Package overview

Summary

The prioritizr R package uses mixed integer linear programming (MILP) techniques to provide a flexible interface for building and solving conservation planning problems (Rodrigues et al. 2000; Billionnet 2013). It supports a broad range of objectives, constraints, and penalties that can be used to custom-tailor conservation planning problems to the specific needs of a conservation planning exercise. Once built, conservation planning problems can be solved using a variety of commercial and open-source exact algorithm solvers. In contrast to the algorithms conventionally used to solve conservation problems, such as heuristics or simulated annealing (Ball et al. 2009), the exact algorithms used here are guaranteed to find optimal solutions. Furthermore, conservation problems can be constructed to optimize the spatial allocation of different management zones (or actions), meaning that conservation practitioners can identify solutions that benefit multiple stakeholders. Finally, this package has the functionality to read input data formatted for the Marxan conservation planning program (Ball et al. 2009), and find much cheaper solutions in a much shorter period of time than Marxan (Beyer et al. 2016).

Introduction

Systematic conservation planning is a rigorous, repeatable, and structured approach to designing new protected areas that efficiently meet conservation objectives (Margules & Pressey 2000). Historically, conservation decision-making has often evaluated parcels opportunistically as they became available for purchase, donation, or under threat. Although purchasing such areas may improve the status quo, such decisions may not substantially enhance the long-term persistence of target species or communities. Faced with this realization, conservation planners began using decision support tools to help simulate alternative reserve designs over a range of different biodiversity and management goals and, ultimately, guide protected area acquisitions and management actions. Due to the systematic, evidence-based nature of these tools, conservation prioritization can help contribute to a transparent, inclusive, and more defensible decision making process.

A conservation planning exercise typically starts by defining a study area. This study area should encompass all the areas relevant to the decision maker or the hypothesis being tested. The extent of a study area could encompass a few important localities (e.g., Stigner et al. 2016), a single state (e.g., Kirkpatrick 1983), an entire country (Fuller et al. 2010), or the entire planet (Butchart et al. 2015). Next, the study area is divided into a set of discrete areas termed planning units. Each planning unit represents a discrete locality in the study area that can be managed independently of other areas. The general idea is that some combination of the planning units can be selected for conservation actions (e.g., protected area establishment, habitat restoration). Planning units are often created as square or hexagon cells that are sized according to the scale of the conservation actions, and the resolution of the data that underpin the planning exercise (but see Klein et al. 2009).

Cost data (or a surrogate thereof) are needed to inform the prioritization process. Specifically, these cost data describe the relative expenditure associated with managing each planning unit for conservation. For example, if the goal of the conservation planning exercise is to identify priority areas for expanding a local protected area system, then the cost data could represent the physical cost of purchasing the land. Alternatively, if such data are not available, then surrogate data are often used instead (e.g., human population density, opportunity cost of foregone commercial activities, or planning unit size).

Conservation planning exercises also require data on the biodiversity elements that are of conservation interest (termed conservation features). These features could be species (e.g., Neofelis nebulosa, the Clouded Leopard), populations, or habitats (e.g., mangroves or cloud forest). After identifying the set of relevant conservation features for a conservation planning exercise, spatially explicit data need to be obtained for each and every feature to describe their spatial distribution (e.g., habitat suitability data, probability of occurrence data, presence/absence data). This is important to ensure that conservation features are adequately covered (represented) by prioritizations. After assembling all the data, the next step is to define the conservation planning problem.

The prioritizr R package is designed to help you build and solve conservation planning problems. Specifically, prioritizations are generated by formulating a mathematical optimization problem and then solving it to generate a solution. These mathematical optimization problems are formulated using the planning unit data, cost data, and feature data, and with information related to the overarching aim of the prioritization process. In general, the goal of an optimization problem is to minimize (or maximize) an objective function that is calculated using a set of decision variables, subject to a series of constraints to ensure that solution exhibits specific properties. The objective function describes the quantity which we are trying to minimize (e.g., cost of the solution) or maximize (e.g., number of features conserved). The decision variables describe the entities that we can control, and indicate which planning units are selected for conservation management and which are not. The constraints can be thought of as rules that the decision variables need to follow. For example, a commonly used constraint is specifying that the solution must not exceed a certain budget.

A wide variety of approaches have been developed for solving optimization problems. Reserve design problems are frequently solved using simulated annealing (Kirkpatrick et al. 1983) or heuristics (Nicholls & Margules 1993; Moilanen 2007). These methods are conceptually simple and can be applied to a wide variety of optimization problems. However, they do not scale well for large or complex problems (Beyer et al. 2016). Additionally, these methods cannot tell you how close any given solution is to the optimal solution. The prioritizr package uses exact algorithms to efficiently solve conservation planning problems to within a pre-specified optimality gap. In other words, you can specify that you need the optimal solution (i.e., a gap of 0%) and the algorithms will, given enough time, find a solution that meets this criteria. In the past, exact algorithms have been too slow for conservation planning exercises (Pressey et al. 1996). However, improvements over the last decade mean that they are now much faster (Achterberg & Wunderling 2013; Beyer et al. 2016).

In this package, optimization problems are expressed using integer linear programming (ILP) so that they can be solved using (linear) exact algorithm solvers. The general form of an integer programming problem can be expressed in matrix notation using the following equation.

\[\text{Minimize} \space \boldsymbol{c}^\text{T} \boldsymbol{x} \space \space \text{subject to} \space A\boldsymbol{x} \space \Box \space \boldsymbol{b}\]

Where \(x\) is a vector of decision variables, \(c\) and \(b\) are vectors of known coefficients, and \(A\) is the constraint matrix. The final term specifies a series of structural constants and the \(\Box\) symbol is used to indicate that the relational operators for the constraints can be either \(\geq\), \(=\), or \(\leq\). In the context of a conservation planning problem, \(c\) could be used to represent the planning unit costs, \(A\) could be used to store the data showing the presence / absence (or amount) of each feature in each planning unit, \(b\) could be used to represent minimum amount of habitat required for each species in the solution, the \(\Box\) could be set to \(\geq\) symbols to indicate that the total amount of each feature in the solution must exceed the quantities in \(b\). But there are many other ways of formulating the reserve selection problem (Rodrigues et al. 2000).

A grammar for conservation planning

The prioritizr R package uses a grammar to describe elements of conservation planning. This means that functions are organized into verbs that relate to specific concepts. For example, all of the functions used to specify the primary objective for optimization end with the _objective suffix (e.g., add_min_set_objective() and add_min_shortfall_objective()). By combining multiple functions together, they can be used to formulate a complete conservation planning problem. Specifically, the verbs for formulating problems are described below.

After building a conservation planning problem, it can be solved to generate a prioritization (using the solve() function). There are also verbs available to help evaluate and interpret solutions. These verbs are described below.

Workflow

The general workflow when using the prioritizr R package starts with creating a new conservation planning problem() object using data. Specifically, the problem() object should be constructed using data that specify the planning units, biodiversity features, management zones (if applicable), and costs. After creating a new problem() object, it can be customized—by adding objectives, penalties, constraints, and other information—to build a precise representation of the conservation planning problem required, and then solved to obtain a solution.

All conservation planning problems require an objective. An objective specifies the property which is used to compare different feasible solutions. Simply put, the objective is the property of the solution which should be maximized or minimized during the optimization process. For instance, with the minimum set objective (specified using add_min_set_objective()), we are seeking to minimize the cost of the solution (similar to Marxan). On the other hand, with the minimum shortfall objective (specified using add_min_shortfall_objective()), we are seeking to minimize the average target shortfall for all features represented in the solution, subject to a budget.

Many objectives require representation targets (e.g., the minimum set objective). These targets are a specialized set of constraints that relate to the total quantity of each feature secured in the solution (e.g., amount of suitable habitat or number of individuals). In the case of the minimum set objective ( add_min_set_objective()), they are used to ensure that solutions secure a sufficient quantity of each feature, and in other objectives, such as the maximum features objective ( add_max_features_objective()) they are used to assess whether a feature has been adequately conserved by a candidate solution. Targets can be expressed numerically as the total amount required for a given feature (using add_absolute_targets()), or as a proportion of the total amount found in the planning units (using add_relative_targets()). Note that not all objectives require targets, and a warning will be thrown if an attempt is made to add targets to a problem with an objective that does not use them.

Constraints and penalties can be added to a conservation planning problem to ensure that solutions exhibit a specific property or penalize solutions which don’t exhibit a specific property (respectively). The difference between constraints and penalties, strictly speaking, is constraints are used to rule out potential solutions that don’t exhibit a specific property. For instance, constraints can be used to ensure that specific planning units are selected in the solution for prioritization (using add_locked_in_constraints()) or not selected in the solution for prioritization (using add_locked_out_constraints()). On the other hand, penalties are combined with the objective of a problem, with a penalty factor, and the overall objective of the problem then becomes to minimize (or maximize) the primary objective function and the penalty function. For example, penalties can be added to a problem to penalize solutions that are excessively fragmented (using add_boundary_penalties()). These penalties have a penalty argument that specifies the relative importance of having spatially clustered solutions. When the argument to penalty is high, then solutions which are less fragmented are valued more highly – even if they cost more – and when the argument to penalty is low, then the solutions which are more fragmented are valued less highly.

After building a conservation problem, it can then be solved to obtain a solution (or portfolio of solutions if desired). The solution is returned in the same format as the planning unit data used to construct the problem. For instance, this means that if raster data was used to initialize the problem, then the solution will also be output in raster format. This can be very helpful when it comes to interpreting and visualizing solutions because it means that the solution data does not first have to be merged with spatial data before they can be plotted on a map.

Usage

Here we will provide an introduction to using the prioritizr R package to build and solve a conservation planning problem. Please note that we will not discuss conservation planning with multiple zones in this vignette, for more information on working with multiple management zones please see the Management zones tutorial.

First, we will load the prioritizr package.

# load package
library(prioritizr)

Data

Now we will load some built-in data sets that are distributed with the prioritizr R package. This package contains several different planning unit data sets. To provide a comprehensive overview of the different ways that we can initialize a conservation planning problem, we will load each of them.

