CoMOLA - Constrained Multi-objective Optimization of Land use Allocation

Michael Strauch and Carola Pätzold

Contact: michael.strauch@ufz.de

Main reference: Strauch et al., 2019

About

CoMOLA is a free Python tool to optimize the allocation of land use for multiple objectives. It builds upon the open source "inspyred" Python library and includes functions for reading, encoding and writing land use maps as well as genome generation and repair mutation algorithms for considering constraints during the optimization procedure. It runs on Windows and Linux and allows for the integration of any model whose prediction (e.g. a value for an ecosystem service) is based on a land use raster map. In its basic form, CoMOLA can be used immediately by inputting a raster map representing the status-quo land use, ready-to-run models written in R including their input data, and (optional) information on constraints. As constraints, the tool can consider (1) transition rules defining which type of land use can be converted into which other type and (2) minimum and maximum area proportions of each land use type within the study area. All relevant settings, such as paths to input data and models as well as optimization-specific parameters (e.g. population size, crossover and mutation rates) and settings related to constraint-handling and raster map-analysis are managed in one single control file ("config.ini").

The tool was systematically tested for different levels of complexity (Strauch et al., 2019) and applied for agricultural case studies in the Netherlands (Kromme Rijn, 219 km²) and Central Germany (Lossa, 141 km²) to best reconcile food production, biodiversity and other ecosystem services (Verhagen et al., 2018; Kaim et al., 2020). Witing et al. (2021) used CoMOLA to optimize riparian reforestation along the Zwalm River (Belgium) and Schwarz et al. (2020) optimized a virtual urban region to foster plant species richness, climate regulation and compactness. Bartkowski et al. (2020) used the tool to investigate the applicability of aligning Agent-Based Modeling with multi-objective land-use allocation. Currently, CoMOLA is providing the optimization environment for the EU research project OPTAIN (grant agreement No. 862756) to explore optimal strategies to retain water and nutrients in 14 small agricultural catchments across Europe.

Installation requirements

CoMOLA was developed and tested for Python 3.9 and above.

• Required Python packages
  • matplotlib

Furthermore you need to install R to run external models.

Input

(see example files in input folder)

Maps

Land use map (required)

Provide a land use raster map in ascii format (with consecutive integer values representing the different land use classes, starting with value 1). If no user-defined patch ID map is given, CoMOLA generates a patch ID map where neighboring raster cells of the same type are aggregated.

Example (land_use.asc): <pre> ncols 10 nrows 10 xllcorner 4376461.4080843 yllcorner 5553063.2189224 cellsize 75 NODATA_value -2 2 6 6 1 1 2 2 3 4 4 4 6 6 1 5 5 3 6 7 8 4 2 1 1 4 4 3 3 5 5 5 2 6 6 8 8 1 1 1 1 5 7 7 2 5 8 8 4 3 3 1 7 7 4 6 8 8 4 3 1 5 2 2 2 6 8 7 5 3 1 5 5 6 6 3 4 7 5 1 1 2 2 6 6 3 4 7 3 3 3 2 6 7 7 3 2 2 1 1 1</pre> This example shows a land use map with 8 land use classes distributed over 100 raster cells. For this example map (and the transition matrix given below) CoMOLA would generate a patch ID map with 39 different patches as shown below.

Automatically generated patch ID map (if not pre-defined by user): <pre> ncols 10 nrows 10 xllcorner 4376461.4080843 yllcorner 5553063.2189224 cellsize 75 NODATA_value -2 1 2 2 3 3 4 4 5 6 6 7 2 2 3 8 8 9 10 11 0 7 12 3 3 13 13 9 9 14 14 15 12 16 16 0 0 17 17 17 17 15 18 18 19 20 0 0 21 22 22 23 18 18 24 25 0 0 21 22 26 27 28 28 28 25 0 29 30 22 26 27 27 31 31 32 33 29 30 26 26 34 34 31 31 32 33 29 35 35 35 34 36 37 37 32 38 38 39 39 39</pre>

The patch ID map is then encoded as a string of integers (each value is called a gene, representing the land use of a patch) to form the genome of the start individual, i.e. the first individual of the initial population.

