/
add_max_utility_objective.html
369 lines (296 loc) · 21.3 KB
/
add_max_utility_objective.html
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
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
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
<!-- Generated by pkgdown: do not edit by hand -->
<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="utf-8">
<meta http-equiv="X-UA-Compatible" content="IE=edge">
<meta name="viewport" content="width=device-width, initial-scale=1.0">
<title>Add maximum utility objective — add_max_utility_objective • prioritizr</title>
<!-- favicons -->
<link rel="icon" type="image/png" sizes="16x16" href="../favicon-16x16.png">
<link rel="icon" type="image/png" sizes="32x32" href="../favicon-32x32.png">
<link rel="apple-touch-icon" type="image/png" sizes="180x180" href="../apple-touch-icon.png" />
<link rel="apple-touch-icon" type="image/png" sizes="120x120" href="../apple-touch-icon-120x120.png" />
<link rel="apple-touch-icon" type="image/png" sizes="76x76" href="../apple-touch-icon-76x76.png" />
<link rel="apple-touch-icon" type="image/png" sizes="60x60" href="../apple-touch-icon-60x60.png" />
<!-- jquery -->
<script src="https://cdnjs.cloudflare.com/ajax/libs/jquery/3.4.1/jquery.min.js" integrity="sha256-CSXorXvZcTkaix6Yvo6HppcZGetbYMGWSFlBw8HfCJo=" crossorigin="anonymous"></script>
<!-- Bootstrap -->
<link href="https://cdnjs.cloudflare.com/ajax/libs/bootswatch/3.4.0/flatly/bootstrap.min.css" rel="stylesheet" crossorigin="anonymous" />
<script src="https://cdnjs.cloudflare.com/ajax/libs/twitter-bootstrap/3.4.1/js/bootstrap.min.js" integrity="sha256-nuL8/2cJ5NDSSwnKD8VqreErSWHtnEP9E7AySL+1ev4=" crossorigin="anonymous"></script>
<!-- bootstrap-toc -->
<link rel="stylesheet" href="../bootstrap-toc.css">
<script src="../bootstrap-toc.js"></script>
<!-- Font Awesome icons -->
<link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.12.1/css/all.min.css" integrity="sha256-mmgLkCYLUQbXn0B1SRqzHar6dCnv9oZFPEC1g1cwlkk=" crossorigin="anonymous" />
<link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.12.1/css/v4-shims.min.css" integrity="sha256-wZjR52fzng1pJHwx4aV2AO3yyTOXrcDW7jBpJtTwVxw=" crossorigin="anonymous" />
<!-- clipboard.js -->
<script src="https://cdnjs.cloudflare.com/ajax/libs/clipboard.js/2.0.6/clipboard.min.js" integrity="sha256-inc5kl9MA1hkeYUt+EC3BhlIgyp/2jDIyBLS6k3UxPI=" crossorigin="anonymous"></script>
<!-- headroom.js -->
<script src="https://cdnjs.cloudflare.com/ajax/libs/headroom/0.11.0/headroom.min.js" integrity="sha256-AsUX4SJE1+yuDu5+mAVzJbuYNPHj/WroHuZ8Ir/CkE0=" crossorigin="anonymous"></script>
<script src="https://cdnjs.cloudflare.com/ajax/libs/headroom/0.11.0/jQuery.headroom.min.js" integrity="sha256-ZX/yNShbjqsohH1k95liqY9Gd8uOiE1S4vZc+9KQ1K4=" crossorigin="anonymous"></script>
<!-- pkgdown -->
<link href="../pkgdown.css" rel="stylesheet">
<script src="../pkgdown.js"></script>
<!-- docsearch -->
<script src="../docsearch.js"></script>
<link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/docsearch.js/2.6.3/docsearch.min.css" integrity="sha256-QOSRU/ra9ActyXkIBbiIB144aDBdtvXBcNc3OTNuX/Q=" crossorigin="anonymous" />
<link href="../docsearch.css" rel="stylesheet">
<script src="https://cdnjs.cloudflare.com/ajax/libs/mark.js/8.11.1/jquery.mark.min.js" integrity="sha256-4HLtjeVgH0eIB3aZ9mLYF6E8oU5chNdjU6p6rrXpl9U=" crossorigin="anonymous"></script>
<link href="../extra.css" rel="stylesheet">
<meta property="og:title" content="Add maximum utility objective — add_max_utility_objective" />
<meta property="og:description" content="Set the objective of a conservation planning problem() to
secure as much of the features as possible without exceeding a budget.
This objective does not use targets, and feature
weights should be used instead to increase the representation of certain
features by a solution.