First, we will load the raster planning unit data (sim_pu_raster). Here, the planning units are represented as a single-layer raster object (i.e., a terra::rast() object) and each pixel corresponds to the spatial extent of each panning unit. The pixel values correspond to the acquisition costs of each planning unit.

## class       : SpatRaster 
## dimensions  : 10, 10, 1  (nrow, ncol, nlyr)
## resolution  : 0.1, 0.1  (x, y)
## extent      : 0, 1, 0, 1  (xmin, xmax, ymin, ymax)
## coord. ref. : Undefined Cartesian SRS 
## source      : sim_pu_raster.tif 
## name        :    layer 
## min value   : 190.1328 
## max value   : 215.8638

Secondly, we will load one of the spatial vector planning unit data sets (sim_pu_polygons). Here, each polygon (i.e., feature using ArcGIS terminology) corresponds to a different planning unit. This data set has an attribute table that contains additional information about each polygon. Namely, the cost field (column) in the attribute table contains the acquisition cost for each planning unit.

## Simple feature collection with 90 features and 3 fields
## Geometry type: POLYGON
## Dimension:     XY
## Bounding box:  xmin: 0 ymin: 0 xmax: 1 ymax: 1
## Projected CRS: Undefined Cartesian SRS
## # A tibble: 90 × 4
##     cost locked_in locked_out                                      geom
##  * <dbl> <lgl>     <lgl>                                  <POLYGON [m]>
##  1  216. FALSE     FALSE            ((0 1, 0.1 1, 0.1 0.9, 0 0.9, 0 1))
##  2  213. FALSE     FALSE      ((0.1 1, 0.2 1, 0.2 0.9, 0.1 0.9, 0.1 1))
##  3  207. FALSE     FALSE      ((0.2 1, 0.3 1, 0.3 0.9, 0.2 0.9, 0.2 1))
##  4  209. FALSE     TRUE       ((0.3 1, 0.4 1, 0.4 0.9, 0.3 0.9, 0.3 1))
##  5  214. FALSE     FALSE      ((0.4 1, 0.5 1, 0.5 0.9, 0.4 0.9, 0.4 1))
##  6  214. FALSE     FALSE      ((0.5 1, 0.6 1, 0.6 0.9, 0.5 0.9, 0.5 1))
##  7  210. FALSE     FALSE      ((0.6 1, 0.7 1, 0.7 0.9, 0.6 0.9, 0.6 1))
##  8  211. FALSE     TRUE       ((0.7 1, 0.8 1, 0.8 0.9, 0.7 0.9, 0.7 1))
##  9  210. FALSE     FALSE      ((0.8 1, 0.9 1, 0.9 0.9, 0.8 0.9, 0.8 1))
## 10  204. FALSE     FALSE          ((0.9 1, 1 1, 1 0.9, 0.9 0.9, 0.9 1))
## # ℹ 80 more rows

Thirdly, we will load some planning unit data stored in tabular format (i.e., data.frame format). For those familiar with Marxan or dealing with very large conservation planning problems (> 10 million planning units), it may be useful to work with data in this format because it does not contain any spatial information which will reduce computational burden. When using tabular data to initialize conservation planning problems, the data must follow the conventions used by Marxan. Specifically, each row in the planning unit table must correspond to a different planning unit. The table must also have an “id” column to provide a unique integer identifier for each planning unit, and it must also have a column that indicates the cost of each planning unit. For more information, please see the official Marxan documentation.

##   id       cost status    xloc     yloc
## 1  3      0.000      0 1116623 -4493479
## 2 30   7527.275      3 1110623 -4496943
## 3 56  37349.075      0 1092623 -4500408
## 4 58  16959.021      0 1116623 -4500408
## 5 84  34220.256      0 1098623 -4503872
## 6 85 178907.584      0 1110623 -4503872

Finally, we will load data showing the spatial distribution of the conservation features. Our conservation features (sim_features) are represented as a multi-layer raster object (i.e., a terra::rast() object), where each layer corresponds to a different feature. The pixel values in each layer correspond to the amount of suitable habitat available in a given planning unit. Note that our planning unit and our feature data have exactly the same spatial properties (i.e., resolution, extent, coordinate reference system) so their pixels line up perfectly.

Initialize a problem

After having loaded our planning unit and feature data, we will now try initializing some conservation planning problems. There are a lot of different ways to initialize a conservation planning problem, so here we will just showcase a few of the more commonly used methods. For an exhaustive description of all the ways you can initialize a conservation problem, see the help file for the problem() function. First off, we will initialize a conservation planning problem using the raster data.

## A conservation problem (<ConservationProblem>)
## ├•data
## │├•features:    "feature_1", "feature_2", "feature_3", "feature_4", and "feature_5" (5 total)
## │└•planning units:
## │ ├•data:       <SpatRaster> (90 total)
## │ ├•costs:      continuous values (between 190.1328 and 215.8638)
## │ ├•extent:     0, 0, 1, 1 (xmin, ymin, xmax, ymax)
## │ └•CRS:        Undefined Cartesian SRS (projected)
## ├•formulation
## │├•objective:   none specified
## │├•penalties:   none specified
## │├•targets:     none specified
## │├•constraints: none specified
## │└•decisions:   binary decision
## └•optimization
##  ├•portfolio:   default portfolio
##  └•solver:      gurobi solver (`gap` = 0.1, `time_limit` = 2147483647, `first_feasible` = FALSE, …)
## # ℹ Use `summary(...)` to see complete formulation.
## [1] 90
## [1] 5

Generally, we recommend initializing problems using raster data where possible. This is because the problem() function needs to calculate the amount of each feature in each planning unit, and by providing both the planning unit and feature data in raster format with the same spatial resolution, extents, and coordinate systems, this means that the problem() function does not need to do any geoprocessing behind the scenes. But sometimes we can’t use raster planning unit data, because our planning units aren’t equal-sized grid cells. So, below is an example showing how we can initialize a conservation planning problem using planning units that are formatted as spatial vector data. Note that we could reduce run-time by pre-computing the amount of each feature in each planning unit and storing the data in the attribute table (e.g., by performing zonal statistics with R or ESRI ArcGIS), and then passing in the names of the columns as an argument to the problem() function (see Examples section for problem() for details).

## A conservation problem (<ConservationProblem>)
## ├•data
## │├•features:    "feature_1", "feature_2", "feature_3", "feature_4", and "feature_5" (5 total)
## │└•planning units:
## │ ├•data:       <sftbl_dftbldata.frame> (90 total)
## │ ├•costs:      continuous values (between 190.1328 and 215.8638)
## │ ├•extent:     0, 0, 1, 1 (xmin, ymin, xmax, ymax)
## │ └•CRS:        Undefined Cartesian SRS (projected)
## ├•formulation
## │├•objective:   none specified
## │├•penalties:   none specified
## │├•targets:     none specified
## │├•constraints: none specified
## │└•decisions:   binary decision
## └•optimization
##  ├•portfolio:   default portfolio
##  └•solver:      gurobi solver (`gap` = 0.1, `time_limit` = 2147483647, `first_feasible` = FALSE, …)
## # ℹ Use `summary(...)` to see complete formulation.

We can also initialize a conservation planning problem using tabular planning unit data (i.e., data.frame format). Since the tabular planning unit data does not contain any spatial information, we also have to provide the feature data in tabular format (i.e., data.frame format) and data showing the amount of each feature in each planning unit in tabular format (i.e., data.frame format). The feature data must have an “id” column containing a unique integer identifier for each feature, and the planning unit by feature data must contain the following three columns: pu corresponding to the planning unit identifiers, species corresponding to the feature identifiers, and amount showing the amount of a given feature in a given planning unit.

##   id prop spf   name
## 1 10  0.3   1  bird1
## 2 11  0.3   1  nvis2
## 3 12  0.3   1  nvis8
## 4 13  0.3   1  nvis9
## 5 14  0.3   1 nvis14
## 6 15  0.3   1 nvis20
##   species  pu     amount
## 1      26  56 120.344884
## 2      26  58  45.167010
## 3      26  84  68.047375
## 4      26  85   9.735624
## 5      26  86   7.803476
## 6      26 111 478.327417
## A conservation problem (<ConservationProblem>)
## ├•data
## │├•features:    "bird1", "nvis2", "nvis8", "nvis9", "nvis14", "nvis20" , … (17 total)
## │└•planning units:
## │ ├•data:       <data.frame> (1751 total)
## │ ├•costs:      continuous values (between 0 and 415692.1938)
## │ ├•extent:     NA
## │ └•CRS:        NA
## ├•formulation
## │├•objective:   none specified
## │├•penalties:   none specified
## │├•targets:     none specified
## │├•constraints: none specified
## │└•decisions:   binary decision
## └•optimization
##  ├•portfolio:   default portfolio
##  └•solver:      gurobi solver (`gap` = 0.1, `time_limit` = 2147483647, `first_feasible` = FALSE, …)
## # ℹ Use `summary(...)` to see complete formulation.

For more information on initializing problems, please see the help page for the problem() function (which you can open by entering the code: ?problem). Now that we have initialized a conservation planning problem, we will show you how you can customize it to suit the exact needs of your conservation planning scenario. Although we initialized the conservation planning problems using several different methods, moving forward, we will only use raster-based planning unit data to keep things simple.

Add an objective

The next step is to add a primary objective to the problem. A problem objective is used to specify the primary goal of the problem (i.e., the quantity that is to be maximized or minimized). All conservation planning problems involve minimizing or maximizing some kind of objective. For instance, we might require a solution that conserves enough habitat for each species while minimizing the overall cost of the reserve network. Alternatively, we might require a solution that maximizes the number of conserved species while ensuring that the cost of the reserve network does not exceed the budget. Please note that objectives are added in the same way regardless of the type of data used to initialize the problem. The following objectives are available.

