SherbyNet - /page/wikibook/entry.mu

Micron Document

<!DOCTYPE html>

<title>Firefly algorithm</title>

</head>

<span id="openzim-page-title" class="mw-page-title-main"><span class="mw-page-title-main">Firefly algorithm</span></span>

</h1>

</header>

<div id="mw-content-text" class="mw-body-content mw-content-ltr" lang="en" dir="ltr"><div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><p>In <a href="Mathematical_optimization" title="Mathematical optimization">mathematical optimization</a>, the <b>firefly algorithm</b> is a <a href="Metaheuristic" title="Metaheuristic">metaheuristic</a> proposed by <a href="Xin-She_Yang" title="Xin-She Yang">Xin-She Yang</a> and inspired by the flashing behavior of <a href="Firefly" title="Firefly">fireflies</a>.<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup>

</p>

<div class="mw-heading mw-heading2"><h2 id="Algorithm">Algorithm</h2></div>

<p>In pseudocode the algorithm can be stated as:

</p>

<pre><b>Begin</b>

1) Objective function: <span class="nowrap"><span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f(\mathbf {x} ),\quad \mathbf {x} =(x_{1},x_{2},...,x_{d})}">

</mrow>

</mrow>

<msub>

</mrow>

</msub>

<msub>

</mrow>

</msub>

<msub>

</mrow>

</msub>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle f(\mathbf {x} ),\quad \mathbf {x} =(x_{1},x_{2},...,x_{d})}</annotation>

</semantics>

</math></span><img src="./bee0a1a32d545b591c1a73c4ee91c41cc19a0cee.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:27.567ex; height:2.843ex;" alt="{\displaystyle f(\mathbf {x} ),\quad \mathbf {x} =(x_{1},x_{2},...,x_{d})}" loading="lazy"></span>;</span>

2) Generate an initial population of fireflies <span class="nowrap"><span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {x} _{i}\quad (i=1,2,\dots ,n)}">

<msub>

</mrow>

</mrow>

</msub>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle \mathbf {x} _{i}\quad (i=1,2,\dots ,n)}</annotation>

</semantics>

</math></span><img src="./7d978bae9f37717c1b2a17085ec2bf3053b4074f.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:20.175ex; height:2.843ex;" alt="{\displaystyle \mathbf {x} _{i}\quad (i=1,2,\dots ,n)}" loading="lazy"></span>;.</span>

3) Formulate light intensity <span class="texhtml mvar" style="font-style:italic;">I</span> so that it is associated with <span class="nowrap"><span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f(\mathbf {x} )}">

</mrow>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle f(\mathbf {x} )}</annotation>

</semantics>

</math></span><img src="./e41ea95e6949bf4cef6426116364ba87e0fdcd60.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.499ex; height:2.843ex;" alt="{\displaystyle f(\mathbf {x} )}" loading="lazy"></span></span>

(for example, for maximization problems, <span class="nowrap"><span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle I\propto f(\mathbf {x} )}">

</mrow>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle I\propto f(\mathbf {x} )}</annotation>

</semantics>

</math></span><img src="./767671362ed38f9d77155d0106c74d87821c0d40.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:8.769ex; height:2.843ex;" alt="{\displaystyle I\propto f(\mathbf {x} )}" loading="lazy"></span> or simply <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle I=f(\mathbf {x} )}">

</mrow>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle I=f(\mathbf {x} )}</annotation>

</semantics>

</math></span><img src="./2bc47376c0b0b8ccc34119027b842e4cdf57d64a.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:8.769ex; height:2.843ex;" alt="{\displaystyle I=f(\mathbf {x} )}" loading="lazy"></span>;)</span>

4) Define absorption coefficient <span class="texhtml mvar" style="font-style:italic;">γ</span>

<b>while</b> (t < MaxGeneration)

<b>for</b> i = 1 : n (all n fireflies)

<b>for</b> j = 1 : i (n fireflies)

<msub>

</mrow>

</msub>

<msub>

</mrow>

</msub>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle I_{j}>I_{i}}</annotation>

</semantics>

</math></span><img src="./36623587ea7702402b8309960d91c74dc674d315.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:6.854ex; height:2.843ex;" alt="{\displaystyle I_{j}>I_{i}}" loading="lazy"></span>),</span>

Vary attractiveness with distance r via <span class="nowrap"><span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \exp(-\gamma \;r)}">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle \exp(-\gamma \;r)}</annotation>

</semantics>

</math></span><img src="./64eea6df09431e372a4a900b6e2b3caefde88faf.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:10.126ex; height:2.843ex;" alt="{\displaystyle \exp(-\gamma \;r)}" loading="lazy"></span>;</span>

move firefly i towards j;

Evaluate new solutions and update light intensity;

<b>end for</b> j

<b>end for</b> i

Rank fireflies and find the current best;

<b>end while</b>

</pre>

<p>Note that the number of objective function evaluations per loop is one evaluation per firefly, even though the above pseudocode suggests it is <i>n</i>×<i>n</i>. (Based on Yang's <a href="MATLAB" title="MATLAB">MATLAB</a> code.) Thus the total number of objective function evaluations is (number of generations) × (number of fireflies).

