build based on 63959f8

previews/PR3889/.documenter-siteinfo.json

@@ -1 +1 @@
-{"documenter":{"julia_version":"1.11.1","generation_timestamp":"2024-11-22T04:07:38","documenter_version":"1.7.0"}}
+{"documenter":{"julia_version":"1.11.1","generation_timestamp":"2024-11-22T04:07:09","documenter_version":"1.7.0"}}

previews/PR3889/moi/reference/models/index.html

@@ -7,7 +7,7 @@
     model::MOI.ModelLike,
     attr::MOI.AbstractConstraintAttribute,
     bridge::AbstractBridge,
-)</code></pre><p>Return the value of the attribute <code>attr</code> of the model <code>model</code> for the constraint bridged by <code>bridge</code>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/jump-dev/MathOptInterface.jl/blob/v1.34.0/src/Bridges/bridge.jl#L133-L142">source</a></section><section><div><pre><code class="language-julia hljs">get(model::GenericModel, attr::MathOptInterface.AbstractOptimizerAttribute)</code></pre><p>Return the value of the attribute <code>attr</code> from the model&#39;s MOI backend.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/jump-dev/JuMP.jl/blob/eb3d99392b86ec08053ce9aba8764915087dfe82/src/optimizer_interface.jl#L987-L991">source</a></section><section><div><pre><code class="language-julia hljs">get(model::GenericModel, attr::MathOptInterface.AbstractModelAttribute)</code></pre><p>Return the value of the attribute <code>attr</code> from the model&#39;s MOI backend.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/jump-dev/JuMP.jl/blob/eb3d99392b86ec08053ce9aba8764915087dfe82/src/optimizer_interface.jl#L1056-L1060">source</a></section><section><div><pre><code class="language-julia hljs">get(optimizer::AbstractOptimizer, attr::AbstractOptimizerAttribute)</code></pre><p>Return an attribute <code>attr</code> of the optimizer <code>optimizer</code>.</p><pre><code class="language-julia hljs">get(model::ModelLike, attr::AbstractModelAttribute)</code></pre><p>Return an attribute <code>attr</code> of the model <code>model</code>.</p><pre><code class="language-julia hljs">get(model::ModelLike, attr::AbstractVariableAttribute, v::VariableIndex)</code></pre><p>If the attribute <code>attr</code> is set for the variable <code>v</code> in the model <code>model</code>, return its value, return <code>nothing</code> otherwise. If the attribute <code>attr</code> is not supported by <code>model</code> then an error should be thrown instead of returning <code>nothing</code>.</p><pre><code class="language-julia hljs">get(model::ModelLike, attr::AbstractVariableAttribute, v::Vector{VariableIndex})</code></pre><p>Return a vector of attributes corresponding to each variable in the collection <code>v</code> in the model <code>model</code>.</p><pre><code class="language-julia hljs">get(model::ModelLike, attr::AbstractConstraintAttribute, c::ConstraintIndex)</code></pre><p>If the attribute <code>attr</code> is set for the constraint <code>c</code> in the model <code>model</code>, return its value, return <code>nothing</code> otherwise. If the attribute <code>attr</code> is not supported by <code>model</code> then an error should be thrown instead of returning <code>nothing</code>.</p><pre><code class="language-julia hljs">get(
+)</code></pre><p>Return the value of the attribute <code>attr</code> of the model <code>model</code> for the constraint bridged by <code>bridge</code>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/jump-dev/MathOptInterface.jl/blob/v1.34.0/src/Bridges/bridge.jl#L133-L142">source</a></section><section><div><pre><code class="language-julia hljs">get(model::GenericModel, attr::MathOptInterface.AbstractOptimizerAttribute)</code></pre><p>Return the value of the attribute <code>attr</code> from the model&#39;s MOI backend.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/jump-dev/JuMP.jl/blob/63959f8dd93a006b211f72f1ffc3f207fbb5f107/src/optimizer_interface.jl#L987-L991">source</a></section><section><div><pre><code class="language-julia hljs">get(model::GenericModel, attr::MathOptInterface.AbstractModelAttribute)</code></pre><p>Return the value of the attribute <code>attr</code> from the model&#39;s MOI backend.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/jump-dev/JuMP.jl/blob/63959f8dd93a006b211f72f1ffc3f207fbb5f107/src/optimizer_interface.jl#L1056-L1060">source</a></section><section><div><pre><code class="language-julia hljs">get(optimizer::AbstractOptimizer, attr::AbstractOptimizerAttribute)</code></pre><p>Return an attribute <code>attr</code> of the optimizer <code>optimizer</code>.</p><pre><code class="language-julia hljs">get(model::ModelLike, attr::AbstractModelAttribute)</code></pre><p>Return an attribute <code>attr</code> of the model <code>model</code>.</p><pre><code class="language-julia hljs">get(model::ModelLike, attr::AbstractVariableAttribute, v::VariableIndex)</code></pre><p>If the attribute <code>attr</code> is set for the variable <code>v</code> in the model <code>model</code>, return its value, return <code>nothing</code> otherwise. If the attribute <code>attr</code> is not supported by <code>model</code> then an error should be thrown instead of returning <code>nothing</code>.</p><pre><code class="language-julia hljs">get(model::ModelLike, attr::AbstractVariableAttribute, v::Vector{VariableIndex})</code></pre><p>Return a vector of attributes corresponding to each variable in the collection <code>v</code> in the model <code>model</code>.</p><pre><code class="language-julia hljs">get(model::ModelLike, attr::AbstractConstraintAttribute, c::ConstraintIndex)</code></pre><p>If the attribute <code>attr</code> is set for the constraint <code>c</code> in the model <code>model</code>, return its value, return <code>nothing</code> otherwise. If the attribute <code>attr</code> is not supported by <code>model</code> then an error should be thrown instead of returning <code>nothing</code>.</p><pre><code class="language-julia hljs">get(
     model::ModelLike,
     attr::AbstractConstraintAttribute,
     c::Vector{ConstraintIndex{F,S}},