## A conservation problem (<ConservationProblem>)
## ├•data
## │├•features:    "feature_1", "feature_2", "feature_3", "feature_4", and "feature_5" (5 total)
## │└•planning units:
## │ ├•data:       <SpatRaster> (90 total)
## │ ├•costs:      continuous values (between 190.1328 and 215.8638)
## │ ├•extent:     0, 0, 1, 1 (xmin, ymin, xmax, ymax)
## │ └•CRS:        Undefined Cartesian SRS (projected)
## ├•formulation
## │├•objective:   minimum set objective
## │├•penalties:   none specified
## │├•targets:     none specified
## │├•constraints: none specified
## │└•decisions:   binary decision
## └•optimization
##  ├•portfolio:   default portfolio
##  └•solver:      gurobi solver (`gap` = 0.1, `time_limit` = 2147483647, `first_feasible` = FALSE, …)
## # ℹ Use `summary(...)` to see complete formulation.
## A conservation problem (<ConservationProblem>)
## ├•data
## │├•features:    "feature_1", "feature_2", "feature_3", "feature_4", and "feature_5" (5 total)
## │└•planning units:
## │ ├•data:       <SpatRaster> (90 total)
## │ ├•costs:      continuous values (between 190.1328 and 215.8638)
## │ ├•extent:     0, 0, 1, 1 (xmin, ymin, xmax, ymax)
## │ └•CRS:        Undefined Cartesian SRS (projected)
## ├•formulation
## │├•objective:   maximum coverage objective (`budget` = 5000)
## │├•penalties:   none specified
## │├•targets:     none specified
## │├•constraints: none specified
## │└•decisions:   binary decision
## └•optimization
##  ├•portfolio:   default portfolio
##  └•solver:      gurobi solver (`gap` = 0.1, `time_limit` = 2147483647, `first_feasible` = FALSE, …)
## # ℹ Use `summary(...)` to see complete formulation.
## A conservation problem (<ConservationProblem>)
## ├•data
## │├•features:    "feature_1", "feature_2", "feature_3", "feature_4", and "feature_5" (5 total)
## │└•planning units:
## │ ├•data:       <SpatRaster> (90 total)
## │ ├•costs:      continuous values (between 190.1328 and 215.8638)
## │ ├•extent:     0, 0, 1, 1 (xmin, ymin, xmax, ymax)
## │ └•CRS:        Undefined Cartesian SRS (projected)
## ├•formulation
## │├•objective:   maximum representation objective (`budget` = 5000)
## │├•penalties:   none specified
## │├•targets:     none specified
## │├•constraints: none specified
## │└•decisions:   binary decision
## └•optimization
##  ├•portfolio:   default portfolio
##  └•solver:      gurobi solver (`gap` = 0.1, `time_limit` = 2147483647, `first_feasible` = FALSE, …)
## # ℹ Use `summary(...)` to see complete formulation.
## A conservation problem (<ConservationProblem>)
## ├•data
## │├•features:    "feature_1", "feature_2", "feature_3", "feature_4", and "feature_5" (5 total)
## │└•planning units:
## │ ├•data:       <SpatRaster> (90 total)
## │ ├•costs:      continuous values (between 190.1328 and 215.8638)
## │ ├•extent:     0, 0, 1, 1 (xmin, ymin, xmax, ymax)
## │ └•CRS:        Undefined Cartesian SRS (projected)
## ├•formulation
## │├•objective:   minimum shortfall objective (`budget` = 5000)
## │├•penalties:   none specified
## │├•targets:     none specified
## │├•constraints: none specified
## │└•decisions:   binary decision
## └•optimization
##  ├•portfolio:   default portfolio
##  └•solver:      gurobi solver (`gap` = 0.1, `time_limit` = 2147483647, `first_feasible` = FALSE, …)
## # ℹ Use `summary(...)` to see complete formulation.
## A conservation problem (<ConservationProblem>)
## ├•data
## │├•features:    "feature_1", "feature_2", "feature_3", "feature_4", and "feature_5" (5 total)
## │└•planning units:
## │ ├•data:       <SpatRaster> (90 total)
## │ ├•costs:      continuous values (between 190.1328 and 215.8638)
## │ ├•extent:     0, 0, 1, 1 (xmin, ymin, xmax, ymax)
## │ └•CRS:        Undefined Cartesian SRS (projected)
## ├•formulation
## │├•objective:   minimum largest shortfall objective (`budget` = 5000)
## │├•penalties:   none specified
## │├•targets:     none specified
## │├•constraints: none specified
## │└•decisions:   binary decision
## └•optimization
##  ├•portfolio:   default portfolio
##  └•solver:      gurobi solver (`gap` = 0.1, `time_limit` = 2147483647, `first_feasible` = FALSE, …)
## # ℹ Use `summary(...)` to see complete formulation.
## A conservation problem (<ConservationProblem>)
## ├•data
## │├•features:    "feature_1", "feature_2", "feature_3", "feature_4", and "feature_5" (5 total)
## │└•planning units:
## │ ├•data:       <SpatRaster> (90 total)
## │ ├•costs:      continuous values (between 190.1328 and 215.8638)
## │ ├•extent:     0, 0, 1, 1 (xmin, ymin, xmax, ymax)
## │ └•CRS:        Undefined Cartesian SRS (projected)
## ├•formulation
## │├•objective:   phylogenetic diversity objective (`budget` = 5000, `tree` = phylogenetic tree (branch lengths between 0.041 and 1.4211))
## │├•penalties:   none specified
## │├•targets:     none specified
## │├•constraints: none specified
## │└•decisions:   binary decision
## └•optimization
##  ├•portfolio:   default portfolio
##  └•solver:      gurobi solver (`gap` = 0.1, `time_limit` = 2147483647, `first_feasible` = FALSE, …)
## # ℹ Use `summary(...)` to see complete formulation.
## A conservation problem (<ConservationProblem>)
## ├•data
## │├•features:    "feature_1", "feature_2", "feature_3", "feature_4", and "feature_5" (5 total)
## │└•planning units:
## │ ├•data:       <SpatRaster> (90 total)
## │ ├•costs:      continuous values (between 190.1328 and 215.8638)
## │ ├•extent:     0, 0, 1, 1 (xmin, ymin, xmax, ymax)
## │ └•CRS:        Undefined Cartesian SRS (projected)
## ├•formulation
## │├•objective:   phylogenetic endemism objective (`budget` = 5000, `tree` = phylogenetic tree (branch lengths between 0.041 and 1.4211))
## │├•penalties:   none specified
## │├•targets:     none specified
## │├•constraints: none specified
## │└•decisions:   binary decision
## └•optimization
##  ├•portfolio:   default portfolio
##  └•solver:      gurobi solver (`gap` = 0.1, `time_limit` = 2147483647, `first_feasible` = FALSE, …)
## # ℹ Use `summary(...)` to see complete formulation.
## A conservation problem (<ConservationProblem>)
## ├•data
## │├•features:    "feature_1", "feature_2", "feature_3", "feature_4", and "feature_5" (5 total)
## │└•planning units:
## │ ├•data:       <SpatRaster> (90 total)
## │ ├•costs:      continuous values (between 190.1328 and 215.8638)
## │ ├•extent:     0, 0, 1, 1 (xmin, ymin, xmax, ymax)
## │ └•CRS:        Undefined Cartesian SRS (projected)
## ├•formulation
## │├•objective:   maximum utility objective (`budget` = 5000)
## │├•penalties:   none specified
## │├•targets:     none specified
## │├•constraints: none specified
## │└•decisions:   binary decision
## └•optimization
##  ├•portfolio:   default portfolio
##  └•solver:      gurobi solver (`gap` = 0.1, `time_limit` = 2147483647, `first_feasible` = FALSE, …)
## # ℹ Use `summary(...)` to see complete formulation.

Add targets

Most conservation planning problems require targets. Targets are used to specify the minimum amount or proportion of a feature’s distribution that needs to be protected in the solution. For example, we may want to develop a reserve network that will secure 20% of the distribution for each feature for minimal cost. The following methods are available for specifying targets.

## A conservation problem (<ConservationProblem>)
## ├•data
## │├•features:    "feature_1", "feature_2", "feature_3", "feature_4", and "feature_5" (5 total)
## │└•planning units:
## │ ├•data:       <SpatRaster> (90 total)
## │ ├•costs:      continuous values (between 190.1328 and 215.8638)
## │ ├•extent:     0, 0, 1, 1 (xmin, ymin, xmax, ymax)
## │ └•CRS:        Undefined Cartesian SRS (projected)
## ├•formulation
## │├•objective:   minimum set objective
## │├•penalties:   none specified
## │├•targets:     absolute targets (between 3 and 3)
## │├•constraints: none specified
## │└•decisions:   binary decision
## └•optimization
##  ├•portfolio:   default portfolio
##  └•solver:      gurobi solver (`gap` = 0.1, `time_limit` = 2147483647, `first_feasible` = FALSE, …)
## # ℹ Use `summary(...)` to see complete formulation.
## A conservation problem (<ConservationProblem>)
## ├•data
## │├•features:    "feature_1", "feature_2", "feature_3", "feature_4", and "feature_5" (5 total)
## │└•planning units:
## │ ├•data:       <SpatRaster> (90 total)
## │ ├•costs:      continuous values (between 190.1328 and 215.8638)
## │ ├•extent:     0, 0, 1, 1 (xmin, ymin, xmax, ymax)
## │ └•CRS:        Undefined Cartesian SRS (projected)
## ├•formulation
## │├•objective:   minimum set objective
## │├•penalties:   none specified
## │├•targets:     relative targets (between 0.1 and 0.1)
## │├•constraints: none specified
## │└•decisions:   binary decision
## └•optimization
##  ├•portfolio:   default portfolio
##  └•solver:      gurobi solver (`gap` = 0.1, `time_limit` = 2147483647, `first_feasible` = FALSE, …)
## # ℹ Use `summary(...)` to see complete formulation.
## A conservation problem (<ConservationProblem>)
## ├•data
## │├•features:    "feature_1", "feature_2", "feature_3", "feature_4", and "feature_5" (5 total)
## │└•planning units:
## │ ├•data:       <SpatRaster> (90 total)
## │ ├•costs:      continuous values (between 190.1328 and 215.8638)
## │ ├•extent:     0, 0, 1, 1 (xmin, ymin, xmax, ymax)
## │ └•CRS:        Undefined Cartesian SRS (projected)
## ├•formulation
## │├•objective:   minimum set objective
## │├•penalties:   none specified
## │├•targets:     relative targets (between 0.1 and 0.3)
## │├•constraints: none specified
## │└•decisions:   binary decision
## └•optimization
##  ├•portfolio:   default portfolio
##  └•solver:      gurobi solver (`gap` = 0.1, `time_limit` = 2147483647, `first_feasible` = FALSE, …)
## # ℹ Use `summary(...)` to see complete formulation.
## A conservation problem (<ConservationProblem>)
## ├•data
## │├•features:    "feature_1", "feature_2", "feature_3", "feature_4", and "feature_5" (5 total)
## │└•planning units:
## │ ├•data:       <SpatRaster> (90 total)
## │ ├•costs:      continuous values (between 190.1328 and 215.8638)
## │ ├•extent:     0, 0, 1, 1 (xmin, ymin, xmax, ymax)
## │ └•CRS:        Undefined Cartesian SRS (projected)
## ├•formulation
## │├•objective:   minimum set objective
## │├•penalties:   none specified
## │├•targets:     absolute targets (between 17.2905 and 21.5906)
## │├•constraints: none specified
## │└•decisions:   binary decision
## └•optimization
##  ├•portfolio:   default portfolio
##  └•solver:      gurobi solver (`gap` = 0.1, `time_limit` = 2147483647, `first_feasible` = FALSE, …)
## # ℹ Use `summary(...)` to see complete formulation.