</p><p>The main update formula for any pair of two fireflies <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {x} _{i}}">

<msub>

</mrow>

</mrow>

</msub>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle \mathbf {x} _{i}}</annotation>

</semantics>

</math></span><img src="./57d2ef3df60acdb53bdf90535264041fea7231cd.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.211ex; height:2.009ex;" alt="{\displaystyle \mathbf {x} _{i}}" loading="lazy"></span> and <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {x} _{j}}">

<msub>

</mrow>

</mrow>

</msub>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle \mathbf {x} _{j}}</annotation>

</semantics>

</math></span><img src="./da7e57d3f8c537992b45488f9586aec0c35a85f0.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:2.321ex; height:2.343ex;" alt="{\displaystyle \mathbf {x} _{j}}" loading="lazy"></span> is

</mrow>

</mrow>

</mrow>

</msubsup>

</mrow>

</mrow>

</mrow>

</msubsup>

</mrow>

</mrow>

</msubsup>

</mrow>

</mrow>

</mrow>

</msubsup>

</mrow>

</mrow>

</mrow>

</msubsup>

<msub>

</mrow>

</msub>

<msub>

</mrow>

</mrow>

</msub>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle \mathbf {x} _{i}^{t+1}=\mathbf {x} _{i}^{t}+\beta \exp[-\gamma r_{ij}^{2}](\mathbf {x} _{j}^{t}-\mathbf {x} _{i}^{t})+\alpha _{t}{\boldsymbol {\epsilon }}_{t}}</annotation>

</semantics>

</math></span></span>

where <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \alpha _{t}}">

<msub>

</mrow>

</msub>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle \alpha _{t}}</annotation>

</semantics>

</math></span><img src="./21f5c448878b19e535a54c80e546a39430e620cb.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.314ex; height:2.009ex;" alt="{\displaystyle \alpha _{t}}" loading="lazy"></span> is a parameter controlling the step size, while <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\boldsymbol {\epsilon }}_{t}}">

<msub>

</mrow>

</mrow>

</msub>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle {\boldsymbol {\epsilon }}_{t}}</annotation>

</semantics>

</math></span><img src="./e4fe4f0f2d4cb88cf34b85e2f9f39324488d069c.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.949ex; height:2.009ex;" alt="{\displaystyle {\boldsymbol {\epsilon }}_{t}}" loading="lazy"></span> is a vector drawn from a Gaussian or other

distribution.

</p><p>It can be shown that the limiting case <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \gamma \rightarrow 0}">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle \gamma \rightarrow 0}</annotation>

</semantics>

</math></span><img src="./3b1b021687f94c07a245dd9aaa50197039869523.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:6.039ex; height:2.676ex;" alt="{\displaystyle \gamma \rightarrow 0}" loading="lazy"></span> corresponds to the standard <a href="Particle_swarm_optimization" title="Particle swarm optimization">particle swarm optimization</a> (PSO). In fact, if the inner loop (for j) is removed and the brightness <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle I_{j}}">

<msub>

</mrow>

</msub>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle I_{j}}</annotation>

</semantics>

</math></span><img src="./b7cb04680c2246f78082e43ec912f72afe7af266.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:1.933ex; height:2.843ex;" alt="{\displaystyle I_{j}}" loading="lazy"></span> is replaced by the current global best <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle g^{*}}">

<msup>

</mrow>

</msup>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle g^{*}}</annotation>

</semantics>

</math></span><img src="./e1b02af7a00ce649e878c0276b16174d438e31a5.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.172ex; height:2.676ex;" alt="{\displaystyle g^{*}}" loading="lazy"></span>, then FA essentially becomes the standard PSO.

</p>

<div class="mw-heading mw-heading2"><h2 id="Criticism">Criticism</h2></div>

<p>Nature-inspired <a href="Metaheuristic" title="Metaheuristic">metaheuristics</a> in general have attracted <a href="List_of_metaphor-inspired_metaheuristics" class="mw-redirect" title="List of metaphor-inspired metaheuristics">criticism in the research community</a> for hiding their lack of novelty behind metaphors. The firefly algorithm has been criticized as differing from the well-established <a href="Particle_swarm_optimization" title="Particle swarm optimization">particle swarm optimization</a> only in a negligible way.<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup>

</p>

<ul><li><a href="Swarm_intelligence" title="Swarm intelligence">Swarm intelligence</a></li></ul>

<div class="mw-heading mw-heading2"><h2 id="References">References</h2></div>

/* start https://en.wikipedia.org/ */

.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}

/* end https://en.wikipedia.org/ */

</style><div class="cite-bracket" style="column-width: <sup id=">

/* start https://en.wikipedia.org/ */

.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("./mw/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("./mw/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("./mw/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("./mw/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}

