Unbalanced Constraints Research Articles

China’s Urban and Rural Development Significantly Affects the Pattern of Human Appropriation of Net Primary Production

Increasing human activities have greatly influenced the ecosystem and the use of ecological resources, and the unbalanced urban–rural development in China (urban and rural areas being two major bases of human activities) has always been accompanied by heterogeneous ecological effects. Human appropriation of net primary production (HANPP) is an integrated indicator quantifying the human domination of productivity and harvest in the biosphere. Identifying the unbalanced constraints of urban and rural development on HANPP has become necessary for improving human–land relationships. This study analyzed the spatial distribution and regional differentiations of the HANPP in China in 2015 and investigated how HANPP and its components responded to unbalanced regional urban–rural development. The results show that the total amount of HANPP was 2.68 PgC and gradually decreased from the southeast to the northwest of China in 2015, representing 60.33% of the NPPpot. In addition, HANPPluc, harvest through cropland, livestock grazing, and forestry contributed 60.70%, 29.86%, 8.53%, and 0.91%, respectively, to the total HANPP, with HANPPluc playing the dominant role in 21 provinces. There was a significant differentiation (p < 0.05) in the spatial distribution of HANPP (gC/m2), HANPPharv (gC/m2), and HANPPluc (gC/m2), especially between the Huanyong Hu Line and the western–eastern part of China, fundamentally resulting from uneven regional development. In addition, biomass production–consumption decoupling existed in most regions in China, 17 provinces were identified as consumption type, and a universal positive correlation (p < 0.05) was identified between the production–consumption ratio of occupied biomass and HANPPharv (%HANPP). Different drive mechanisms were found between urban–rural development and HANPP, and each HANPP index was more likely to be affected by urban economy (UE), rural population (RP), and rural agricultural technology (RA) in China. The higher regional average nighttime light intensity, the proportion of the built-up area, and the urban road area corresponded with a large HANPPluc value. Conversely, HANPP would decrease as the proportion of urban green spaces increased. Furthermore, HANPP (%NPPpot) and HANPP (gC/m2) mostly depended on the rural development index, while HANPPluc and HANPPharv were mainly controlled by urban and rural development, respectively. Our findings help understand, first, how unbalanced regional development influences human-induced biomass occupation, the comprehensive urban ecological construction, and rural ecological restoration and, second, that the overall planning of urban–rural integration development must be strengthened to face greater ecological pressures in the future.

Issues in calibrating models with multiple unbalanced constraints: the significance of systematic model and data errors

Abstract Calibrating process‐based models using multiple constraints often improves the identifiability of model parameters, helps to avoid several errors compensating each other and produces model predictions that are more consistent with underlying processes. However, using multiple constraints can lead to predictions for some variables getting worse. This is particularly common when combining data sources with very different sample sizes. Such unbalanced model‐data fusion efforts are becoming increasingly common, for example when combining manual and automated measurements. Here we use a series of simulated virtual data experiments that aim to demonstrate and disentangle the underlying cause of issues that can occur when calibrating models with multiple unbalanced constraints in combination with systematic errors in models and data. We propose a diagnostic tool to help identify whether a calibration is failing due to these factors. We also test the utility of adding terms representing uncertainty in systematic model/data systematic error in calibrations. We show that unbalanced data by itself is not the problem—when fitting simulated data to the ‘true’ model, we can correctly recover model parameters and the true dynamics of latent variables. However, when there are systematic errors in the model or the data, we cannot recover the correct parameters. Consequently, the modelled dynamics of the low data volume variables departs significantly from the true values. We demonstrate the utility of the diagnostic tool and show that it can also be used to identify the extent of the imbalance before the calibration starts to ignore the more sparse data. Finally, we show that representing uncertainty in model structural errors and data biases in the calibration can greatly improve the model fit to low‐volume data, and improve coverage of uncertainty estimates. We conclude that the underlying issue is not one of sample size or information content per se, despite the popularity of ad hoc approaches that focus on ‘weighting’ datasets to achieve balance. Our results emphasize the importance of considering model structural deficiencies and data systematic biases in the calibration of process‐based models.

Optimal Dispatch of Integrated Energy System Considering Demand Response and Load Inertia

Renewable energy has the characteristics of strong anti-peak regulation and uncertainty, which cause severe challenges to system peak shaving and renewable energy accommodation. To cope with the challenges of system peak shaving and renewable energy accommodation, this paper proposes an optimal dispatch model of integrated energy system (IES), which considers the price-based demand response and load inertia. Firstly, the impact of changes in energy price on users’ energy consumption is analyzed, and the cool and heat loads inertias are considered in their unbalanced constraints. Secondly, the objective function of the minimum operation costs of the IES is established, including the penalty cost of wind power and photovoltaics curtailments, and operation costs. Finally, the optimal dispatch model of IES is established and solved by YALMIP and GUROBI, respectively. The proposed model is compared with other conventional models. The accommodation capacity of renewable energy with the proposed model is enhanced.

Handling multi-objective optimization problems with unbalanced constraints and their effects on evolutionary algorithm performance

Abstract Despite the successful application of an extension of the Multi-Objective Evolution Algorithm based on Decomposition (MOEA/D-M2M) to solve unbalanced multi-objective optimization problems (UMOPs), its use in constrained unbalanced multi-objective optimization problems has not been fully explored. In an earlier paper, a definition of UMOPs was suggested that had two necessary conditions: 1) finding a favored subset of the Pareto set is easier than finding an unfavored subset, and 2) the favored subset of the Pareto set dominates a large part of the feasible space. The second condition strongly reduces the fraction of MOPs that are considered UMOPs. In this paper, we eliminate that second condition and consider a broader class of UMOPs. We design an unbalanced constrained multi-objective test suite with three different types of biased constraints, yielding three different types of constrained test problems in which the degree of imbalance is scalable via a set of parameters introduced for each problem. We analyse the characteristics of three types of constraints and the difficulties they present for potential solution algorithms–i.e., NSGA-II, MOEA/D and MOEA/D-M2M, with four constraint-handling techniques. MOEA/D-M2M is shown to significantly outperform the other algorithms on these problems due to its decomposition strategy.

Approximation algorithms for MAX RES CUT with limited unbalanced constraints

Two kinds of MAX RES CUT problems, the MAX s−t CUT and the MAX s−t−v CUT, with limited unbalanced constraints are considered. Approximation algorithms used in Frieze and Jerrum (Integer Programming and Combinatorial Optimization, vol. 920, pp. 1–13, Springer, Berlin, 1995), Galbiati and Maffioli (Theor. Comput. Sci. 385:78–87, 2007), Han et al. (Math. Program. Ser. B 92:509–535, 2002) and Ye (Math. Programm. 90:101–111, 2001) are extended to the two MAX RES CUT problems. A special matrix P is constructed by which it can ensure that the given nodes s,t are feasible to equality constraints with probability one for the MAX s−t CUT and s,t,v are feasible to equality constraints with at least probability 0.912 for the MAX s−t−v CUT. A fussy greedy sizing-adjusted procedure is then proposed to confirm that the round solution is feasible for all constraints. We find these extensions are nontrivial and some interesting results about performance ratio are obtained for the MAX RES CUT problem with limited unbalanced constraints.