previews/PR3889/tutorials/algorithms/benders_decomposition/index.html

@@ -66,7 +66,7 @@
   Dual objective value : NaN
 
 * Work counters
-  Solve time (sec)   : 1.51134e-03
+  Solve time (sec)   : 1.97172e-03
   Simplex iterations : 15
   Barrier iterations : -1
   Node count         : 1

previews/PR3889/tutorials/algorithms/cutting_stock_column_generation/index.html

@@ -118,8 +118,8 @@
   Dual objective value : NaN
 
 * Work counters
-  Solve time (sec)   : 5.05371e+00
-  Simplex iterations : 20697
+  Solve time (sec)   : 5.04854e+00
+  Simplex iterations : 20481
   Barrier iterations : -1
   Node count         : 0
 </code></pre><p>However, there is a formulation that solves much faster, and that is to use a column generation scheme.</p><h2 id="Column-generation-theory"><a class="docs-heading-anchor" href="#Column-generation-theory">Column generation theory</a><a id="Column-generation-theory-1"></a><a class="docs-heading-anchor-permalink" href="#Column-generation-theory" title="Permalink"></a></h2><p>The key insight for column generation is to recognize that feasible columns in the <span>$x$</span> matrix of variables encode <em>cutting patterns</em>.</p><p>For example, if we look only at the roll <span>$j=1$</span>, then a feasible solution is:</p><ul><li><span>$x_{1,1} = 1$</span> (1 unit of piece #1)</li><li><span>$x_{13,1} = 1$</span> (1 unit of piece #13)</li><li>All other <span>$x_{i,1} = 0$</span></li></ul><p>Another solution is</p><ul><li><span>$x_{20,1} = 19$</span> (19 unit of piece #20)</li><li>All other <span>$x_{i,1} = 0$</span></li></ul><p>Cutting patterns like <span>$x_{1,1} = 1$</span> and <span>$x_{2,1} = 1$</span> are infeasible because the combined length is greater than <span>$W$</span>.</p><p>Since there are a finite number of ways that we could cut a roll into a valid cutting pattern, we could create a set of all possible cutting patterns <span>$p = 1,\ldots,P$</span>, with data <span>$a_{i,p}$</span> indicating how many units of piece <span>$i$</span> we cut in pattern <span>$p$</span>. Then, we can formulate our mixed-integer linear program as:</p><p class="math-container">\[\begin{align}
@@ -189,7 +189,7 @@
     return plot
 end
 