/* end https://en.wikipedia.org/ */

</style><cite id="CITEREFYang2008" class="citation book cs1">Yang, X. S. (2008). <i>Nature-Inspired Metaheuristic Algorithms</i>. Luniver Press. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-1-905986-10-1</bdi>.</cite></span>

</li>

<li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text"><cite id="CITEREFAlmasiRouhani2016" class="citation journal cs1">Almasi, Omid N.; Rouhani, Modjtaba (2016). <a rel="nofollow" class="external text" href="https://doi.org/10.3906%2Felk-1310-253">"A new fuzzy membership assignment and model selection approach based on dynamic class centers for fuzzy SVM family using the firefly algorithm"</a>. <i>Turkish Journal of Electrical Engineering & Computer Sciences</i>. <b>4</b>: <span class="nowrap">1–</span>19. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.3906%2Felk-1310-253">10.3906/elk-1310-253</a></span>. <q>Practical application of FA on UCI datasets.</q></cite></span>

</li>

<li id="cite_note-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-3">^</a></b></span> <span class="reference-text"><cite id="CITEREFLones2014" class="citation book cs1">Lones, Michael A. (2014). <a rel="nofollow" class="external text" href="http://www.macs.hw.ac.uk/~ml355/common/papers/lones-gecco2014-metaheuristics.pdf">"Metaheuristics in nature-inspired algorithms"</a> <span class="cs1-format">(PDF)</span>. <i>Proceedings of the Companion Publication of the 2014 Annual Conference on Genetic and Evolutionary Computation</i>. pp. <span class="nowrap">1419–</span>1422. <a href="CiteSeerX_(identifier)" class="mw-redirect" title="CiteSeerX (identifier)">CiteSeerX</a> <span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.699.1825">10.1.1.699.1825</a></span>. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1145%2F2598394.2609841">10.1145/2598394.2609841</a>. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>9781450328814</bdi>. <a href="S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:14997975">14997975</a>. <q>FA, on the other hand, has little to distinguish it from PSO, with the inverse-square law having a similar effect to crowding and fitness sharing in EAs, and the use of multi-swarms in PSO.</q></cite></span>

</li>

<li id="cite_note-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-4">^</a></b></span> <span class="reference-text"><cite id="CITEREFWeyland2015" class="citation journal cs1">Weyland, Dennis (2015). <a rel="nofollow" class="external text" href="https://doi.org/10.1016%2Fj.orp.2015.04.001">"A critical analysis of the harmony search algorithm—How not to solve sudoku"</a>. <i>Operations Research Perspectives</i>. <b>2</b>: <span class="nowrap">97–</span>105. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1016%2Fj.orp.2015.04.001">10.1016/j.orp.2015.04.001</a></span>. <a href="Hdl_(identifier)" class="mw-redirect" title="Hdl (identifier)">hdl</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://hdl.handle.net/10419%2F178253">10419/178253</a></span>. <q>For example, the differences between the particle swarm optimization metaheuristic and "novel" metaheuristics like the firefly algorithm, the fruit fly optimization algorithm, the fish swarm optimization algorithm or the cat swarm optimization algorithm seem negligible.</q></cite></span>

</li>

<li id="cite_note-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-5">^</a></b></span> <span class="reference-text">Ariyaratne MKA, Pemarathne WPJ (2015) A review of recent advancements of firefly algorithm: a modern nature inspired algorithm. In: Proceedings of the 8th international research conference, 61–66, KDU, Published November 2015, <a rel="nofollow" class="external free" href="http://ir.kdu.ac.lk/bitstream/handle/345/1038/com-047.pdf?sequence=1&isAllowed=y">http://ir.kdu.ac.lk/bitstream/handle/345/1038/com-047.pdf?sequence=1&isAllowed=y</a></span>

</li>

</ol></div>

<div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2></div>

<ul><li><a rel="nofollow" class="external autonumber" href="https://www.mathworks.com/matlabcentral/fileexchange/29693-firefly-algorithm">[1]</a> Files of the Matlab programs included in the book: Xin-She Yang, Nature-Inspired Metaheuristic Algorithms, Second Edition, Luniver Press, (2010).</li></ul>