As with the functions for specifying the objective of a problem, if we try adding multiple targets to a problem, only the most recently added set of targets are used.

Add constraints

A constraint can be added to a conservation planning problem to ensure that all solutions exhibit a specific property. For example, they can be used to make sure that all solutions select a specific planning unit or that all selected planning units in the solution follow a certain configuration. The following constraints are available.

## A conservation problem (<ConservationProblem>)
## ├•data
## │├•features:    "feature_1", "feature_2", "feature_3", "feature_4", and "feature_5" (5 total)
## │└•planning units:
## │ ├•data:       <SpatRaster> (90 total)
## │ ├•costs:      continuous values (between 190.1328 and 215.8638)
## │ ├•extent:     0, 0, 1, 1 (xmin, ymin, xmax, ymax)
## │ └•CRS:        Undefined Cartesian SRS (projected)
## ├•formulation
## │├•objective:   minimum set objective
## │├•penalties:   none specified
## │├•targets:     relative targets (between 0.1 and 0.1)
## │├•constraints:
## ││└•1:          locked in constraints (1 planning units)
## │└•decisions:   binary decision
## └•optimization
##  ├•portfolio:   default portfolio
##  └•solver:      gurobi solver (`gap` = 0.1, `time_limit` = 2147483647, `first_feasible` = FALSE, …)
## # ℹ Use `summary(...)` to see complete formulation.
## A conservation problem (<ConservationProblem>)
## ├•data
## │├•features:    "feature_1", "feature_2", "feature_3", "feature_4", and "feature_5" (5 total)
## │└•planning units:
## │ ├•data:       <SpatRaster> (90 total)
## │ ├•costs:      continuous values (between 190.1328 and 215.8638)
## │ ├•extent:     0, 0, 1, 1 (xmin, ymin, xmax, ymax)
## │ └•CRS:        Undefined Cartesian SRS (projected)
## ├•formulation
## │├•objective:   minimum set objective
## │├•penalties:   none specified
## │├•targets:     relative targets (between 0.1 and 0.1)
## │├•constraints:
## ││└•1:          locked out constraints (1 planning units)
## │└•decisions:   binary decision
## └•optimization
##  ├•portfolio:   default portfolio
##  └•solver:      gurobi solver (`gap` = 0.1, `time_limit` = 2147483647, `first_feasible` = FALSE, …)
## # ℹ Use `summary(...)` to see complete formulation.
## A conservation problem (<ConservationProblem>)
## ├•data
## │├•features:    "feature_1", "feature_2", "feature_3", "feature_4", and "feature_5" (5 total)
## │└•planning units:
## │ ├•data:       <SpatRaster> (90 total)
## │ ├•costs:      continuous values (between 190.1328 and 215.8638)
## │ ├•extent:     0, 0, 1, 1 (xmin, ymin, xmax, ymax)
## │ └•CRS:        Undefined Cartesian SRS (projected)
## ├•formulation
## │├•objective:   minimum set objective
## │├•penalties:   none specified
## │├•targets:     relative targets (between 0.1 and 0.1)
## │├•constraints:
## ││└•1:          neighbor constraints (`k` = 1, `clamp` = TRUE, …)
## │└•decisions:   binary decision
## └•optimization
##  ├•portfolio:   default portfolio
##  └•solver:      gurobi solver (`gap` = 0.1, `time_limit` = 2147483647, `first_feasible` = FALSE, …)
## # ℹ Use `summary(...)` to see complete formulation.
## A conservation problem (<ConservationProblem>)
## ├•data
## │├•features:    "feature_1", "feature_2", "feature_3", "feature_4", and "feature_5" (5 total)
## │└•planning units:
## │ ├•data:       <SpatRaster> (90 total)
## │ ├•costs:      continuous values (between 190.1328 and 215.8638)
## │ ├•extent:     0, 0, 1, 1 (xmin, ymin, xmax, ymax)
## │ └•CRS:        Undefined Cartesian SRS (projected)
## ├•formulation
## │├•objective:   minimum set objective
## │├•penalties:   none specified
## │├•targets:     relative targets (between 0.1 and 0.1)
## │├•constraints:
## ││└•1:          contiguity constraints
## │└•decisions:   binary decision
## └•optimization
##  ├•portfolio:   default portfolio
##  └•solver:      gurobi solver (`gap` = 0.1, `time_limit` = 2147483647, `first_feasible` = FALSE, …)
## # ℹ Use `summary(...)` to see complete formulation.
## A conservation problem (<ConservationProblem>)
## ├•data
## │├•features:    "feature_1", "feature_2", "feature_3", "feature_4", and "feature_5" (5 total)
## │└•planning units:
## │ ├•data:       <SpatRaster> (90 total)
## │ ├•costs:      continuous values (between 190.1328 and 215.8638)
## │ ├•extent:     0, 0, 1, 1 (xmin, ymin, xmax, ymax)
## │ └•CRS:        Undefined Cartesian SRS (projected)
## ├•formulation
## │├•objective:   minimum set objective
## │├•penalties:   none specified
## │├•targets:     relative targets (between 0.1 and 0.1)
## │├•constraints:
## ││└•1:          feature contiguity constraints
## │└•decisions:   binary decision
## └•optimization
##  ├•portfolio:   default portfolio
##  └•solver:      gurobi solver (`gap` = 0.1, `time_limit` = 2147483647, `first_feasible` = FALSE, …)
## # ℹ Use `summary(...)` to see complete formulation.
## A conservation problem (<ConservationProblem>)
## ├•data
## │├•features:    "feature_1", "feature_2", "feature_3", "feature_4", and "feature_5" (5 total)
## │└•planning units:
## │ ├•data:       <SpatRaster> (90 total)
## │ ├•costs:      continuous values (between 190.1328 and 215.8638)
## │ ├•extent:     0, 0, 1, 1 (xmin, ymin, xmax, ymax)
## │ └•CRS:        Undefined Cartesian SRS (projected)
## ├•formulation
## │├•objective:   minimum shortfall objective (`budget` = 1800)
## │├•penalties:   none specified
## │├•targets:     relative targets (between 0.1 and 0.1)
## │├•constraints:
## ││└•1:          linear constraints (`threshold` = 190, `sense` = "<=" (1 total), …)
## │└•decisions:   binary decision
## └•optimization
##  ├•portfolio:   default portfolio
##  └•solver:      gurobi solver (`gap` = 0.1, `time_limit` = 2147483647, `first_feasible` = FALSE, …)
## # ℹ Use `summary(...)` to see complete formulation.

In particular, The add_locked_in_constraints and add_locked_out_constraints functions are incredibly useful for real-world conservation planning exercises, so it’s worth pointing out that there are several ways we can specify which planning units should be locked in or out of the solutions. If we use raster planning unit data, we can also use raster data to specify which planning units should be locked in or locked out.

## A conservation problem (<ConservationProblem>)
## ├•data
## │├•features:    "feature_1", "feature_2", "feature_3", "feature_4", and "feature_5" (5 total)
## │└•planning units:
## │ ├•data:       <SpatRaster> (90 total)
## │ ├•costs:      continuous values (between 190.1328 and 215.8638)
## │ ├•extent:     0, 0, 1, 1 (xmin, ymin, xmax, ymax)
## │ └•CRS:        Undefined Cartesian SRS (projected)
## ├•formulation
## │├•objective:   minimum set objective
## │├•penalties:   none specified
## │├•targets:     relative targets (between 0.1 and 0.1)
## │├•constraints:
## ││├•1:          locked in constraints (10 planning units)
## ││└•2:          locked out constraints (10 planning units)
## │└•decisions:   binary decision
## └•optimization
##  ├•portfolio:   default portfolio
##  └•solver:      gurobi solver (`gap` = 0.1, `time_limit` = 2147483647, `first_feasible` = FALSE, …)
## # ℹ Use `summary(...)` to see complete formulation.

If our planning unit data are in a spatial vector format (similar to the sim_pu_polygons data) or a tabular format (similar to pu_dat), we can use the field names in the data to refer to which planning units should be locked in and / or out. For example, the sim_pu_polygons object has TRUE / FALSE values in the “locked_in” field which indicate which planning units should be selected in the solution. We could use the data in this field to specify that those planning units with TRUE values should be locked in using the following methods.