Pre-defined patch ID map (optional)

If appropriate provide your own patch ID map as ascii file to delineate the spatial optimization units as needed in your specific case (with consecutive integer values representing the different patches, starting with value 1). For a cell-level optimization, an individual ID must be assigned to each cell. The spatial resolution must be the same as for the land use map. A value of 0 defines patches with a static land use. Whether a land use class is static or not must be also defined in the transition matrix (see below). Static land use classes will be excluded from the optimization.

Example (patch_IDmap_eachcell_constraint.asc): <pre> ncols 10 nrows 10 xllcorner 4376461.4080843 yllcorner 5553063.2189224 cellsize 75 NODATA_value -2 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 0 20 21 22 23 24 25 26 27 28 29 30 31 32 33 0 0 34 35 36 37 38 39 40 41 42 0 0 43 44 45 46 47 48 49 50 0 0 51 52 53 54 55 56 57 58 0 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92</pre> In this example each cell is a patch and subject to optimization, except those cells with value 0 (which is here land use class 8). Be aware, the more patches you include the more complex is the optimization problem and the more computation time is needed. CoMOLA might perform poor if the numbers of patches is too large (>100).

Constraints

CoMOLA can handle two types of land use change constraints (simultaneously or stand-alone):

(1) Transition matrix

A matrix provided as .txt file defining which type of land use (given in rows) can be converted into which other type (given in columns). 1 = transition is possible, 0 = transition is not possible.

Example (transition_matrix.txt): <pre> -2 1 2 3 4 5 6 7 8 1 1 1 1 1 1 1 1 0 2 1 1 1 1 1 1 1 0 3 1 1 1 1 1 1 1 0 4 1 1 1 1 1 1 1 0 5 1 1 1 1 1 1 1 0 6 0 0 0 0 0 1 1 0 7 0 0 0 0 0 0 1 0 8 0 0 0 0 0 0 0 1</pre> Please note, land use class 8 is defined as static since it cannot be converted into another class, nor can a another class be converted into class 8.

(2) Total area

A table provided as .txt file defining minimum and maximum area proportions of each land use type as percentage on total area.

Example (min_max.txt): <pre> land_use 1 2 3 4 5 6 7 8 min 0 0 0 0 0 10 10 0 max 100 100 100 100 100 25 30 100</pre>

External models

CoMOLA handles up to four external models which must be provided as R scripts and stored in separate directories within the models folder (together with their specific input data). Each model evaluates the land use ascii map (as given above) for a specific objective that should be maximized (e.g. a certain ecosystem service). The output of each model is a single value representative for the whole study area (e.g. total agricultural yield) and needs to be written in a .csv file. If the objective value should be minimzed during optimization, multiply the model output with -1.

Configuration and optimization settings (config.ini)

All relevant settings, such as paths to input data and models as well as optimization-specific parameters and settings related to constraint-handling and raster map-analysis are managed in one single control file called "config.ini". Lines starting with a semicolon (;) are commented out and not used by the algorithm.

config.ini example and description of variables: <pre> [Dictionary] ; ----------------------------------------- ; config_model , Variable Description: ; ---------- ------------ ; file_path_R | file path for R ; file_path_Python | file path for Python ; modelx_folder | file name of model x folder (1 <= x <= 4) ; file_modelx | file name of the model x script ; file_outputx | file name of the output file from model x ; update_filesx | file names which files of the model folder x ; should be updated in the helping folders ; max_range | maximum number of land use classes ; opt_algorithm (string) | definition of the optimization algorithm, ; available choices are GA or NSGA2 (default)
; RPy_available (string) | if RPy2 is available than True or False (default) ; map | if True individuals are printed as ascii map files into the ; model folders else (default) as vectors in a csv file ; del_help_folders | if True (default) delete and create all helping folders ; each time the tool starts, if False you can alternatively ; use the update_filex entries for updating important files ; ----------------------------------------- ; config_optimization_algorithm , Variable Description [default value]: ; ---------- ------------ ; pop_size | number of individuals per generation [100] ; max_generations | maximum number of generations [1] ; mutation_rate | probability for mutation [0.1] ; crossover_rate | probability for cross over [1.0] ; priority | land use from NSGA2 candidate is pref