/* start https://en.wikipedia.org/ */

.mw-parser-output .hlist dl,.mw-parser-output .hlist ol,.mw-parser-output .hlist ul{margin:0;padding:0}.mw-parser-output .hlist dd,.mw-parser-output .hlist dt,.mw-parser-output .hlist li{margin:0;display:inline}.mw-parser-output .hlist.inline,.mw-parser-output .hlist.inline dl,.mw-parser-output .hlist.inline ol,.mw-parser-output .hlist.inline ul,.mw-parser-output .hlist dl dl,.mw-parser-output .hlist dl ol,.mw-parser-output .hlist dl ul,.mw-parser-output .hlist ol dl,.mw-parser-output .hlist ol ol,.mw-parser-output .hlist ol ul,.mw-parser-output .hlist ul dl,.mw-parser-output .hlist ul ol,.mw-parser-output .hlist ul ul{display:inline}.mw-parser-output .hlist .mw-empty-li{display:none}.mw-parser-output .hlist dt::after{content:": "}.mw-parser-output .hlist dd::after,.mw-parser-output .hlist li::after{content:" · ";font-weight:bold}.mw-parser-output .hlist dd:last-child::after,.mw-parser-output .hlist dt:last-child::after,.mw-parser-output .hlist li:last-child::after{content:none}.mw-parser-output .hlist dd dd:first-child::before,.mw-parser-output .hlist dd dt:first-child::before,.mw-parser-output .hlist dd li:first-child::before,.mw-parser-output .hlist dt dd:first-child::before,.mw-parser-output .hlist dt dt:first-child::before,.mw-parser-output .hlist dt li:first-child::before,.mw-parser-output .hlist li dd:first-child::before,.mw-parser-output .hlist li dt:first-child::before,.mw-parser-output .hlist li li:first-child::before{content:" (";font-weight:normal}.mw-parser-output .hlist dd dd:last-child::after,.mw-parser-output .hlist dd dt:last-child::after,.mw-parser-output .hlist dd li:last-child::after,.mw-parser-output .hlist dt dd:last-child::after,.mw-parser-output .hlist dt dt:last-child::after,.mw-parser-output .hlist dt li:last-child::after,.mw-parser-output .hlist li dd:last-child::after,.mw-parser-output .hlist li dt:last-child::after,.mw-parser-output .hlist li li:last-child::after{content:")";font-weight:normal}.mw-parser-output .hlist ol{counter-reset:listitem}.mw-parser-output .hlist ol>li{counter-increment:listitem}.mw-parser-output .hlist ol>li::before{content:" "counter(listitem)"\a0 "}.mw-parser-output .hlist dd ol>li:first-child::before,.mw-parser-output .hlist dt ol>li:first-child::before,.mw-parser-output .hlist li ol>li:first-child::before{content:" ("counter(listitem)"\a0 "}

/* end https://en.wikipedia.org/ */

</style><style data-mw-deduplicate="TemplateStyles:r1236075235">

/* start https://en.wikipedia.org/ */

.mw-parser-output .navbox{box-sizing:border-box;border:1px solid #a2a9b1;width:100%;clear:both;font-size:88%;text-align:center;padding:1px;margin:1em auto 0}.mw-parser-output .navbox .navbox{margin-top:0}.mw-parser-output .navbox+.navbox,.mw-parser-output .navbox+.navbox-styles+.navbox{margin-top:-1px}.mw-parser-output .navbox-inner,.mw-parser-output .navbox-subgroup{width:100%}.mw-parser-output .navbox-group,.mw-parser-output .navbox-title,.mw-parser-output .navbox-abovebelow{padding:0.25em 1em;line-height:1.5em;text-align:center}.mw-parser-output .navbox-group{white-space:nowrap;text-align:right}.mw-parser-output .navbox,.mw-parser-output .navbox-subgroup{background-color:#fdfdfd}.mw-parser-output .navbox-list{line-height:1.5em;border-color:#fdfdfd}.mw-parser-output .navbox-list-with-group{text-align:left;border-left-width:2px;border-left-style:solid}.mw-parser-output tr+tr>.navbox-abovebelow,.mw-parser-output tr+tr>.navbox-group,.mw-parser-output tr+tr>.navbox-image,.mw-parser-output tr+tr>.navbox-list{border-top:2px solid #fdfdfd}.mw-parser-output .navbox-title{background-color:#ccf}.mw-parser-output .navbox-abovebelow,.mw-parser-output .navbox-group,.mw-parser-output .navbox-subgroup .navbox-title{background-color:#ddf}.mw-parser-output .navbox-subgroup .navbox-group,.mw-parser-output .navbox-subgroup .navbox-abovebelow{background-color:#e6e6ff}.mw-parser-output .navbox-even{background-color:#f7f7f7}.mw-parser-output .navbox-odd{background-color:transparent}.mw-parser-output .navbox .hlist td dl,.mw-parser-output .navbox .hlist td ol,.mw-parser-output .navbox .hlist td ul,.mw-parser-output .navbox td.hlist dl,.mw-parser-output .navbox td.hlist ol,.mw-parser-output .navbox td.hlist ul{padding:0.125em 0}.mw-parser-output .navbox .navbar{display:block;font-size:100%}.mw-parser-output .navbox-title .navbar{float:left;text-align:left;margin-right:0.5em}body.skin--responsive .mw-parser-output .navbox-image img{max-width:none!important}@media print{body.ns-0 .mw-parser-output .navbox{display:none!important}}