Note that this objective does not aim to maximize as much of each feature as
possible, and so often results in solutions that are heavily biased towards
just a few features." />
<meta property="og:image" content="https://prioritizr.net/logo.png" />
<!-- mathjax -->
<script src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/MathJax.js" integrity="sha256-nvJJv9wWKEm88qvoQl9ekL2J+k/RWIsaSScxxlsrv8k=" crossorigin="anonymous"></script>
<script src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/config/TeX-AMS-MML_HTMLorMML.js" integrity="sha256-84DKXVJXs0/F8OTMzX4UR909+jtl4G7SPypPavF+GfA=" crossorigin="anonymous"></script>
<!--[if lt IE 9]>
<script src="https://oss.maxcdn.com/html5shiv/3.7.3/html5shiv.min.js"></script>
<script src="https://oss.maxcdn.com/respond/1.4.2/respond.min.js"></script>
<![endif]-->
<!-- Global site tag (gtag.js) - Google Analytics -->
<script async src="https://www.googletagmanager.com/gtag/js?id=UA-70466840-4"></script>
<script>
window.dataLayer = window.dataLayer || [];
function gtag(){dataLayer.push(arguments);}
gtag('js', new Date());
gtag('config', 'UA-70466840-4');
</script>
</head>
<body data-spy="scroll" data-target="#toc">
<div class="container template-reference-topic">
<header>
<div class="navbar navbar-default navbar-fixed-top" role="navigation">
<div class="container">
<div class="navbar-header">
<button type="button" class="navbar-toggle collapsed" data-toggle="collapse" data-target="#navbar" aria-expanded="false">
<span class="sr-only">Toggle navigation</span>
<span class="icon-bar"></span>
<span class="icon-bar"></span>
<span class="icon-bar"></span>
</button>
<span class="navbar-brand">
<a class="navbar-link" href="../index.html">prioritizr</a>
<span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="Released version">7.1.0.3</span>
</span>
</div>
<div id="navbar" class="navbar-collapse collapse">
<ul class="nav navbar-nav">
<li>
<a href="../articles/prioritizr.html">Get started</a>
</li>
<li>
<a href="../reference/index.html">Reference</a>
</li>
<li class="dropdown">
<a href="#" class="dropdown-toggle" data-toggle="dropdown" role="button" aria-expanded="false">
Articles
<span class="caret"></span>
</a>
<ul class="dropdown-menu" role="menu">
<li>
<a href="../articles/gurobi_installation.html">Gurobi Installation Guide</a>
</li>
<li>
<a href="../articles/publication_record.html">Publication Record</a>
</li>
<li>
<a href="../articles/saltspring.html">Salt Spring Island Tutorial</a>
</li>
<li>
<a href="../articles/solver_benchmark.html">Solver Benchmarks</a>
</li>
<li>
<a href="../articles/tasmania.html">Tasmania Tutorial</a>
</li>
<li>
<a href="../articles/zones.html">Management Zones</a>
</li>
</ul>
</li>
<li>
<a href="../news/index.html">Changelog</a>
</li>
</ul>
<ul class="nav navbar-nav navbar-right">
<li>
<a href="https://github.com/prioritizr/prioritizr/">
<span class="fab fa-github fa-lg"></span>
</a>
</li>
</ul>
<form class="navbar-form navbar-right hidden-xs hidden-sm" role="search">
<div class="form-group">
<input type="search" class="form-control" name="search-input" id="search-input" placeholder="Search..." aria-label="Search for..." autocomplete="off">
</div>
</form>
</div><!--/.nav-collapse -->
</div><!--/.container -->
</div><!--/.navbar -->
</header>
<div class="row">
<div class="col-md-9 contents">
<div class="page-header">
<h1>Add maximum utility objective</h1>
<small class="dont-index">Source: <a href='https://github.com/prioritizr/prioritizr/blob/master/R/add_max_utility_objective.R'><code>R/add_max_utility_objective.R</code></a></small>
<div class="hidden name"><code>add_max_utility_objective.Rd</code></div>
</div>
<div class="ref-description">
<p>Set the objective of a conservation planning <code><a href='problem.html'>problem()</a></code> to
secure as much of the features as possible without exceeding a budget.
This objective does not use targets, and feature
weights should be used instead to increase the representation of certain
features by a solution.