-plot_patterns(data, patterns)</code></pre><img src="ceb79ef1.svg" alt="Example block output"/><h2 id="The-base-problem"><a class="docs-heading-anchor" href="#The-base-problem">The base problem</a><a id="The-base-problem-1"></a><a class="docs-heading-anchor-permalink" href="#The-base-problem" title="Permalink"></a></h2><p>Using the initial set of patterns, we can create and optimize our base model:</p><pre><code class="language-julia hljs">model = Model(HiGHS.Optimizer)
+plot_patterns(data, patterns)</code></pre><img src="cac66ad5.svg" alt="Example block output"/><h2 id="The-base-problem"><a class="docs-heading-anchor" href="#The-base-problem">The base problem</a><a id="The-base-problem-1"></a><a class="docs-heading-anchor-permalink" href="#The-base-problem" title="Permalink"></a></h2><p>Using the initial set of patterns, we can create and optimize our base model:</p><pre><code class="language-julia hljs">model = Model(HiGHS.Optimizer)
 set_silent(model)
 @variable(model, x[1:length(patterns)] &gt;= 0, Int)
 @objective(model, Min, sum(x))
@@ -213,7 +213,7 @@
   Dual objective value : NaN
 
 * Work counters
-  Solve time (sec)   : 1.46389e-04
+  Solve time (sec)   : 1.51396e-04
   Simplex iterations : 0
   Barrier iterations : -1
   Node count         : 0
@@ -285,7 +285,7 @@
 <span class="sgr36"><span class="sgr1">[ Info: </span></span>No new patterns, terminating the algorithm.</code></pre><p>We found lots of new patterns. Here&#39;s pattern 21:</p><pre><code class="language-julia hljs">patterns[21]</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">20-element SparseArrays.SparseVector{Int64, Int64} with 3 stored entries:
   [9 ]  =  1
   [13]  =  2
-  [17]  =  1</code></pre><p>Let&#39;s have a look at the patterns now:</p><pre><code class="language-julia hljs">plot_patterns(data, patterns)</code></pre><img src="4090efe1.svg" alt="Example block output"/><h2 id="Looking-at-the-solution"><a class="docs-heading-anchor" href="#Looking-at-the-solution">Looking at the solution</a><a id="Looking-at-the-solution-1"></a><a class="docs-heading-anchor-permalink" href="#Looking-at-the-solution" title="Permalink"></a></h2><p>Let&#39;s see how many of each column we need:</p><pre><code class="language-julia hljs">solution = DataFrames.DataFrame([
+  [17]  =  1</code></pre><p>Let&#39;s have a look at the patterns now:</p><pre><code class="language-julia hljs">plot_patterns(data, patterns)</code></pre><img src="de7f340e.svg" alt="Example block output"/><h2 id="Looking-at-the-solution"><a class="docs-heading-anchor" href="#Looking-at-the-solution">Looking at the solution</a><a id="Looking-at-the-solution-1"></a><a class="docs-heading-anchor-permalink" href="#Looking-at-the-solution" title="Permalink"></a></h2><p>Let&#39;s see how many of each column we need:</p><pre><code class="language-julia hljs">solution = DataFrames.DataFrame([
     (pattern = p, rolls = value(x_p)) for (p, x_p) in enumerate(x)
 ])
 filter!(row -&gt; row.rolls &gt; 0, solution)</code></pre><div><div style = "float: left;"><span>16×2 DataFrame</span></div><div style = "clear: both;"></div></div><div class = "data-frame" style = "overflow-x: scroll;"><table class = "data-frame" style = "margin-bottom: 6px;"><thead><tr class = "header"><th class = "rowNumber" style = "font-weight: bold; text-align: right;">Row</th><th style = "text-align: left;">pattern</th><th style = "text-align: left;">rolls</th></tr><tr class = "subheader headerLastRow"><th class = "rowNumber" style = "font-weight: bold; text-align: right;"></th><th title = "Int64" style = "text-align: left;">Int64</th><th title = "Float64" style = "text-align: left;">Float64</th></tr></thead><tbody><tr><td class = "rowNumber" style = "font-weight: bold; text-align: right;">1</td><td style = "text-align: right;">1</td><td style = "text-align: right;">38.0</td></tr><tr><td class = "rowNumber" style = "font-weight: bold; text-align: right;">2</td><td style = "text-align: right;">2</td><td style = "text-align: right;">44.0</td></tr><tr><td class = "rowNumber" style = "font-weight: bold; text-align: right;">3</td><td style = "text-align: right;">3</td><td style = "text-align: right;">30.0</td></tr><tr><td class = "rowNumber" style = "font-weight: bold; text-align: right;">4</td><td style = "text-align: right;">21</td><td style = "text-align: right;">0.5</td></tr><tr><td class = "rowNumber" style = "font-weight: bold; text-align: right;">5</td><td style = "text-align: right;">22</td><td style = "text-align: right;">10.2</td></tr><tr><td class = "rowNumber" style = "font-weight: bold; text-align: right;">6</td><td style = "text-align: right;">23</td><td style = "text-align: right;">14.65</td></tr><tr><td class = "rowNumber" style = "font-weight: bold; text-align: right;">7</td><td style = "text-align: right;">24</td><td style = "text-align: right;">23.1</td></tr><tr><td class = "rowNumber" style = "font-weight: bold; text-align: right;">8</td><td style = "text-align: right;">25</td><td style = "text-align: right;">11.25</td></tr><tr><td class = "rowNumber" style = "font-weight: bold; text-align: right;">9</td><td style = "text-align: right;">26</td><td style = "text-align: right;">21.35</td></tr><tr><td class = "rowNumber" style = "font-weight: bold; text-align: right;">10</td><td style = "text-align: right;">28</td><td style = "text-align: right;">4.3</td></tr><tr><td class = "rowNumber" style = "font-weight: bold; text-align: right;">11</td><td style = "text-align: right;">29</td><td style = "text-align: right;">19.55</td></tr><tr><td class = "rowNumber" style = "font-weight: bold; text-align: right;">12</td><td style = "text-align: right;">30</td><td style = "text-align: right;">11.25</td></tr><tr><td class = "rowNumber" style = "font-weight: bold; text-align: right;">13</td><td style = "text-align: right;">31</td><td style = "text-align: right;">17.45</td></tr><tr><td class = "rowNumber" style = "font-weight: bold; text-align: right;">14</td><td style = "text-align: right;">33</td><td style = "text-align: right;">36.0</td></tr><tr><td class = "rowNumber" style = "font-weight: bold; text-align: right;">15</td><td style = "text-align: right;">34</td><td style = "text-align: right;">11.4</td></tr><tr><td class = "rowNumber" style = "font-weight: bold; text-align: right;">16</td><td style = "text-align: right;">35</td><td style = "text-align: right;">41.0</td></tr></tbody></table></div><p>Since we solved a linear program, some of our columns have fractional solutions. We can create a integer feasible solution by rounding up the orders. This requires 341 rolls:</p><pre><code class="language-julia hljs">sum(ceil.(Int, solution.rolls))</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">341</code></pre><p>Alternatively, we can re-introduce the integrality constraints and resolve the problem:</p><pre><code class="language-julia hljs">set_integer.(x)