/* end https://en.wikipedia.org/ */

</style></div><div role="navigation" class="navbox" aria-labelledby="Optimization:_Algorithms,_methods,_and_heuristics381" style="padding:3px"><table class="nowraplinks hlist mw-collapsible uncollapsed navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="3"><style data-mw-deduplicate="TemplateStyles:r1239400231">

/* start https://en.wikipedia.org/ */

.mw-parser-output .navbar{display:inline;font-size:88%;font-weight:normal}.mw-parser-output .navbar-collapse{float:left;text-align:left}.mw-parser-output .navbar-boxtext{word-spacing:0}.mw-parser-output .navbar ul{display:inline-block;white-space:nowrap;line-height:inherit}.mw-parser-output .navbar-brackets::before{margin-right:-0.125em;content:"[ "}.mw-parser-output .navbar-brackets::after{margin-left:-0.125em;content:" ]"}.mw-parser-output .navbar li{word-spacing:-0.125em}.mw-parser-output .navbar a>span,.mw-parser-output .navbar a>abbr{text-decoration:inherit}.mw-parser-output .navbar-mini abbr{font-variant:small-caps;border-bottom:none;text-decoration:none;cursor:inherit}.mw-parser-output .navbar-ct-full{font-size:114%;margin:0 7em}.mw-parser-output .navbar-ct-mini{font-size:114%;margin:0 4em}html.skin-theme-clientpref-night .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}@media(prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}}@media print{.mw-parser-output .navbar{display:none!important}}

/* end https://en.wikipedia.org/ */

</style><div id="Optimization:_Algorithms,_methods,_and_heuristics381" style="font-size:114%;margin:0 4em"><a href="Mathematical_optimization" title="Mathematical optimization">Optimization</a>: <a href="Optimization_algorithm" class="mw-redirect" title="Optimization algorithm">Algorithms</a>, <a href="Iterative_method" title="Iterative method">methods</a>, and <a href="Heuristic_algorithm" class="mw-redirect" title="Heuristic algorithm">heuristics</a></div></th></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks mw-collapsible mw-collapsed navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div id="Unconstrained_nonlinear381" style="font-size:114%;margin:0 4em"><a href="Nonlinear_programming" title="Nonlinear programming">Unconstrained nonlinear</a></div></th></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Function_(mathematics)" title="Function (mathematics)">Functions</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Golden-section_search" title="Golden-section search">Golden-section search</a></li>

<li><a href="Powell's_method" title="Powell's method">Powell's method</a></li>

<li><a href="Line_search" title="Line search">Line search</a></li>

<li><a href="Nelder%E2%80%93Mead_method" title="Nelder–Mead method">Nelder–Mead method</a></li>

<li><a href="Successive_parabolic_interpolation" title="Successive parabolic interpolation">Successive parabolic interpolation</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Gradient" title="Gradient">Gradients</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Local_convergence" title="Local convergence">Convergence</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Trust_region" title="Trust region">Trust region</a></li>

<li><a href="Wolfe_conditions" title="Wolfe conditions">Wolfe conditions</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Quasi-Newton_method" title="Quasi-Newton method">Quasi–Newton</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Berndt%E2%80%93Hall%E2%80%93Hall%E2%80%93Hausman_algorithm" title="Berndt–Hall–Hall–Hausman algorithm">Berndt–Hall–Hall–Hausman</a></li>

<li><a href="Broyden%E2%80%93Fletcher%E2%80%93Goldfarb%E2%80%93Shanno_algorithm" title="Broyden–Fletcher–Goldfarb–Shanno algorithm">Broyden–Fletcher–Goldfarb–Shanno</a> and <a href="Limited-memory_BFGS" title="Limited-memory BFGS">L-BFGS</a></li>

<li><a href="Davidon%E2%80%93Fletcher%E2%80%93Powell_formula" title="Davidon–Fletcher–Powell formula">Davidon–Fletcher–Powell</a></li>

<li><a href="Symmetric_rank-one" title="Symmetric rank-one">Symmetric rank-one (SR1)</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Iterative_method" title="Iterative method">Other methods</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Nonlinear_conjugate_gradient_method" title="Nonlinear conjugate gradient method">Conjugate gradient</a></li>

<li><a href="Gauss%E2%80%93Newton_algorithm" title="Gauss–Newton algorithm">Gauss–Newton</a></li>

<li><a href="Gradient_descent" title="Gradient descent">Gradient</a></li>

<li><a href="Mirror_descent" title="Mirror descent">Mirror</a></li>

<li><a href="Levenberg%E2%80%93Marquardt_algorithm" title="Levenberg–Marquardt algorithm">Levenberg–Marquardt</a></li>

<li><a href="Powell's_dog_leg_method" title="Powell's dog leg method">Powell's dog leg method</a></li>

<li><a href="Truncated_Newton_method" title="Truncated Newton method">Truncated Newton</a></li></ul>

