Optimization Modeling, Linear Programming

The optimization of land-use structure is the core of optimizing the allocation of land

resources, including the optimization of quantity and space (Ma and Nakamori, 2009). Optimization modelling has structured a number of decision methods based on quantity structure optimization such as Multi-objective Optimization, Linear Programming, Multi- criteria Optimization and System Dynamics etc, and spatial optimization methods which include Landscape Ecology and Cellular Automata (CA) models (Xiao et al., 2007; Ma and Nakamori, 2009). However, using traditional methods such as multi-objective programming models used in landscape ecology; this is very difficult to make the space structure and the amount structure united effectively (Ma and Nakamori, 2009; Abdollahi, 2011).

The progress and improvement of geographic information system (GIS) and computer technology has offered a strong and great technical support for the analysis and investigation of spatial data when making spatial optimization decisions about land-use (Abdollahi, 2011). Combining the mathematical methods of linear programming units with GIS and realizing the reasonable and sensible allocation of land allocation resources both in quantity and space, has become a hotspot to scientists and researchers, and it also promotes and supports the development of scientific research about land-use (Bonilla et al., 2010; Bek and Stanislav , 2011).

The relationship between the land and the activity in optimization models can be linear and non-linear. Nowadays, there are different types of models which are mainly used for optimization modelling such as; General Algebra Modelling System (GAMS), Multi- objective Genetic Algorithm (MOGA) and Multi objective Cellular Automata (MOCA). Although the genetic algorithm has strong capability for global optimization, it involves complicated map spot coding, which makes the program difficult to realize, and it does not have a strong capability of spatial correlation (Khare and Singh, 2011). The multi-objective cellular automaton model performs timing simulation based on the results of multi-objective optimization, which can not realize trans-space search (Voinov et al., 2002; Li et al., 2011;

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Mizgier et al., 2012). As a result, the General Algebra Modelling System (GAMS) is mainly tool used for optimizing.

In the case of this modelling (Optimization), the variations of constraints and purposes in the model input (control) are performed automatically, as well as the procedure of the output. The heart of this procedure is the algorithm of numerical optimization that makes the decision on how to define and analyze the outputs and scenarios based on the available and accessible information about the results of previous model runs (Ma and Nakamori, 2009; Bonilla et al., 2010). This optimization process connects the scenarios, the simulation procedure and the performance and presentation standard and criterion. ‘Algorithms of optimization are capable of performing a systematic search in the space of control variables to find an input vector which controls the systems in the desired way, specified by the goal function’ Voinov et al., 2000; Bek and Jezek, 2011; Singh et al., 2011).

In most cases to measure the outcome and result of a scenario in terms of economic, environmental, social aspects, more than one output and parameter variable needs to be considered. To evaluate different scenarios, output variables need to be integrated into a scalar value (or to analyze and examine a multidimensional decision problem). This function that can be chosen to integrate or combine several results or output variables is identified as an objective function or ‘performance criterion’ and is a mathematical formalisation of the situation of the system that should be maximized or minimized to reach the desired state (Seppelt and Voino, 2002). The scope of ecosystem and land management problems ranges from forest management and timber harvest (Loehle, 2000; Seppelt and Voino, 2002) to agricultural problems (Markides et al., 2011) to general and specific issues of land use change (Voinov et al., 2002; Li et al., 2011), and to habitat suitability (Bonilla et al., 2010). The models used differ in terms of mathematical structure. Modelling varies from combined and aggregated dynamic models based on variation or deviation equations of exponential growth (Bonilla et al., 2010) to complex models based on systems of non-linear differential (derived function) equations (Voinov et al., 2002; Abdollahi, 2011).

In relation to these research reviews, in this thesis it has been evaluated that the appropriate combination of methods, in relation to the research aim, is Optimization modelling (Linear Programming). A Spatial Decision Support System (SDSS) is used to relate the aspatial model results to a realistic distribution of land cover in the landscape; the two approaches are therefore complementary in examining the feasibility of different options for increasing carbon sequestration through land use change. Planning support systems provides a conceptual context within which the data sets necessary for this work can be integrated.

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2.8 Conclusions

This chapter reviews all of the aspects of science and policy that impinge on the PhD thesis. There is a common agreement (between the government and policy-makers) that there is still a need for quantification of the most promising alternatives for landscape change for climate change mitigation. There are a large number of possibilities for changes in land management, but all are subject to environmental, social, political and economic constraints. The analysis in this study provides a pathway for the identification and consideration of scenarios for the future with a realistic range of drivers (environmental, climatic, policy, and socio-economic) and a spatially explicit analysis at the landscape scale. The large number of constraints shows that the development of these changes cannot be isolated. Interventions such as the use of improved crop varieties cannot be made without conceding the social, political and economic context of the total system. A major gap in research at present is the lack of approaches for developing and modelling the impacts of different scenarios with a range of drivers at the landscape scale. Whilst other studies have provided national and regional estimates of total changes (e.g. King et al., 2004; Smith et al., 2008), there is very limited use of spatially explicit landscape change scenarios based on land suitability analysis to explore the potential of a range of options for climate change mitigation at the local and regional level. As has been noted before, carbon storage approach in the land use management and mitigation of GHG emissions of agriculture and forestry lands are the key issue.

Furthermore, it is important to mention that land use change is not only spatially but also temporally dynamic and the balance of positive and negative consequences of any changes may alter over time.

This study thus aims to provide a new spatially- explicit approach to quantifying soil and biomass carbon and greenhouse gas emissions associated with major land uses. It also provides a conceptual framework for scenario development and assessment of spatial models of landscape change over time using GIS modelling. The scenarios that are explored provide a much improved understanding of the implications of potential land use changes for climate change mitigation and impacts on the landscape. In turn it is hoped that these scenarios will provide a basis for demonstrating the potential for climate change mitigation to planners and managers and for evaluating their impacts on the landscape and socio-economics of the region.

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Chapter 3