previews/PR3889/tutorials/algorithms/pdhg/index.html

@@ -314,7 +314,7 @@
     c3 : [-1.93193e-06,2.50002e-01,1.50000e+00]
 
 * Work counters
-  Solve time (sec)   : 2.05041e-01
+  Solve time (sec)   : 2.29210e-01
   Barrier iterations : 8365
 </code></pre><p>But we could also have written:</p><pre><code class="language-julia hljs">model = Model(Optimizer)
 @variable(model, x &gt;= 0)
@@ -352,7 +352,7 @@
     c2 : 1.50000e+00
 
 * Work counters
-  Solve time (sec)   : 1.91402e-03
+  Solve time (sec)   : 2.21205e-03
   Barrier iterations : 8365
 </code></pre><p>Other variations are also possible:</p><pre><code class="language-julia hljs">model = Model(Optimizer)
 @variable(model, x[1:5] &gt;= 0)
@@ -390,6 +390,6 @@
     c4 : multiple constraints with the same name
 
 * Work counters
-  Solve time (sec)   : 1.89614e-03
+  Solve time (sec)   : 1.79887e-03
   Barrier iterations : 8365
 </code></pre><p>Behind the scenes, JuMP and MathOptInterface reformulate the problem from the modeller&#39;s form into the standard form defined by our <code>Optimizer</code>.</p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../parallelism/">« Parallelism</a><a class="docs-footer-nextpage" href="../../applications/power_systems/">Power Systems »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Friday 22 November 2024 04:06">Friday 22 November 2024</span>. Using Julia version 1.11.1.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>