</div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Hessian_matrix" title="Hessian matrix">Hessians</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Newton's_method_in_optimization" title="Newton's method in optimization">Newton's method</a></li></ul>

</div></td></tr></tbody></table><div></div></td></tr></tbody></table><div></div></td><td class="noviewer navbox-image" rowspan="5" style="width:1px;padding:0 0 0 2px"><div></div></td></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks mw-collapsible mw-collapsed navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div id="Constrained_nonlinear381" style="font-size:114%;margin:0 4em"><a href="Nonlinear_programming" title="Nonlinear programming">Constrained nonlinear</a></div></th></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%">General</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Barrier_function" title="Barrier function">Barrier methods</a></li>

<li><a href="Penalty_method" title="Penalty method">Penalty methods</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Differentiable</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Augmented_Lagrangian_method" title="Augmented Lagrangian method">Augmented Lagrangian methods</a></li>

<li><a href="Sequential_quadratic_programming" title="Sequential quadratic programming">Sequential quadratic programming</a></li>

<li><a href="Successive_linear_programming" title="Successive linear programming">Successive linear programming</a></li></ul>

</div></td></tr></tbody></table><div></div></td></tr></tbody></table><div></div></td></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks mw-collapsible mw-collapsed navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div id="Convex_optimization381" style="font-size:114%;margin:0 4em"><a href="Convex_optimization" title="Convex optimization">Convex optimization</a></div></th></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Convex_minimization" class="mw-redirect" title="Convex minimization">Convex<br> minimization</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Cutting-plane_method" title="Cutting-plane method">Cutting-plane method</a></li>

<li><a href="Frank%E2%80%93Wolfe_algorithm" title="Frank–Wolfe algorithm">Reduced gradient (Frank–Wolfe)</a></li>

<li><a href="Subgradient_method" title="Subgradient method">Subgradient method</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Linear_programming" title="Linear programming">Linear</a> and<br><a href="Quadratic_programming" title="Quadratic programming">quadratic</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Linear_programming#Interior_point" title="Linear programming">Interior point</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Affine_scaling" title="Affine scaling">Affine scaling</a></li>

<li><a href="Ellipsoid_method" title="Ellipsoid method">Ellipsoid algorithm of Khachiyan</a></li>

<li><a href="Karmarkar's_algorithm" title="Karmarkar's algorithm">Projective algorithm of Karmarkar</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Matroid" title="Matroid">Basis-</a><a href="Exchange_algorithm" class="mw-redirect" title="Exchange algorithm">exchange</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Simplex_algorithm" title="Simplex algorithm">Simplex algorithm of Dantzig</a></li>

<li><a href="Revised_simplex_method" title="Revised simplex method">Revised simplex algorithm</a></li>

<li><a href="Criss-cross_algorithm" title="Criss-cross algorithm">Criss-cross algorithm</a></li>

<li><a href="Lemke's_algorithm" title="Lemke's algorithm">Principal pivoting algorithm of Lemke</a></li>

<li><a href="Active-set_method" title="Active-set method">Active-set method</a></li></ul>

</div></td></tr></tbody></table><div></div></td></tr></tbody></table><div></div></td></tr></tbody></table><div></div></td></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks mw-collapsible mw-collapsed navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div id="Combinatorial381" style="font-size:114%;margin:0 4em"><a href="Combinatorial_optimization" title="Combinatorial optimization">Combinatorial</a></div></th></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%">Paradigms</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Approximation_algorithm" title="Approximation algorithm">Approximation algorithm</a></li>

<li><a href="Dynamic_programming" title="Dynamic programming">Dynamic programming</a></li>

<li><a href="Greedy_algorithm" title="Greedy algorithm">Greedy algorithm</a></li>

<li><a href="Integer_programming" title="Integer programming">Integer programming</a>

<ul><li><a href="Branch_and_bound" title="Branch and bound">Branch and bound</a>/<a href="Branch_and_cut" title="Branch and cut">cut</a></li></ul></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Graph_algorithm" class="mw-redirect" title="Graph algorithm">Graph<br> algorithms</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th id="Minimum_spanning_tree52" scope="row" class="navbox-group" style="width:1%"><a href="Minimum_spanning_tree" title="Minimum spanning tree">Minimum<br> spanning tree</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Bor%C5%AFvka's_algorithm" title="Borůvka's algorithm">Borůvka</a></li>

<li><a href="Kruskal's_algorithm" title="Kruskal's algorithm">Kruskal</a></li></ul>

</div></td></tr></tbody></table><div>

</div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th id="Shortest_path39" scope="row" class="navbox-group" style="width:1%"><a href="Shortest_path_problem" title="Shortest path problem">Shortest path</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Bellman%E2%80%93Ford_algorithm" title="Bellman–Ford algorithm">Bellman–Ford</a>

<li><a href="Dijkstra's_algorithm" title="Dijkstra's algorithm">Dijkstra</a></li>