## Simple feature collection with 90 features and 3 fields
## Geometry type: POLYGON
## Dimension:     XY
## Bounding box:  xmin: 0 ymin: 0 xmax: 1 ymax: 1
## Projected CRS: Undefined Cartesian SRS
## # A tibble: 90 × 4
##     cost locked_in locked_out                                      geom
##  * <dbl> <lgl>     <lgl>                                  <POLYGON [m]>
##  1  216. FALSE     FALSE            ((0 1, 0.1 1, 0.1 0.9, 0 0.9, 0 1))
##  2  213. FALSE     FALSE      ((0.1 1, 0.2 1, 0.2 0.9, 0.1 0.9, 0.1 1))
##  3  207. FALSE     FALSE      ((0.2 1, 0.3 1, 0.3 0.9, 0.2 0.9, 0.2 1))
##  4  209. FALSE     TRUE       ((0.3 1, 0.4 1, 0.4 0.9, 0.3 0.9, 0.3 1))
##  5  214. FALSE     FALSE      ((0.4 1, 0.5 1, 0.5 0.9, 0.4 0.9, 0.4 1))
##  6  214. FALSE     FALSE      ((0.5 1, 0.6 1, 0.6 0.9, 0.5 0.9, 0.5 1))
##  7  210. FALSE     FALSE      ((0.6 1, 0.7 1, 0.7 0.9, 0.6 0.9, 0.6 1))
##  8  211. FALSE     TRUE       ((0.7 1, 0.8 1, 0.8 0.9, 0.7 0.9, 0.7 1))
##  9  210. FALSE     FALSE      ((0.8 1, 0.9 1, 0.9 0.9, 0.8 0.9, 0.8 1))
## 10  204. FALSE     FALSE          ((0.9 1, 1 1, 1 0.9, 0.9 0.9, 0.9 1))
## # ℹ 80 more rows
## A conservation problem (<ConservationProblem>)
## ├•data
## │├•features:    "feature_1", "feature_2", "feature_3", "feature_4", and "feature_5" (5 total)
## │└•planning units:
## │ ├•data:       <sftbl_dftbldata.frame> (90 total)
## │ ├•costs:      continuous values (between 190.1328 and 215.8638)
## │ ├•extent:     0, 0, 1, 1 (xmin, ymin, xmax, ymax)
## │ └•CRS:        Undefined Cartesian SRS (projected)
## ├•formulation
## │├•objective:   minimum set objective
## │├•penalties:   none specified
## │├•targets:     relative targets (between 0.1 and 0.1)
## │├•constraints:
## ││└•1:          locked in constraints (10 planning units)
## │└•decisions:   binary decision
## └•optimization
##  ├•portfolio:   default portfolio
##  └•solver:      gurobi solver (`gap` = 0.1, `time_limit` = 2147483647, `first_feasible` = FALSE, …)
## # ℹ Use `summary(...)` to see complete formulation.
## A conservation problem (<ConservationProblem>)
## ├•data
## │├•features:    "feature_1", "feature_2", "feature_3", "feature_4", and "feature_5" (5 total)
## │└•planning units:
## │ ├•data:       <sftbl_dftbldata.frame> (90 total)
## │ ├•costs:      continuous values (between 190.1328 and 215.8638)
## │ ├•extent:     0, 0, 1, 1 (xmin, ymin, xmax, ymax)
## │ └•CRS:        Undefined Cartesian SRS (projected)
## ├•formulation
## │├•objective:   minimum set objective
## │├•penalties:   none specified
## │├•targets:     relative targets (between 0.1 and 0.1)
## │├•constraints:
## ││└•1:          locked in constraints (10 planning units)
## │└•decisions:   binary decision
## └•optimization
##  ├•portfolio:   default portfolio
##  └•solver:      gurobi solver (`gap` = 0.1, `time_limit` = 2147483647, `first_feasible` = FALSE, …)
## # ℹ Use `summary(...)` to see complete formulation.

Add penalties

We can also add penalties to a problem to favor or penalize solutions according to a secondary objective. Unlike the constraint functions, these functions will add extra information to the objective function of the optimization function to penalize solutions that do not exhibit specific characteristics. For example, penalties can be added to a problem to avoid highly fragmented solutions at the expense of accepting slightly more expensive solutions. All penalty functions have a penalty argument that controls the relative importance of the secondary penalty function compared to the primary objective function. It is worth noting that incredibly low or incredibly high penalty values – relative to the main objective function – can cause problems to take a very long time to solve, so when trying out a range of different penalty values it can be helpful to limit the solver to run for a set period of time. The following penalties are available.

## A conservation problem (<ConservationProblem>)
## ├•data
## │├•features:    "feature_1", "feature_2", "feature_3", "feature_4", and "feature_5" (5 total)
## │└•planning units:
## │ ├•data:       <SpatRaster> (90 total)
## │ ├•costs:      continuous values (between 190.1328 and 215.8638)
## │ ├•extent:     0, 0, 1, 1 (xmin, ymin, xmax, ymax)
## │ └•CRS:        Undefined Cartesian SRS (projected)
## ├•formulation
## │├•objective:   minimum set objective
## │├•penalties:
## ││└•1:          boundary penalties (`penalty` = 0.01, `edge_factor` = 0.5, …)
## │├•targets:     relative targets (between 0.1 and 0.1)
## │├•constraints: none specified
## │└•decisions:   binary decision
## └•optimization
##  ├•portfolio:   default portfolio
##  └•solver:      gurobi solver (`gap` = 0.1, `time_limit` = 2147483647, `first_feasible` = FALSE, …)
## # ℹ Use `summary(...)` to see complete formulation.
## A conservation problem (<ConservationProblem>)
## ├•data
## │├•features:    "feature_1", "feature_2", "feature_3", and "feature_4" (4 total)
## │└•planning units:
## │ ├•data:       <SpatRaster> (90 total)
## │ ├•costs:      continuous values (between 190.1328 and 215.8638)
## │ ├•extent:     0, 0, 1, 1 (xmin, ymin, xmax, ymax)
## │ └•CRS:        Undefined Cartesian SRS (projected)
## ├•formulation
## │├•objective:   minimum set objective
## │├•penalties:
## ││└•1:          connectivity penalties (`penalty` = 5, …)
## │├•targets:     relative targets (between 0.1 and 0.1)
## │├•constraints: none specified
## │└•decisions:   binary decision
## └•optimization
##  ├•portfolio:   default portfolio
##  └•solver:      gurobi solver (`gap` = 0.1, `time_limit` = 2147483647, `first_feasible` = FALSE, …)
## # ℹ Use `summary(...)` to see complete formulation.
## A conservation problem (<ConservationProblem>)
## ├•data
## │├•features:    "feature_1", "feature_2", "feature_3", and "feature_4" (4 total)
## │└•planning units:
## │ ├•data:       <SpatRaster> (90 total)
## │ ├•costs:      continuous values (between 190.1328 and 215.8638)
## │ ├•extent:     0, 0, 1, 1 (xmin, ymin, xmax, ymax)
## │ └•CRS:        Undefined Cartesian SRS (projected)
## ├•formulation
## │├•objective:   minimum set objective
## │├•penalties:
## ││└•1:          asymmetric connectivity penalties (`penalty` = 5, …)
## │├•targets:     relative targets (between 0.1 and 0.1)
## │├•constraints: none specified
## │└•decisions:   binary decision
## └•optimization
##  ├•portfolio:   default portfolio
##  └•solver:      gurobi solver (`gap` = 0.1, `time_limit` = 2147483647, `first_feasible` = FALSE, …)
## # ℹ Use `summary(...)` to see complete formulation.
## A conservation problem (<ConservationProblem>)
## ├•data
## │├•features:    "feature_1", "feature_2", "feature_3", "feature_4", and "feature_5" (5 total)
## │└•planning units:
## │ ├•data:       <SpatRaster> (90 total)
## │ ├•costs:      continuous values (between 190.1328 and 215.8638)
## │ ├•extent:     0, 0, 1, 1 (xmin, ymin, xmax, ymax)
## │ └•CRS:        Undefined Cartesian SRS (projected)
## ├•formulation
## │├•objective:   minimum set objective
## │├•penalties:
## ││└•1:          linear penalties (`penalty` = 5, …)
## │├•targets:     relative targets (between 0.1 and 0.1)
## │├•constraints: none specified
## │└•decisions:   binary decision
## └•optimization
##  ├•portfolio:   default portfolio
##  └•solver:      gurobi solver (`gap` = 0.1, `time_limit` = 2147483647, `first_feasible` = FALSE, …)
## # ℹ Use `summary(...)` to see complete formulation.

Add the decision types

Conservation planning problems involve making decisions on how planning units will be managed. These decisions are then associated with management actions (e.g., turning a planning unit into a protected area). The type of decision describes how the action is applied to planning units. For instance, the default decision-type is a binary decision type, meaning that we are either selecting or not selecting planning units for management. The following decision types are available.

## A conservation problem (<ConservationProblem>)
## ├•data
## │├•features:    "feature_1", "feature_2", "feature_3", "feature_4", and "feature_5" (5 total)
## │└•planning units:
## │ ├•data:       <SpatRaster> (90 total)
## │ ├•costs:      continuous values (between 190.1328 and 215.8638)
## │ ├•extent:     0, 0, 1, 1 (xmin, ymin, xmax, ymax)
## │ └•CRS:        Undefined Cartesian SRS (projected)
## ├•formulation
## │├•objective:   minimum set objective
## │├•penalties:   none specified
## │├•targets:     relative targets (between 0.1 and 0.1)
## │├•constraints: none specified
## │└•decisions:   binary decision
## └•optimization
##  ├•portfolio:   default portfolio
##  └•solver:      gurobi solver (`gap` = 0.1, `time_limit` = 2147483647, `first_feasible` = FALSE, …)
## # ℹ Use `summary(...)` to see complete formulation.
## A conservation problem (<ConservationProblem>)
## ├•data
## │├•features:    "feature_1", "feature_2", "feature_3", "feature_4", and "feature_5" (5 total)
## │└•planning units:
## │ ├•data:       <SpatRaster> (90 total)
## │ ├•costs:      continuous values (between 190.1328 and 215.8638)
## │ ├•extent:     0, 0, 1, 1 (xmin, ymin, xmax, ymax)
## │ └•CRS:        Undefined Cartesian SRS (projected)
## ├•formulation
## │├•objective:   minimum set objective
## │├•penalties:   none specified
## │├•targets:     relative targets (between 0.1 and 0.1)
## │├•constraints: none specified
## │└•decisions:   proportion decision
## └•optimization
##  ├•portfolio:   default portfolio
##  └•solver:      gurobi solver (`gap` = 0.1, `time_limit` = 2147483647, `first_feasible` = FALSE, …)
## # ℹ Use `summary(...)` to see complete formulation.
## A conservation problem (<ConservationProblem>)
## ├•data
## │├•features:    "feature_1", "feature_2", "feature_3", "feature_4", and "feature_5" (5 total)
## │└•planning units:
## │ ├•data:       <SpatRaster> (90 total)
## │ ├•costs:      continuous values (between 190.1328 and 215.8638)
## │ ├•extent:     0, 0, 1, 1 (xmin, ymin, xmax, ymax)
## │ └•CRS:        Undefined Cartesian SRS (projected)
## ├•formulation
## │├•objective:   minimum set objective
## │├•penalties:   none specified
## │├•targets:     relative targets (between 0.1 and 0.1)
## │├•constraints: none specified
## │└•decisions:   semicontinuous decision (`upper_limit` = 0.5)
## └•optimization
##  ├•portfolio:   default portfolio
##  └•solver:      gurobi solver (`gap` = 0.1, `time_limit` = 2147483647, `first_feasible` = FALSE, …)
## # ℹ Use `summary(...)` to see complete formulation.