Note that this objective does not aim to maximize as much of each feature as
possible, and so often results in solutions that are heavily biased towards
just a few features.</p>
</div>
<div class="ref-usage sourceCode"><pre class='sourceCode r'><code><span class='fu'>add_max_utility_objective</span><span class='op'>(</span><span class='va'>x</span>, <span class='va'>budget</span><span class='op'>)</span></code></pre></div>
<h2 class="hasAnchor" id="arguments"><a class="anchor" href="#arguments"></a>Arguments</h2>
<table class="ref-arguments">
<colgroup><col class="name" /><col class="desc" /></colgroup>
<tr>
<th>x</th>
<td><p><code><a href='problem.html'>problem()</a></code> (i.e. <code><a href='ConservationProblem-class.html'>ConservationProblem</a></code>) object.</p></td>
</tr>
<tr>
<th>budget</th>
<td><p><code>numeric</code> value specifying the maximum expenditure of
the prioritization. For problems with multiple zones, the argument
to <code>budget</code> can be (i) a single <code>numeric</code> value to specify a single budget
for the entire solution or (ii) a <code>numeric</code> vector to specify
a separate budget for each management zone.</p></td>
</tr>
</table>
<h2 class="hasAnchor" id="value"><a class="anchor" href="#value"></a>Value</h2>
<p>Object (i.e. <code><a href='ConservationProblem-class.html'>ConservationProblem</a></code>) with the objective
added to it.</p>
<h2 class="hasAnchor" id="details"><a class="anchor" href="#details"></a>Details</h2>
<p>The maximum utility objective seeks to maximize the overall level of
representation across a suite of conservation features, while keeping cost
within a fixed budget.
Additionally, weights can be used to favor the
representation of certain features over other features (see
<code><a href='add_feature_weights.html'>add_feature_weights()</a></code>).</p>
<h2 class="hasAnchor" id="mathematical-formulation"><a class="anchor" href="#mathematical-formulation"></a>Mathematical formulation</h2>
<p>This objective can be expressed mathematically for a set of planning units
(\(I\) indexed by \(i\)) and a set of features (\(J\) indexed
by \(j\)) as:</p>
<p>$$\mathit{Maximize} \space \sum_{i = 1}^{I} -s \space c_i \space x_i +
\sum_{j = 1}^{J} a_j w_j \\
\mathit{subject \space to} \\ a_j = \sum_{i = 1}^{I} x_i r_{ij} \space
\forall j \in J \\ \sum_{i = 1}^{I} x_i c_i \leq B$$</p>
<p>Here, \(x_i\) is the <a href='decisions.html'>decisions</a> variable (e.g.
specifying whether planning unit \(i\) has been selected (1) or not
(0)), \(r_{ij}\) is the amount of feature \(j\) in planning
unit \(i\), \(A_j\) is the amount of feature \(j\)
represented in in the solution, and \(w_j\) is the weight for
feature \(j\) (defaults to 1 for all features; see
<code><a href='add_feature_weights.html'>add_feature_weights()</a></code>
to specify weights). Additionally, \(B\) is the budget allocated for
the solution, \(c_i\) is the cost of planning unit \(i\), and
\(s\) is a scaling factor used to shrink the costs so that the problem
will return a cheapest solution when there are multiple solutions that
represent the same amount of all features within the budget.</p>
<h2 class="hasAnchor" id="notes"><a class="anchor" href="#notes"></a>Notes</h2>
<p>In early versions (< 3.0.0.0), this function was named as
the <code>add_max_cover_objective</code> function. It was renamed to avoid
confusion with existing terminology.</p>
<h2 class="hasAnchor" id="see-also"><a class="anchor" href="#see-also"></a>See also</h2>
<div class='dont-index'><p>See <a href='objectives.html'>objectives</a> for an overview of all functions for adding objectives.
