by alternative baseline models.
Table 5 provides a comparative analysis of agricultural land forecasting performance for the same five models across the four countries using MSE and SMAPE. Compared with the GDP results, the best single-step values are more frequently distributed across different models. Even so, XOS-ELM-GA remains highly competitive, especially in average performance.
For Malaysia, SVR achieves the lowest MSE at Step 1 (5.77E-05) and Step 5 (7.82E-04), whereas XOS-ELM-GA performs best at Step 10 (5.59E-04) and in the average (9.14E-04). A similar pattern is observed in SMAPE: SVR is best at Step 1 (1.51%) and Step 5 (4.33%), while XOS-ELM-GA gives the lowest Step 10 SMAPE (4.23%) and the lowest average SMAPE (5.90%).
For Mauritius, SVR yields the lowest Step 1 MSE (2.46E-04), while XOS-ELM-GA performs best at Step 5 (2.07E-03), Step 10 (1.56E-03), and in the average (2.49E-03). For SMAPE, ELM performs best at Step 1 (1.30%) and Step 5 (3.19%), whereas XOS-ELM-GA gives the lowest values at Step 10 (3.74%) and in the average (4.24%).
For Sri Lanka, OS-ELM-GA achieves the best Step 1 performance in both MSE (7.21E-04) and SMAPE (2.36%). XOS-ELM-GA performs best at Step 5, Step 10, and in the average, with MSE values of 8.14E-04, 2.97E-03, and 1.76E-03, and SMAPE values of 2.87%, 4.57%, and 3.77%, respectively.
For Madagascar, OS-ELM-GA achieves the lowest Step 1 MSE (3.98E-04), while XOS-ELM-GA gives the best MSE values at Step 5 (2.93E-03), Step 10 (3.90E-03), and in the average (2.22E-03). For SMAPE, ELM performs best at Step 1 (1.29%), while XOS-ELM-GA provides the lowest values at Step 5 (3.89%), Step 10 (2.94%), and in the average (2.99%).
Therefore, the agricultural land forecasting results suggest that XOS-ELM-GA remains a highly effective predictor and frequently achieves the best average performance, especially in Malaysia, Mauritius, and Sri Lanka.
According to the above discussion, the XOS-ELM-GA model has shown a superior ability in forecasting annual GDP and the area of agricultural land. To visualize its performance across the four datasets, Fig. 4 depicts the convergence line based on SMAPE values, which offers a clear view of the tend of model’s predictive precision as it progresses through the iterations. Furthermore, Fig. 5 presents a line chart that compares the predictive values from the XOS-ELM-GA model with the actual ground truth values, thereby illustrating the effectiveness of model’s forecasting in relation to real-world data. In Fig. 4, GA assists XOS-ELM on searching suitable parameters for forecasting annual GDP and area of agriculture land in four countries. In Malaysia, our proposed model appears to reach the lowest SMAPE within the first 10 iterations in two types of datasets. Similarly, in the case of Madagascar, the lowest SMAPE is achieved within the first 10 iterations as well. Sri Lanka’s datasets also show a quick convergence for annual GDP dataset. However, for area of agriculture land in Sri Lanka, the lowest SMAPE is achieved in around 20 iterations. Lastly, Mauritius’s datasets exhibit a similar pattern, with the lowest SMAPE being attained within the initial 10 iterations.
The convergence chart using XOS-ELM-GA for four IORA countries.
Figure 5 presents a comparative line chart analysis of predictive values against actual values for area of agricultural land (right subplots) and annual GDP (left subplots), as forecasted by the XOS-ELM-GA model, across four countries: Malaysia, Madagascar, Sri Lanka, and Mauritius. Each subplot corresponds to a country, with the x-axis representing time and the y-axis denoting the normalized annual GDP and area of agricultural land. The ’Ground Truth’ is depicted in blue, while the ’Prediction’ is shown in red, allowing for a visual assessment of the model’s forecasting accuracy. In Malaysia, the prediction closely follows the ground truth, with a slight deviation towards the latter time points. Madagascar’s chart shows an initial close match, with a notable divergence occurring around the mid-time point, after which the prediction aligns again with the ground truth. Sri Lanka’s data exhibit a prediction that is consistently lower than the ground truth, particularly in the middle time frame, before converging. Mauritius displays a prediction that closely mirrors the ground truth with minor fluctuations. Overall, the charts illustrate the XOS-ELM-GA model’s variable performance across the four countries, with generally good predictive capabilities.
Line chart of four countries for predictive values based on XOS-ELM-GA and actual values.