Add a solver

Next, after specifying the mathematical formulation that underpins your conservation planning problem, you can specify how the problem should be solved. If you do not specify this information, the prioritizr R package will automatically use the best solver currently installed on your system with some reasonable defaults. We strongly recommend installing the Gurobi software suite and the gurobi R package to solve problems, and for more information on this topic please refer to the Gurobi Installation Guide. The following solvers are available.

## A conservation problem (<ConservationProblem>)
## ├•data
## │├•features:    "feature_1", "feature_2", "feature_3", "feature_4", and "feature_5" (5 total)
## │└•planning units:
## │ ├•data:       <SpatRaster> (90 total)
## │ ├•costs:      continuous values (between 190.1328 and 215.8638)
## │ ├•extent:     0, 0, 1, 1 (xmin, ymin, xmax, ymax)
## │ └•CRS:        Undefined Cartesian SRS (projected)
## ├•formulation
## │├•objective:   minimum set objective
## │├•penalties:   none specified
## │├•targets:     relative targets (between 0.1 and 0.1)
## │├•constraints: none specified
## │└•decisions:   binary decision
## └•optimization
##  ├•portfolio:   default portfolio
##  └•solver:      gurobi solver (`gap` = 0, `time_limit` = 2147483647, `first_feasible` = FALSE, …)
## # ℹ Use `summary(...)` to see complete formulation.
## A conservation problem (<ConservationProblem>)
## ├•data
## │├•features:    "feature_1", "feature_2", "feature_3", "feature_4", and "feature_5" (5 total)
## │└•planning units:
## │ ├•data:       <SpatRaster> (90 total)
## │ ├•costs:      continuous values (between 190.1328 and 215.8638)
## │ ├•extent:     0, 0, 1, 1 (xmin, ymin, xmax, ymax)
## │ └•CRS:        Undefined Cartesian SRS (projected)
## ├•formulation
## │├•objective:   minimum set objective
## │├•penalties:   none specified
## │├•targets:     relative targets (between 0.1 and 0.1)
## │├•constraints: none specified
## │└•decisions:   binary decision
## └•optimization
##  ├•portfolio:   default portfolio
##  └•solver:      cplex solver (`gap` = 0, `time_limit` = 2147483647, …)
## # ℹ Use `summary(...)` to see complete formulation.
## A conservation problem (<ConservationProblem>)
## ├•data
## │├•features:    "feature_1", "feature_2", "feature_3", "feature_4", and "feature_5" (5 total)
## │└•planning units:
## │ ├•data:       <SpatRaster> (90 total)
## │ ├•costs:      continuous values (between 190.1328 and 215.8638)
## │ ├•extent:     0, 0, 1, 1 (xmin, ymin, xmax, ymax)
## │ └•CRS:        Undefined Cartesian SRS (projected)
## ├•formulation
## │├•objective:   minimum set objective
## │├•penalties:   none specified
## │├•targets:     relative targets (between 0.1 and 0.1)
## │├•constraints: none specified
## │└•decisions:   binary decision
## └•optimization
##  ├•portfolio:   default portfolio
##  └•solver:      cbc solver (`gap` = 0, `time_limit` = 2147483647, `first_feasible` = FALSE, …)
## # ℹ Use `summary(...)` to see complete formulation.
## A conservation problem (<ConservationProblem>)
## ├•data
## │├•features:    "feature_1", "feature_2", "feature_3", "feature_4", and "feature_5" (5 total)
## │└•planning units:
## │ ├•data:       <SpatRaster> (90 total)
## │ ├•costs:      continuous values (between 190.1328 and 215.8638)
## │ ├•extent:     0, 0, 1, 1 (xmin, ymin, xmax, ymax)
## │ └•CRS:        Undefined Cartesian SRS (projected)
## ├•formulation
## │├•objective:   minimum set objective
## │├•penalties:   none specified
## │├•targets:     relative targets (between 0.1 and 0.1)
## │├•constraints: none specified
## │└•decisions:   binary decision
## └•optimization
##  ├•portfolio:   default portfolio
##  └•solver:      highs solver (`gap` = 0, `time_limit` = 2147483647, …)
## # ℹ Use `summary(...)` to see complete formulation.
## A conservation problem (<ConservationProblem>)
## ├•data
## │├•features:    "feature_1", "feature_2", "feature_3", "feature_4", and "feature_5" (5 total)
## │└•planning units:
## │ ├•data:       <SpatRaster> (90 total)
## │ ├•costs:      continuous values (between 190.1328 and 215.8638)
## │ ├•extent:     0, 0, 1, 1 (xmin, ymin, xmax, ymax)
## │ └•CRS:        Undefined Cartesian SRS (projected)
## ├•formulation
## │├•objective:   minimum set objective
## │├•penalties:   none specified
## │├•targets:     relative targets (between 0.1 and 0.1)
## │├•constraints: none specified
## │└•decisions:   binary decision
## └•optimization
##  ├•portfolio:   default portfolio
##  └•solver:      lpsymphony (`gap` = 0, `time_limit` = 2147483647, `first_feasible` = FALSE, …)
## # ℹ Use `summary(...)` to see complete formulation.
## A conservation problem (<ConservationProblem>)
## ├•data
## │├•features:    "feature_1", "feature_2", "feature_3", "feature_4", and "feature_5" (5 total)
## │└•planning units:
## │ ├•data:       <SpatRaster> (90 total)
## │ ├•costs:      continuous values (between 190.1328 and 215.8638)
## │ ├•extent:     0, 0, 1, 1 (xmin, ymin, xmax, ymax)
## │ └•CRS:        Undefined Cartesian SRS (projected)
## ├•formulation
## │├•objective:   minimum set objective
## │├•penalties:   none specified
## │├•targets:     relative targets (between 0.1 and 0.1)
## │├•constraints: none specified
## │└•decisions:   binary decision
## └•optimization
##  ├•portfolio:   default portfolio
##  └•solver:      rsymphony solver (`gap` = 0, `time_limit` = 2147483647, `first_feasible` = FALSE, …)
## # ℹ Use `summary(...)` to see complete formulation.

Add a portfolio

Many conservation planning exercises require a portfolio of solutions. For example, real-world exercises can involve presenting decision makers with a range of near-optimal decisions. Additionally, the number of times that different planning units are selected in different solutions can provide insight into their relative importance. The following portfolio methods are available.

## A conservation problem (<ConservationProblem>)
## ├•data
## │├•features:    "feature_1", "feature_2", "feature_3", "feature_4", and "feature_5" (5 total)
## │└•planning units:
## │ ├•data:       <SpatRaster> (90 total)
## │ ├•costs:      continuous values (between 190.1328 and 215.8638)
## │ ├•extent:     0, 0, 1, 1 (xmin, ymin, xmax, ymax)
## │ └•CRS:        Undefined Cartesian SRS (projected)
## ├•formulation
## │├•objective:   minimum set objective
## │├•penalties:   none specified
## │├•targets:     relative targets (between 0.1 and 0.1)
## │├•constraints: none specified
## │└•decisions:   binary decision
## └•optimization
##  ├•portfolio:   gap portfolio (`number_solutions` = 5, `pool_gap` = 0.2)
##  └•solver:      gurobi solver (`gap` = 0.1, `time_limit` = 2147483647, `first_feasible` = FALSE, …)
## # ℹ Use `summary(...)` to see complete formulation.
## A conservation problem (<ConservationProblem>)
## ├•data
## │├•features:    "feature_1", "feature_2", "feature_3", "feature_4", and "feature_5" (5 total)
## │└•planning units:
## │ ├•data:       <SpatRaster> (90 total)
## │ ├•costs:      continuous values (between 190.1328 and 215.8638)
## │ ├•extent:     0, 0, 1, 1 (xmin, ymin, xmax, ymax)
## │ └•CRS:        Undefined Cartesian SRS (projected)
## ├•formulation
## │├•objective:   minimum set objective
## │├•penalties:   none specified
## │├•targets:     relative targets (between 0.1 and 0.1)
## │├•constraints: none specified
## │└•decisions:   binary decision
## └•optimization
##  ├•portfolio:   top portfolio (`number_solutions` = 5)
##  └•solver:      gurobi solver (`gap` = 0.1, `time_limit` = 2147483647, `first_feasible` = FALSE, …)
## # ℹ Use `summary(...)` to see complete formulation.
## A conservation problem (<ConservationProblem>)
## ├•data
## │├•features:    "feature_1", "feature_2", "feature_3", "feature_4", and "feature_5" (5 total)
## │└•planning units:
## │ ├•data:       <SpatRaster> (90 total)
## │ ├•costs:      continuous values (between 190.1328 and 215.8638)
## │ ├•extent:     0, 0, 1, 1 (xmin, ymin, xmax, ymax)
## │ └•CRS:        Undefined Cartesian SRS (projected)
## ├•formulation
## │├•objective:   minimum set objective
## │├•penalties:   none specified
## │├•targets:     relative targets (between 0.1 and 0.1)
## │├•constraints: none specified
## │└•decisions:   binary decision
## └•optimization
##  ├•portfolio:   extra portfolio
##  └•solver:      gurobi solver (`gap` = 0.1, `time_limit` = 2147483647, `first_feasible` = FALSE, …)
## # ℹ Use `summary(...)` to see complete formulation.
## A conservation problem (<ConservationProblem>)
## ├•data
## │├•features:    "feature_1", "feature_2", "feature_3", "feature_4", and "feature_5" (5 total)
## │└•planning units:
## │ ├•data:       <SpatRaster> (90 total)
## │ ├•costs:      continuous values (between 190.1328 and 215.8638)
## │ ├•extent:     0, 0, 1, 1 (xmin, ymin, xmax, ymax)
## │ └•CRS:        Undefined Cartesian SRS (projected)
## ├•formulation
## │├•objective:   minimum set objective
## │├•penalties:   none specified
## │├•targets:     relative targets (between 0.1 and 0.1)
## │├•constraints: none specified
## │└•decisions:   binary decision
## └•optimization
##  ├•portfolio:   cuts portfolio (`number_solutions` = 10)
##  └•solver:      gurobi solver (`gap` = 0.1, `time_limit` = 2147483647, `first_feasible` = FALSE, …)
## # ℹ Use `summary(...)` to see complete formulation.
## A conservation problem (<ConservationProblem>)
## ├•data
## │├•features:    "feature_1", "feature_2", "feature_3", "feature_4", and "feature_5" (5 total)
## │└•planning units:
## │ ├•data:       <SpatRaster> (90 total)
## │ ├•costs:      continuous values (between 190.1328 and 215.8638)
## │ ├•extent:     0, 0, 1, 1 (xmin, ymin, xmax, ymax)
## │ └•CRS:        Undefined Cartesian SRS (projected)
## ├•formulation
## │├•objective:   minimum set objective
## │├•penalties:   none specified
## │├•targets:     relative targets (between 0.1 and 0.1)
## │├•constraints: none specified
## │└•decisions:   binary decision
## └•optimization
##  ├•portfolio:   shuffle portfolio (`number_solutions` = 10, …)
##  └•solver:      gurobi solver (`gap` = 0.1, `time_limit` = 2147483647, `first_feasible` = FALSE, …)
## # ℹ Use `summary(...)` to see complete formulation.