Also, see <code><a href='add_feature_weights.html'>add_feature_weights()</a></code> to specify weights for different features.</p>
<p>Other objectives:
<code><a href='add_max_cover_objective.html'>add_max_cover_objective</a>()</code>,
<code><a href='add_max_features_objective.html'>add_max_features_objective</a>()</code>,
<code><a href='add_max_phylo_div_objective.html'>add_max_phylo_div_objective</a>()</code>,
<code><a href='add_max_phylo_end_objective.html'>add_max_phylo_end_objective</a>()</code>,
<code><a href='add_min_largest_shortfall_objective.html'>add_min_largest_shortfall_objective</a>()</code>,
<code><a href='add_min_set_objective.html'>add_min_set_objective</a>()</code>,
<code><a href='add_min_shortfall_objective.html'>add_min_shortfall_objective</a>()</code></p></div>
<h2 class="hasAnchor" id="examples"><a class="anchor" href="#examples"></a>Examples</h2>
<div class="ref-examples sourceCode"><pre class='sourceCode r'><code><span class='r-in'><span class='co'># load data</span></span>
<span class='r-in'><span class='fu'><a href='https://rdrr.io/r/utils/data.html'>data</a></span><span class='op'>(</span><span class='va'>sim_pu_raster</span>, <span class='va'>sim_pu_zones_stack</span>, <span class='va'>sim_features</span>, <span class='va'>sim_features_zones</span><span class='op'>)</span></span>
<span class='r-in'></span>
<span class='r-in'><span class='co'># create problem with maximum utility objective</span></span>
<span class='r-in'><span class='va'>p1</span> <span class='op'><-</span> <span class='fu'><a href='problem.html'>problem</a></span><span class='op'>(</span><span class='va'>sim_pu_raster</span>, <span class='va'>sim_features</span><span class='op'>)</span> <span class='op'><a href='pipe.html'>%>%</a></span></span>
<span class='r-in'> <span class='fu'>add_max_utility_objective</span><span class='op'>(</span><span class='fl'>5000</span><span class='op'>)</span> <span class='op'><a href='pipe.html'>%>%</a></span></span>
<span class='r-in'> <span class='fu'><a href='add_binary_decisions.html'>add_binary_decisions</a></span><span class='op'>(</span><span class='op'>)</span> <span class='op'><a href='pipe.html'>%>%</a></span></span>
<span class='r-in'> <span class='fu'><a href='add_default_solver.html'>add_default_solver</a></span><span class='op'>(</span>gap <span class='op'>=</span> <span class='fl'>0</span>, verbose <span class='op'>=</span> <span class='cn'>FALSE</span><span class='op'>)</span></span>
<span class='r-in'><span class='co'># \dontrun{</span></span>
<span class='r-in'><span class='co'># solve problem</span></span>
<span class='r-in'><span class='va'>s1</span> <span class='op'><-</span> <span class='fu'><a href='solve.html'>solve</a></span><span class='op'>(</span><span class='va'>p1</span><span class='op'>)</span></span>
<span class='r-in'></span>
<span class='r-in'><span class='co'># plot solution</span></span>
<span class='r-in'><span class='fu'><a href='https://rdrr.io/pkg/raster/man/plot.html'>plot</a></span><span class='op'>(</span><span class='va'>s1</span>, main <span class='op'>=</span> <span class='st'>"solution"</span>, axes <span class='op'>=</span> <span class='cn'>FALSE</span>, box <span class='op'>=</span> <span class='cn'>FALSE</span><span class='op'>)</span></span>
<span class='r-plt'><img src='add_max_utility_objective-1.png' alt='' width='700' height='433' /></span>
<span class='r-in'><span class='co'># }</span></span>
<span class='r-in'></span>
<span class='r-in'><span class='co'># create multi-zone problem with maximum utility objective that</span></span>
<span class='r-in'><span class='co'># has a single budget for all zones</span></span>
<span class='r-in'><span class='va'>p2</span> <span class='op'><-</span> <span class='fu'><a href='problem.html'>problem</a></span><span class='op'>(</span><span class='va'>sim_pu_zones_stack</span>, <span class='va'>sim_features_zones</span><span class='op'>)</span> <span class='op'><a href='pipe.html'>%>%</a></span></span>
<span class='r-in'> <span class='fu'>add_max_utility_objective</span><span class='op'>(</span><span class='fl'>5000</span><span class='op'>)</span> <span class='op'><a href='pipe.html'>%>%</a></span></span>
<span class='r-in'> <span class='fu'><a href='add_binary_decisions.html'>add_binary_decisions</a></span><span class='op'>(</span><span class='op'>)</span> <span class='op'><a href='pipe.html'>%>%</a></span></span>
<span class='r-in'> <span class='fu'><a href='add_default_solver.html'>add_default_solver</a></span><span class='op'>(</span>gap <span class='op'>=</span> <span class='fl'>0</span>, verbose <span class='op'>=</span> <span class='cn'>FALSE</span><span class='op'>)</span></span>
<span class='r-in'><span class='co'># \dontrun{</span></span>
<span class='r-in'><span class='co'># solve problem</span></span>