<li><a href="Floyd%E2%80%93Warshall_algorithm" title="Floyd–Warshall algorithm">Floyd–Warshall</a></li></ul>

</div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Flow_network" title="Flow network">Network flows</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Dinic's_algorithm" title="Dinic's algorithm">Dinic</a></li>

<li><a href="Edmonds%E2%80%93Karp_algorithm" title="Edmonds–Karp algorithm">Edmonds–Karp</a></li>

<li><a href="Ford%E2%80%93Fulkerson_algorithm" title="Ford–Fulkerson algorithm">Ford–Fulkerson</a></li>

<li><a href="Push%E2%80%93relabel_maximum_flow_algorithm" title="Push–relabel maximum flow algorithm">Push–relabel maximum flow</a></li></ul>

<ul><li><a href="Evolutionary_algorithm" title="Evolutionary algorithm">Evolutionary algorithm</a></li>

<li><a href="Hill_climbing" title="Hill climbing">Hill climbing</a></li>

<li><a href="Local_search_(optimization)" title="Local search (optimization)">Local search</a></li>

<li><a href="Parallel_metaheuristic" title="Parallel metaheuristic">Parallel metaheuristics</a></li>

<li><a href="Simulated_annealing" title="Simulated annealing">Simulated annealing</a></li>

<li><a href="Spiral_optimization_algorithm" title="Spiral optimization algorithm">Spiral optimization algorithm</a></li>

<li><a href="Tabu_search" title="Tabu search">Tabu search</a></li></ul>

</div></td></tr></tbody></table><div></div></td></tr><tr><td class="navbox-abovebelow" colspan="3"><div>

<ul><li><a href="Comparison_of_optimization_software" title="Comparison of optimization software">Software</a></li></ul>

</div></td></tr></tbody></table></div>

<div class="navbox-styles"></div><div role="navigation" class="navbox" aria-labelledby="Swarming203" style="padding:3px"><table class="nowraplinks mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="3"><div id="Swarming203" style="font-size:114%;margin:0 4em"><a href="Swarm_behaviour" title="Swarm behaviour">Swarming</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Swarm_behaviour#Biological_swarming" title="Swarm behaviour">Biological swarming</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Agent-based_model_in_biology" title="Agent-based model in biology">Agent-based model in biology</a></li>

<li><a href="Collective_animal_behavior" title="Collective animal behavior">Collective animal behavior</a></li>

<li><a href="Droving" title="Droving">Droving</a></li>

<li><a href="Flock_(birds)" title="Flock (birds)">Flock</a>

<ul><li><a href="Flocking_(behavior)" class="mw-redirect" title="Flocking (behavior)">flocking</a></li>

<ul><li><a href="Herd_behavior" title="Herd behavior">herd behavior</a></li></ul></li>

<li><a href="Locust" title="Locust">Locust</a></li>

<li><a href="Mixed-species_foraging_flock" title="Mixed-species foraging flock">Mixed-species foraging flock</a></li>

<li><a href="Mobbing_(animal_behavior)" title="Mobbing (animal behavior)">Mobbing behavior</a>

<ul><li><a href="Feeding_frenzy" title="Feeding frenzy">feeding frenzy</a></li></ul></li>

<ul><li><a href="Pack_hunter" title="Pack hunter">pack hunter</a></li></ul></li>

<li><a href="Patterns_of_self-organization_in_ants" title="Patterns of self-organization in ants">Patterns of self-organization in ants</a>

<li><a href="Symmetry_breaking_of_escaping_ants" title="Symmetry breaking of escaping ants">symmetry breaking of escaping ants</a></li></ul></li>

<li><a href="Shoaling_and_schooling" title="Shoaling and schooling">Shoaling and schooling</a>

<li><a href="Swarm_behaviour" title="Swarm behaviour">Swarming behaviour</a></li>

<li><a href="Swarming_(honey_bee)" title="Swarming (honey bee)">Swarming (honey bee)</a></li>

<li><a href="Swarming_motility" title="Swarming motility">Swarming motility</a></li></ul>

</div></td><td class="noviewer navbox-image" rowspan="6" style="width:1px;padding:0 0 0 2px"><div><span typeof="mw:File"></span></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Animal_migration" title="Animal migration">Animal migration</a></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Animal_migration" title="Animal migration">Animal migration</a>

<ul><li><a href="Altitudinal_migration" title="Altitudinal migration">altitudinal</a></li>

<li><a href="Animal_migration_tracking" title="Animal migration tracking">tracking</a>

<ul><li><a href="History_of_wildlife_tracking_technology" title="History of wildlife tracking technology">history</a></li></ul></li>

<li><a href="Coded_wire_tag" title="Coded wire tag">coded wire tag</a></li></ul></li>

<li><a href="Bird_migration" title="Bird migration">Bird migration</a>

<ul><li>flyways</li>

<li><a href="Reverse_migration_(birds)" title="Reverse migration (birds)">reverse migration</a></li></ul></li>