Solve the problem

After formulating our conservation planning problem and specifying how the problem should be solved, we can use the solve() function to obtain a solution. Note that the solver will typically print out some information describing the size of the problem and report its progress when searching for a suitable solution.

## A conservation problem (<ConservationProblem>)
## ├•data
## │├•features:    "feature_1", "feature_2", "feature_3", "feature_4", and "feature_5" (5 total)
## │└•planning units:
## │ ├•data:       <SpatRaster> (90 total)
## │ ├•costs:      continuous values (between 190.1328 and 215.8638)
## │ ├•extent:     0, 0, 1, 1 (xmin, ymin, xmax, ymax)
## │ └•CRS:        Undefined Cartesian SRS (projected)
## ├•formulation
## │├•objective:   minimum set objective
## │├•penalties:
## ││└•1:          boundary penalties (`penalty` = 500, `edge_factor` = 0.5, …)
## │├•targets:     relative targets (between 0.1 and 0.1)
## │├•constraints: none specified
## │└•decisions:   binary decision
## └•optimization
##  ├•portfolio:   default portfolio
##  └•solver:      gurobi solver (`gap` = 0.1, `time_limit` = 2147483647, `first_feasible` = FALSE, …)
## # ℹ Use `summary(...)` to see complete formulation.
## Set parameter Username
## Set parameter TimeLimit to value 2147483647
## Set parameter MIPGap to value 0.1
## Set parameter Presolve to value 2
## Set parameter Threads to value 1
## Academic license - for non-commercial use only - expires 2025-06-05
## Gurobi Optimizer version 11.0.0 build v11.0.0rc2 (linux64 - "Ubuntu 20.04.6 LTS")
## 
## CPU model: AMD Ryzen Threadripper 3960X 24-Core Processor, instruction set [SSE2|AVX|AVX2]
## Thread count: 24 physical cores, 48 logical processors, using up to 1 threads
## 
## Optimize a model with 293 rows, 234 columns and 1026 nonzeros
## Model fingerprint: 0xb4b90756
## Variable types: 0 continuous, 234 integer (234 binary)
## Coefficient statistics:
##   Matrix range     [2e-01, 1e+00]
##   Objective range  [1e+02, 4e+02]
##   Bounds range     [1e+00, 1e+00]
##   RHS range        [3e+00, 8e+00]
## Found heuristic solution: objective 20287.197006
## Found heuristic solution: objective 3087.9617767
## Presolve time: 0.00s
## Presolved: 293 rows, 234 columns, 1026 nonzeros
## Variable types: 0 continuous, 234 integer (234 binary)
## Root relaxation presolved: 293 rows, 234 columns, 1026 nonzeros
## 
## 
## Root relaxation: objective 2.265862e+03, 228 iterations, 0.00 seconds (0.00 work units)
## 
##     Nodes    |    Current Node    |     Objective Bounds      |     Work
##  Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time
## 
##      0     0 2265.86242    0  234 3087.96178 2265.86242  26.6%     -    0s
##      0     0 2328.27423    0  232 3087.96178 2328.27423  24.6%     -    0s
##      0     0 2357.91894    0  229 3087.96178 2357.91894  23.6%     -    0s
## H    0     0                    3034.0204010 2357.91894  22.3%     -    0s
##      0     0 2379.43275    0  197 3034.02040 2379.43275  21.6%     -    0s
##      0     0 2379.43275    0  197 3034.02040 2379.43275  21.6%     -    0s
## H    0     0                    2890.8754120 2379.43275  17.7%     -    0s
## H    0     0                    2814.4777374 2379.43275  15.5%     -    0s
##      0     2 2379.78730    0  197 2814.47774 2379.78730  15.4%     -    0s
## H   20    20                    2648.2596588 2382.48313  10.0%  23.4    0s
## 
## Cutting planes:
##   Gomory: 3
## 
## Explored 34 nodes (1117 simplex iterations) in 0.11 seconds (0.12 work units)
## Thread count was 1 (of 48 available processors)
## 
## Solution count 6: 2648.26 2814.48 2890.88 ... 20287.2
## 
## Optimal solution found (tolerance 1.00e-01)
## Best objective 2.648259658813e+03, best bound 2.391338223393e+03, gap 9.7015%

We can plot this solution because the planning unit input data are spatially referenced in a raster format. The output format will always match the planning unit data used to initialize the problem. For example, the solution to a problem with planning units in a spatial vector (shapefile) format would also be in a spatial vector format. Similarly, if the planning units were in a tabular format (i.e., data.frame), the solution would also be returned in a tabular format.

We can also extract attributes from the solution that describe the quality of the solution and the optimization process.

## solution_1 
##    2648.26
## solution_1 
##       0.11
## solution_1 
##  "OPTIMAL"

Evaluate the solution

Conservation planning involves making trade-offs between different criteria (e.g., overall cost, feature representation, connectivity). After obtaining a solution to a conservation planning problem, it is important to evaluate it to help understand the trade-offs made by the prioritization. This is also useful to compare different solutions with each other.

Evaluating performance

Summary statistics can be computed to evaluate the overall performance of a solution based on certain criteria. The following summaries can be computed.

The following functions are available to summarize a solution:

## # A tibble: 1 × 2
##   summary     n
##   <chr>   <dbl>
## 1 overall    10
## # A tibble: 1 × 2
##   summary  cost
##   <chr>   <dbl>
## 1 overall 2048.
## # A tibble: 5 × 5
##   summary feature   total_amount absolute_held relative_held
##   <chr>   <chr>            <dbl>         <dbl>         <dbl>
## 1 overall feature_1         83.3          8.57         0.103
## 2 overall feature_2         31.2          3.18         0.102
## 3 overall feature_3         72.0          7.28         0.101
## 4 overall feature_4         42.7          5.01         0.118
## 5 overall feature_5         56.7          5.71         0.101
## # A tibble: 5 × 9
##   feature   met   total_amount absolute_target absolute_held absolute_shortfall
##   <chr>     <lgl>        <dbl>           <dbl>         <dbl>              <dbl>
## 1 feature_1 TRUE          83.3            8.33          8.57                  0
## 2 feature_2 TRUE          31.2            3.12          3.18                  0
## 3 feature_3 TRUE          72.0            7.20          7.28                  0
## 4 feature_4 TRUE          42.7            4.27          5.01                  0
## 5 feature_5 TRUE          56.7            5.67          5.71                  0
## # ℹ 3 more variables: relative_target <dbl>, relative_held <dbl>,
## #   relative_shortfall <dbl>
## # A tibble: 1 × 2
##   summary boundary
##   <chr>      <dbl>
## 1 overall      1.2
## # A tibble: 1 × 2
##   summary connectivity
##   <chr>          <dbl>
## 1 overall           24
## # A tibble: 1 × 2
##   summary asym_connectivity
##   <chr>               <dbl>
## 1 overall              46.8

Evaluating relative importance

Conservation plans can take a long time to implement. Since funding availability and habitat quality can decline over time, it is critical that the most important places in a prioritization are scheduled for management as early as possible. For instance, some planning units in a solution might contain many rare species which do not occur in any other planning units. Alternatively, some planning units might offer an especially high return on investment that reduces costs considerably. As a consequence, conservation planners often need information on which planning units selected in a prioritization are most important to the overall success of the prioritization. To achieve this, conservation planners can use importance scores for each planning unit selected by a solution.

Let’s generate a prioritization so that can compare the different importance methods.