<span class='r-in'><span class='va'>s2</span> <span class='op'><-</span> <span class='fu'><a href='solve.html'>solve</a></span><span class='op'>(</span><span class='va'>p2</span><span class='op'>)</span></span>
<span class='r-in'></span>
<span class='r-in'><span class='co'># plot solution</span></span>
<span class='r-in'><span class='fu'><a href='https://rdrr.io/pkg/raster/man/plot.html'>plot</a></span><span class='op'>(</span><span class='fu'><a href='category_layer.html'>category_layer</a></span><span class='op'>(</span><span class='va'>s2</span><span class='op'>)</span>, main <span class='op'>=</span> <span class='st'>"solution"</span>, axes <span class='op'>=</span> <span class='cn'>FALSE</span>, box <span class='op'>=</span> <span class='cn'>FALSE</span><span class='op'>)</span></span>
<span class='r-plt'><img src='add_max_utility_objective-2.png' alt='' width='700' height='433' /></span>
<span class='r-in'><span class='co'># }</span></span>
<span class='r-in'></span>
<span class='r-in'><span class='co'># create multi-zone problem with maximum utility objective that</span></span>
<span class='r-in'><span class='co'># has separate budgets for each zone</span></span>
<span class='r-in'><span class='va'>p3</span> <span class='op'><-</span> <span class='fu'><a href='problem.html'>problem</a></span><span class='op'>(</span><span class='va'>sim_pu_zones_stack</span>, <span class='va'>sim_features_zones</span><span class='op'>)</span> <span class='op'><a href='pipe.html'>%>%</a></span></span>
<span class='r-in'> <span class='fu'>add_max_utility_objective</span><span class='op'>(</span><span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span><span class='op'>(</span><span class='fl'>1000</span>, <span class='fl'>2000</span>, <span class='fl'>3000</span><span class='op'>)</span><span class='op'>)</span> <span class='op'><a href='pipe.html'>%>%</a></span></span>
<span class='r-in'> <span class='fu'><a href='add_binary_decisions.html'>add_binary_decisions</a></span><span class='op'>(</span><span class='op'>)</span> <span class='op'><a href='pipe.html'>%>%</a></span></span>
<span class='r-in'> <span class='fu'><a href='add_default_solver.html'>add_default_solver</a></span><span class='op'>(</span>gap <span class='op'>=</span> <span class='fl'>0</span>, verbose <span class='op'>=</span> <span class='cn'>FALSE</span><span class='op'>)</span></span>
<span class='r-in'><span class='co'># \dontrun{</span></span>
<span class='r-in'><span class='co'># solve problem</span></span>
<span class='r-in'><span class='va'>s3</span> <span class='op'><-</span> <span class='fu'><a href='solve.html'>solve</a></span><span class='op'>(</span><span class='va'>p3</span><span class='op'>)</span></span>
<span class='r-in'></span>
<span class='r-in'><span class='co'># plot solution</span></span>
<span class='r-in'><span class='fu'><a href='https://rdrr.io/pkg/raster/man/plot.html'>plot</a></span><span class='op'>(</span><span class='fu'><a href='category_layer.html'>category_layer</a></span><span class='op'>(</span><span class='va'>s3</span><span class='op'>)</span>, main <span class='op'>=</span> <span class='st'>"solution"</span>, axes <span class='op'>=</span> <span class='cn'>FALSE</span>, box <span class='op'>=</span> <span class='cn'>FALSE</span><span class='op'>)</span></span>
<span class='r-plt'><img src='add_max_utility_objective-3.png' alt='' width='700' height='433' /></span>
<span class='r-in'><span class='co'># }</span></span>
</code></pre></div>
</div>
<div class="col-md-3 hidden-xs hidden-sm" id="pkgdown-sidebar">
<nav id="toc" data-toggle="toc" class="sticky-top">
<h2 data-toc-skip>Contents</h2>
</nav>
</div>
</div>
<footer>
<div class="copyright">
<p><p>Developed by <a href="https://jeffrey-hanson.com" class="external-link">Jeffrey O Hanson</a>, <a href="http://www.richard-schuster.com" class="external-link">Richard Schuster</a>, Nina Morrell, <a href="http://strimas.com" class="external-link">Matthew Strimas-Mackey</a>, Matthew E Watts, <a href="https://arcese.forestry.ubc.ca" class="external-link">Peter Arcese</a>, <a href="https://josephrbennett.wordpress.com" class="external-link">Joseph Bennett</a>, <a href="http://www.possinghamlab.org" class="external-link">Hugh P Possingham</a>.</p></p>
</div>
<div class="pkgdown">
<p><p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 1.6.1.9001.</p></p>
</div>
</footer>
</div>
<script src="https://cdnjs.cloudflare.com/ajax/libs/docsearch.js/2.6.1/docsearch.min.js" integrity="sha256-GKvGqXDznoRYHCwKXGnuchvKSwmx9SRMrZOTh2g4Sb0=" crossorigin="anonymous"></script>
<script>
docsearch({
apiKey: '486efa122ea6783724263412c5f28ab3',
indexName: 'prioritizr',
inputSelector: 'input#search-input.form-control',
transformData: function(hits) {
return hits.map(function (hit) {
hit.url = updateHitURL(hit);
return hit;
});
}
});
</script>
</body>
</html>