Prediction and discussion
Section Experimental setting and evaluation proved that model XOS-ELM-GA had super forecasting ability for annual GDP rather than others based on LOO cross-validation. In this section, we will visualize the annual GDP and area of agriculture land from XOS-ELM-GA in 10 future years (2021–2030) for Malaysia, Madagascar, Sri Lanka, and Mauritius.
Firstly, all transformed matrix of each countries data sets as training data in XOS-ELM-GA. The most suitable number of hidden neurons in XOS-ELM will be optimized by GA when our proposed model achieves training. Based on the comparison between the predictive values and the actual values depicted in Figure 5, it is evident that the forecast trends are closely matched with the observed trends in the historical data. This suggests that the predictive model XOS-ELM-GA has accurately captured the underlying patterns and is likely to provide reliable insights into future performance. From a methodological perspective, the superior performance of XOS-ELM-GA can be attributed to the combined effect of the Xavier-based weight initialization and the GA-based parameter search. Compared with OS-ELM, the proposed model reduces instability caused by random initialization, while compared with OS-ELM-GA, it provides a more stable hidden representation before sequential updating. This explains why the model achieved lower average forecasting errors across multiple country-specific datasets. At the application level, the results also reveal that the CO\(_2\)–GDP–land nexus is not uniform across IORA countries. Malaysia and Mauritius exhibit stronger coupling between projected economic growth and carbon-emission-related pressure, whereas Madagascar and Sri Lanka show more pronounced land-use sensitivity, implying differentiated sustainability pathways rather than a common regional trajectory.
These findings indicate that predictive improvement is not only a technical gain but also relevant for sustainability-oriented interpretation. More accurate forecasts may help identify whether future growth is likely to be accompanied by expanded agricultural land demand or continued carbon-intensive development. In this sense, the model may provide exploratory scenario support for discussing country-specific development pressures related to low-carbon transition and land-use governance under long-term sustainability goals.
Conditional forecast trajectories of annual GDP and area of agriculture land from 2021 to 2030 under the adopted future CO2 input setting.
For future multi-step forecasting, the initial testing window is first constructed using the observed CO\(_{2}\) emissions and observed target values over 2011–2020. The trained XOS-ELM-GA model then generates the next-step forecast, after which the target sequence in the input window is updated recursively by appending the newly predicted value and shifting the window forward. Because CO\(_{2}\) emissions are also included in the predictor structure, the resulting long-horizon trajectories should be interpreted as conditional forecasts under the adopted CO\(_{2}\) input setting. In this sense, the projected paths for 2021–2030 provide forecasting-based evidence under the specified input configuration, rather than unconditional future realizations. Next, based on the trained XOS-ELM-GA model, we use 10-year CO\(_2\) emissions (2011–2020) and 10-year annual GDP (2011–2020) as the testing features to generate the subsequent ten-year annual GDP forecasts (2021–2030) through a recurrent multi-step forecasting procedure. The ten-year annual GDP (2021–2030) can be predicted as Figure 6, which shows the tendency of development of annual GDP and area of agriculture land in recent ten years. For Malaysia, the forecast results indicate a continued upward GDP trajectory over the coming decade, with a relatively stable growth pattern compared with the other countries. Madagascar also shows an overall increasing trend, although the projected path contains more fluctuations, reflecting a comparatively weaker and less stable predictive relationship. Sri Lanka exhibits a gradual increase in the earlier years followed by a more pronounced upward tendency toward the end of the forecast horizon. Mauritius likewise maintains a generally positive growth trajectory, suggesting continued economic expansion over the projected period. Overall, all four countries are projected to experience GDP growth, although the smoothness and magnitude of this growth differ across national contexts.