## Set parameter Username
## Set parameter TimeLimit to value 2147483647
## Set parameter MIPGap to value 0.1
## Set parameter Presolve to value 2
## Set parameter Threads to value 1
## Academic license - for non-commercial use only - expires 2025-06-05
## Gurobi Optimizer version 11.0.0 build v11.0.0rc2 (linux64 - "Ubuntu 20.04.6 LTS")
## 
## CPU model: AMD Ryzen Threadripper 3960X 24-Core Processor, instruction set [SSE2|AVX|AVX2]
## Thread count: 24 physical cores, 48 logical processors, using up to 1 threads
## 
## Optimize a model with 5 rows, 90 columns and 450 nonzeros
## Model fingerprint: 0x4bb5d283
## Variable types: 0 continuous, 90 integer (90 binary)
## Coefficient statistics:
##   Matrix range     [2e-01, 9e-01]
##   Objective range  [2e+02, 2e+02]
##   Bounds range     [1e+00, 1e+00]
##   RHS range        [3e+00, 8e+00]
## Found heuristic solution: objective 2337.9617767
## Presolve time: 0.00s
## Presolved: 5 rows, 90 columns, 450 nonzeros
## Variable types: 0 continuous, 90 integer (90 binary)
## Found heuristic solution: objective 2332.1004028
## Root relaxation presolved: 5 rows, 90 columns, 450 nonzeros
## 
## 
## Root relaxation: objective 1.931582e+03, 12 iterations, 0.00 seconds (0.00 work units)
## 
##     Nodes    |    Current Node    |     Objective Bounds      |     Work
##  Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time
## 
##      0     0 1931.58191    0    4 2332.10040 1931.58191  17.2%     -    0s
## H    0     0                    1987.3985291 1931.58191  2.81%     -    0s
## 
## Explored 1 nodes (12 simplex iterations) in 0.00 seconds (0.00 work units)
## Thread count was 1 (of 48 available processors)
## 
## Solution count 3: 1987.4 2332.1 2337.96 
## 
## Optimal solution found (tolerance 1.00e-01)
## Best objective 1.987398529053e+03, best bound 1.931581907658e+03, gap 2.8085%

The following methods are available for computing importance scores.

* Ferrier method: Evaluate importance by computing irreplaceability scores following Ferrier et al. (???). The advantages of this method are that it (i) can be computed relatively quickly for moderate and large-sized problems, and (ii) calculates a score for each feature within each planning unit to provide insight into why certain planning units are more important than others. The disadvantage with this method is that it can only be applied to conservation problems that use targets and have a single zone (i.e., similar to Marxan-type problems).

* Rarity weighted richness: Evaluate importance by computing rarity weighted richness scores (Williams et al. 1996). The only advantage with this method is that it can be computed very quickly for very large problems. The key disadvantage with this approach is that it merely describes the spatial patterns of biodiversity, and does not consider any of the goals that underpin conservation planning exercise. For instance, it does not account for planning costs, management zones, objective functions, or feature representation targets.

In general, we recommend using replacement cost scores for small and moderate sized problems (e.g., less than 30,000 planning units) when it is feasible to do so. It can take a very long time to compute replacement cost scores, and so it is simply not feasible to compute these scores for particularly large problems. For moderate and large sized problems (e.g., more than 30,000 planning units), we recommend using the Ferrier method. This is because it explicitly accounts for representation targets, unlike the rarity weighted richness scores. We almost never recommend using the rarity weighted richness scores. This is because they do not consider criteria needed to inform conservation decision making (Brown et al. 2015).

Marxan problems

Although we encourage users to build and tailor conservation planning problems to suit their own needs, sometimes it just simply easier to use something you’re already familiar with. The marxan_problem() function is provided as a convenient wrapper for building and solving Marxan-style conservation problems. If users already have their conservation planning data formatted for use with Marxan, this function can also read Marxan data files and solve the Marxan-style problems using exact algorithm solvers. Please note that problems built using the marxan_problem() function are still solved the same way as a problem initialized using the problem() function, and therefore still require the installation of one of the solver packages.

Here is a short example showing how the marxan_problem() function can be used to read Marxan input files and the solve function can be used to solve the problem.

# set file path for Marxan input file
minput <- system.file("extdata/marxan/input.dat", package = "prioritizr")

# read Marxan input file
mp <- marxan_problem(minput)

# print problem
print(mp)
## A conservation problem (<ConservationProblem>)
## ├•data
## │├•features:    "bird1", "nvis2", "nvis8", "nvis9", "nvis14", "nvis20" , … (17 total)
## │└•planning units:
## │ ├•data:       <data.frame> (1751 total)
## │ ├•costs:      continuous values (between 0 and 415692.1938)
## │ ├•extent:     NA
## │ └•CRS:        NA
## ├•formulation
## │├•objective:   minimum set objective
## │├•penalties:
## ││└•1:          boundary penalties (`penalty` = 1, `edge_factor` = 1, …)
## │├•targets:     relative targets (between 0.3 and 0.3)
## │├•constraints:
## ││├•1:          locked in constraints (317 planning units)
## ││└•2:          locked out constraints (1 planning units)
## │└•decisions:   binary decision
## └•optimization
##  ├•portfolio:   default portfolio
##  └•solver:      gurobi solver (`gap` = 0.1, `time_limit` = 2147483647, `first_feasible` = FALSE, …)
## # ℹ Use `summary(...)` to see complete formulation.
# solve the problem
ms <- solve(mp)
## Set parameter Username
## Set parameter TimeLimit to value 2147483647
## Set parameter MIPGap to value 0.1
## Set parameter Presolve to value 2
## Set parameter Threads to value 1
## Academic license - for non-commercial use only - expires 2025-06-05
## Gurobi Optimizer version 11.0.0 build v11.0.0rc2 (linux64 - "Ubuntu 20.04.6 LTS")
## 
## CPU model: AMD Ryzen Threadripper 3960X 24-Core Processor, instruction set [SSE2|AVX|AVX2]
## Thread count: 24 physical cores, 48 logical processors, using up to 1 threads
## 
## Optimize a model with 10075 rows, 6780 columns and 24778 nonzeros
## Model fingerprint: 0x7cea1a5d
## Variable types: 0 continuous, 6780 integer (6780 binary)
## Coefficient statistics:
##   Matrix range     [5e-05, 4e+03]
##   Objective range  [8e+03, 4e+05]
##   Bounds range     [1e+00, 1e+00]
##   RHS range        [5e+03, 3e+05]
## Found heuristic solution: objective 1.255825e+08
## Presolve removed 4707 rows and 3103 columns
## Presolve time: 0.05s
## Presolved: 5368 rows, 3677 columns, 12704 nonzeros
## Variable types: 0 continuous, 3677 integer (3677 binary)
## Found heuristic solution: objective 1.065946e+08
## Root relaxation presolved: 5368 rows, 3677 columns, 12704 nonzeros
## 
## 
## Root relaxation: interrupted, 11 iterations, 0.01 seconds (0.01 work units)
## 
##     Nodes    |    Current Node    |     Objective Bounds      |     Work
##  Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time
## 
##      0     0          -    0      1.0659e+08 9.5941e+07  10.0%     -    0s
## 
## Explored 1 nodes (11 simplex iterations) in 0.06 seconds (0.09 work units)
## Thread count was 1 (of 48 available processors)
## 
## Solution count 2: 1.06595e+08 1.25582e+08 
## 
## Optimal solution found (tolerance 1.00e-01)
## Best objective 1.065946314895e+08, best bound 9.594065554616e+07, gap 9.9949%
# since the Marxan data was in a tabular format, the solution is also returned
# in a tabular format, so we will print the first six rows of the table
# containing the solution
head(ms)
##   id       cost status    xloc     yloc locked_in locked_out solution_1
## 1  3      0.000      0 1116623 -4493479     FALSE      FALSE          0
## 2 30   7527.275      3 1110623 -4496943     FALSE       TRUE          0
## 3 56  37349.075      0 1092623 -4500408     FALSE      FALSE          0
## 4 58  16959.021      0 1116623 -4500408     FALSE      FALSE          0
## 5 84  34220.256      0 1098623 -4503872     FALSE      FALSE          0
## 6 85 178907.584      0 1110623 -4503872     FALSE      FALSE          0

Alternatively, rather then using a Marxan input file to construct the problem, we can manually read in the Marxan data files and input these to the marxan_problem() function.

# load data
pu <-
  system.file("extdata/marxan/input/pu.dat", package = "prioritizr") %>%
  read.table(sep = ",", header = TRUE)
features <-
  system.file("extdata/marxan/input/spec.dat", package = "prioritizr") %>%
  read.table(sep = ",", header = TRUE)
bound <-
  system.file("extdata/marxan/input/bound.dat", package = "prioritizr") %>%
  read.table(sep = "\t", header = TRUE)
rij <-
  system.file("extdata/marxan/input/puvspr.dat", package = "prioritizr") %>%
  read.table(sep = ",", header = TRUE)

# build Marxan problem using data.frame objects
mp2 <- marxan_problem(
  x = pu, spec = features, puvspr = rij, bound = bound, blm = 0
)

# print problem
print(mp2)
## A conservation problem (<ConservationProblem>)
## ├•data
## │├•features:    "bird1", "nvis2", "nvis8", "nvis9", "nvis14", "nvis20" , … (17 total)
## │└•planning units:
## │ ├•data:       <data.frame> (1751 total)
## │ ├•costs:      continuous values (between 0 and 415692.1938)
## │ ├•extent:     NA
## │ └•CRS:        NA
## ├•formulation
## │├•objective:   minimum set objective
## │├•penalties:
## ││└•1:          boundary penalties (`penalty` = 0, `edge_factor` = 1, …)
## │├•targets:     relative targets (between 0.3 and 0.3)
## │├•constraints:
## ││├•1:          locked in constraints (317 planning units)
## ││└•2:          locked out constraints (1 planning units)
## │└•decisions:   binary decision
## └•optimization
##  ├•portfolio:   default portfolio
##  └•solver:      gurobi solver (`gap` = 0.1, `time_limit` = 2147483647, `first_feasible` = FALSE, …)
## # ℹ Use `summary(...)` to see complete formulation.

Conservation planning problems that are built using the marxan_problem() function can also be customized. For example, we could change the decision type for mp2 to involve selecting a proportion of each planing unit (using the add_proportion_decisions() function).

Conclusion

Hopefully, this vignette has provided an informative overview of the prioritizr R package. For more examples using the package, please see the other vignettes. Perhaps, one of the best ways to learn a new piece of software is to just try it out. Test it, try breaking it, make mistakes, and learn from them. We would recommend trying to build conservation planning problems that resemble those you face in your own work—but using the built-in example data sets. This way you can quickly verify that the problems you build actually mean what you think they mean. For instance, you can try playing around with the targets and see what effect they have on the solutions, or try playing around with penalties and see what effect they have on the solutions. Finally, if you have any questions about using the package or suggestions for it, please post an issue on the package’s online coding repository.

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