<li><a href="Cell_migration" title="Cell migration">Cell migration</a></li>

<li><a href="Fish_migration" title="Fish migration">Fish migration</a>

<ul><li><a href="Diel_vertical_migration" title="Diel vertical migration">diel vertical</a></li>

<li><a href="Lessepsian_migration" title="Lessepsian migration">Lessepsian</a></li>

<li><a href="Salmon_run" title="Salmon run">salmon run</a></li>

<li><a href="Sardine_run" title="Sardine run">sardine run</a></li></ul></li>

<li><a href="Homing_(biology)" title="Homing (biology)">Homing</a>

<ul><li><a href="Natal_homing" title="Natal homing">natal</a></li>

<li><a href="Philopatry" title="Philopatry">philopatry</a></li></ul></li>

<li><a href="Insect_migration" title="Insect migration">Insect migration</a>

<ul><li><a href="Lepidoptera_migration" title="Lepidoptera migration">butterflies</a>

<ul><li><a href="Monarch_butterfly_migration" title="Monarch butterfly migration">monarch</a></li></ul></li></ul></li>

<li><a href="Sea_turtle_migration" title="Sea turtle migration">Sea turtle migration</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Swarm_behaviour#Models" title="Swarm behaviour">Swarm algorithms</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Agent-based_model" title="Agent-based model">Agent-based models</a></li>

<li><a href="Ant_colony_optimization_algorithm" class="mw-redirect" title="Ant colony optimization algorithm">Ant colony optimization</a></li>

<li><a href="Boids" title="Boids">Boids</a></li>

<li><a href="Crowd_simulation" title="Crowd simulation">Crowd simulation</a></li>

<li><a href="Particle_swarm_optimization" title="Particle swarm optimization">Particle swarm optimization</a></li>

<li><a href="Swarm_intelligence" title="Swarm intelligence">Swarm intelligence</a></li>

<li><a href="Swarm_(simulation)" title="Swarm (simulation)">Swarm (simulation)</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Collective_motion" title="Collective motion">Collective motion</a></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Active_matter" title="Active matter">Active matter</a></li>

<li><a href="Collective_motion" title="Collective motion">Collective motion</a></li>

<li><a href="Self-propelled_particles" title="Self-propelled particles">Self-propelled particles</a>

<ul><li><a href="Clustering_of_self-propelled_particles" title="Clustering of self-propelled particles">clustering</a></li></ul></li>

<li><a href="Vicsek_model" title="Vicsek model">Vicsek model</a></li>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Swarm_robotics" title="Swarm robotics">Swarm robotics</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Ant_robotics" title="Ant robotics">Ant robotics</a></li>

<li><a href="Microbotics" title="Microbotics">Microbotics</a></li>

<li><a href="Nanorobotics" title="Nanorobotics">Nanorobotics</a></li>

<li><a href="Swarm_robotics" title="Swarm robotics">Swarm robotics</a></li>

<li><a href="Symbrion" title="Symbrion">Symbrion</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Related topics</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Allee_effect" title="Allee effect">Allee effect</a></li>

<li><a href="Animal_navigation" title="Animal navigation">Animal navigation</a></li>

<li><a href="Collective_intelligence" title="Collective intelligence">Collective intelligence</a></li>

<li><a href="Decentralised_system" title="Decentralised system">Decentralised system</a></li>

<li><a href="Eusociality" title="Eusociality">Eusociality</a></li>

<li><a href="Group_size_measures" title="Group size measures">Group size measures</a></li>

<li><a href="Microbial_intelligence" title="Microbial intelligence">Microbial intelligence</a></li>

<li><a href="Mutualism_(biology)" title="Mutualism (biology)">Mutualism</a></li>

<li><a href="Predator_satiation" title="Predator satiation">Predator satiation</a></li>

<li><a href="Quorum_sensing" title="Quorum sensing">Quorum sensing</a></li>

<li><a href="Spatial_organization" title="Spatial organization">Spatial organization</a></li>

<li><a href="Stigmergy" title="Stigmergy">Stigmergy</a></li>

<li><a href="Swarming_(military)" title="Swarming (military)">Military swarming</a></li>

<li><a href="Task_allocation_and_partitioning_of_social_insects" class="mw-redirect" title="Task allocation and partitioning of social insects">Task allocation and partitioning of social insects</a></li></ul>

</div></td></tr></tbody></table></div></div><div><div class="zim-footer">

This article is issued from <a class="external text" title="Last edited on 2025-02-09" href="https://en.wikipedia.org/wiki/?title=Firefly_algorithm&oldid=1274751345">Wikipedia</a>. The text is available under <a class="external text" href="https://creativecommons.org/licenses/by-sa/4.0/deed.en">Creative Commons Attribution-Share Alike 4.0</a> unless otherwise noted. Additional terms may apply for the media files.

</div>

</div></div>

</div>

</main>

</div>

</body></html>