The same recursive forecasting setting is adopted for agricultural land prediction, where the initial testing window is constructed from the observed CO\(_{2}\) emissions and agricultural land values over 2011–2020, and the target sequence is subsequently updated step by step during the forecasting horizon. Furthermore, Fig. 6 also provides the future trend of the area of agricultural land in four countries. For Malaysia, the historical data (red line) shows a gradual increase in agricultural land use, starting at approximately 25 thousand square kilometers in 2011 and reaching around 40 thousand square kilometers by 2019. The predictive data (blue line) suggests a significant rise post-2020, peaking at about 45 thousand square kilometers in 2025, with a slight decline towards 2029. Madagascar’s historical trend (red line) indicates a stable use of agricultural land around 70,290 square kilometers from 2011 to 2019. The predictive line (blue) shows a sharp increase starting in 2020, with a steady rise expected to reach approximately 70,300 square kilometers by 2029. Sri Lanka’s historical data (red line) reveals a slight increase in agricultural land use from about 44 thousand square kilometers in 2011 to around 46 thousand square kilometers in 2019. The predictive trend (blue line) shows a more pronounced increase, with a peak at approximately 52 thousand square kilometers in 2027, followed by a decline towards 2029. Mauritius’s historical trend (red line) is relatively stable, with a slight decrease from around 45 thousand square kilometers in 2011 to about 40 thousand square kilometers in 2020. The predictive data (blue line) indicates a sharp increase starting in 2021, peaking at approximately 55 thousand square kilometers in 2027, and then a decline towards 2029. Although these forecast trajectories provide useful evidence for understanding possible land-use tendencies, they should be interpreted in light of the simplified predictor specification adopted in this study. In particular, the agricultural land forecasting task is based on CO\(_2\) emissions together with historical target information, and therefore does not explicitly represent other important drivers such as land-use policy, commodity markets, urban expansion, or institutional conditions. For countries such as Madagascar and Sri Lanka, where the statistical association between CO\(_2\) emissions and agricultural land is comparatively weaker, the forecast trajectories are more appropriately understood as indicative predictive patterns under a parsimonious input specification, rather than as strong structural evidence of land-use dynamics. The different paths for agricultural land use predicted for nations such as Madagascar and Mauritius reflect unique socio-environmental responses to climate pressures. Within the scope of the present forecasting framework, these patterns are useful for identifying possible sustainability pressures associated with future land-use change. In Madagascar, the expected growth of agricultural areas, while driven by economic needs, represents a direct risk to local carbon storage and biodiversity centers. This result highlights the importance of land-sensitive development planning in contexts where economic expansion may coincide with increasing pressure on natural systems. For IORA countries, these findings are more appropriately interpreted as exploratory forecasting evidence that may inform discussion on land-use sensitivity and broader sustainability challenges, rather than as direct policy prescription. Overall, the predictive data for all countries show an upward trend in agricultural land use, with some fluctuations and a peak in the latter years of the decade, except for Mauritius, which shows a decline after the peak.
The relatively higher forecasting errors observed for Madagascar should also be interpreted in light of the weaker statistical relationship between CO\(_\text {2}\) emissions and the target variables in this dataset, which makes the predictive task itself more challenging even under optimized parameter search. Nevertheless, the forecasting results across the four countries still reveal a complex and interlinked relationship among CO\(_\text {2}\) emissions, GDP, and agricultural land use, with direct implications for sustainability. The projected GDP growth in all four countries, although reflecting a positive development trend, may simultaneously intensify climate mitigation pressure. This concern is particularly evident in Malaysia and Mauritius, where the stronger historical relationship between GDP and CO\(_\text {2}\) emissions suggests a greater risk of continued dependence on carbon-intensive development pathways. For the land-use results, the discussion should likewise be understood within the boundaries of the present predictor design. The projected expansion of agricultural land in Madagascar and Sri Lanka points to potentially greater environmental pressure, but these results are more appropriately interpreted as forecasting-based warning signals than as complete structural explanations of land-use dynamics. In contrast, the projected expansion of agricultural land in Madagascar and Sri Lanka raises broader environmental concerns beyond economic development itself. Such changes may not only increase the risk of deforestation and biodiversity loss, but also affect soil stability, surface runoff processes, and catchment hydrology, thereby creating additional pressure on land and water systems. Furthermore, if the projected GDP growth in Malaysia and Mauritius continues to be accompanied by relatively high carbon-emission levels, the associated climate forcing may further threaten vulnerable coastal and marine ecosystems. Taken together, these findings highlight a fundamental sustainability trade-off: economic growth, agricultural expansion, and climate action may evolve in conflicting directions if no effective intervention is implemented. Within this scope, the forecasting results may provide exploratory scenario support for discussing differentiated sustainability pressures across the four IORA countries, as summarized in Table 6.
More broadly, the predictive results from the proposed framework highlight two areas of potential relevance for regional sustainability discussion. First, the close association between GDP and CO\(_{2}\) levels suggests that economic growth and emissions may remain difficult to decouple in some IORA countries. Second, the projected relationship between carbon emissions and agricultural land change indicates that land-use responses may differ substantially across local contexts. These findings may therefore provide useful exploratory evidence for discussing differentiated development pathways and context-sensitive sustainability strategies within the IORA region.
Therefore, the proposed model may be useful as an exploratory forecasting tool for identifying where economic growth, emissions, and land-use change appear to move together under the observed statistical relationships, thereby supporting scenario-oriented discussion of sustainable development challenges.
