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<!doctype html>
<html>
<head>
<meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1.0, maximum-scale=1.0, user-scalable=no">
<title>3.1 Multi-Objective Optimisation</title>
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<div class="reveal">
<div class="slides">
<section>
<h1>Evolutionary Computation</h1>
<h3>Multi-objective Optimization</h3>
<br />
<img src="../imgs/logo.png" width="30%" height="auto">
</section>
<section>
<h2>Multi-objective Optimization</h2>
<br/>
The study of optimizing <b>more than one</b> objective function <b>simultaneously</b>.
<br/>
<img src="https://media1.tenor.com/images/aa68352126d8f6152f05f82656fdd70f/tenor.gif?itemid=5327473" width="30%">
<br/>
<br/>
<ul>
<li>Multi-objective evolutionary algorithms</li>
<li>Pareto dominance</li>
<li>NSGA-II</li>
<li>Many-objective optimization</li>
<ul>
<li>If F(x) = f_1(x), f_2(x), ...</li>
</ul>
</ul>
</section>
<section>
<h2>MOEAs</h2>
<br/>
Multi-objective evolutionary algorithms
<br/>
<br/>
<ul>
<li><b>NSGA</b>: Srinivas, Nidamarthi, and Kalyanmoy Deb. "Muiltiobjective optimization using nondominated sorting in genetic algorithms." Evolutionary computation 2.3 (1994): 221-248.</li>
<li><b>SPEA2</b>: Zitzler, Eckart, Marco Laumanns, and Lothar Thiele. "SPEA2: Improving the strength Pareto evolutionary algorithm." TIK-report 103 (2001).</li>
<li><b>NSGA-II</b>: Deb, Kalyanmoy, et al. "A fast and elitist multiobjective genetic algorithm: NSGA-II." IEEE transactions on evolutionary computation 6.2 (2002): 182-197.</li>
<li>Deb, Kalyanmoy (2001) Multi-objective optimization using evolutionary algorithms. John-Wiley, Chichester</li>
<li><b>MOEA/D</b>: Zhang, Qingfu, and Hui Li. "MOEA/D: A multiobjective evolutionary algorithm based on decomposition." IEEE Transactions on evolutionary computation 11.6 (2007): 712-731.</li>
<li><b>SMS-EMOA</b>: Beume, N., Naujoks, B., & Emmerich, M. (2007). SMS-EMOA: Multiobjective selection based on dominated hypervolume. European Journal of Operational Research, 181(3), 1653-1669.</li>
<li>Emmerich, Michael TM, and André H. Deutz. "A tutorial on multiobjective optimization: fundamentals and evolutionary methods." Natural computing 17.3 (2018): 585-609. [<a href="https://link.springer.com/content/pdf/10.1007/s11047-018-9685-y.pdf">pdf</a>]</li>
</ul>
</section>
<section>
<h2>Travelling Salesman Problem</h2>
<br/>
<img src="../imgs/tarif_autoroute.jpg" width="50%" height="auto">
</section>
<section>
<h2>Pareto dominance</h2>
<br/>
<img src="../imgs/Maxima_of_a_point_set.svg.png" width="30%" height="auto">
<ul>A solution is said to Pareto dominate another if it is more optimal in all dimensions.</ul>
<ul>Solutions which are not dominated by any other are called "non-dominated".</ul>
</section>
<section>
<h2>Why dominance?</h2>
<br/>
<img src="../imgs/pareto_dominance.png" width="50%" height="auto"><br/>
<ul>In single-objective problems it's easy to find the highest performing individual - highest fitness.</ul>
<ul>In multi-objective problems the the highest performing individual in an objective could be horrible in another objective!</ul>
<ul><li>We have f_1(S1) < f_1(S3) and f_2(S1) > f_2(S3) -> S1 and S3 are equally good.</li></ul>
</section>
<section>
<h2>Pareto front</h2>
<br/>
<img src="../imgs/pareto.png" width="50%" height="auto" display="block"margin-left="auto" margin-right="auto">
<br/>
<ul>The Pareto Front is the set of Pareto Optimal solutions.</ul>
<ul>Red points are non-dominated by each other and dominate the other points.</ul>
</section>
<section>
<h2>Pareto front</h2>
<br/>
<img src="../imgs/pareto.webp" width="50%" height="auto">
</section>
<section>
<h2>NSGA-II Overview</h2>
<br/>
<img src="../imgs/nsga2_flowchat.png" width="50%" height="auto">
<br/>
<div class="textbox"><small>
Deb, Kalyanmoy, et al. "A fast and elitist multiobjective genetic algorithm: NSGA-II." IEEE transactions on evolutionary computation 6.2 (2002): 182-197.
<a href="http://repository.ias.ac.in/83498/1/2-a.pdf">[pdf]</a>
</small>
</div>
</section>
<section>
<h2>Non-dominated sorting</h2>
<br/>
<img src="../imgs/Diagram-of-nondominated-sorting.png" width="40%" height="auto">
<br/>
<div class="textbox"><small>
Wang, H. S., C. H. Tu, and K. H. Chen. "Supplier selection and production planning by using guided genetic algorithm and dynamic nondominated sorting genetic algorithm II approaches." Mathematical Problems in Engineering 2015 (2015).
</small>
</div>
</section>
<!-- <section>
<h2>Fast non-dominated sort</h2>
<br/>
<img src="../imgs/fast_non_dominated.png" width="50%" height="auto">
<br/>
<div class="textbox"><small>
Deb, Kalyanmoy, et al. "A fast and elitist multiobjective genetic algorithm: NSGA-II." IEEE transactions on evolutionary computation 6.2 (2002): 182-197.
<a href="http://repository.ias.ac.in/83498/1/2-a.pdf">[pdf]</a>
</small>
</div>
</section> -->
<section>
<h2>Crowding Distance Assignment</h2>
<!-- <br/>
<img src="../imgs/crowding_distance.png" width="50%" height="auto">
<br/> -->
<br/>
<img src="../imgs/crowding_distance_calculation.png" width="35%" height="auto">
<br/>
<div class="textbox"><small>
Deb, Kalyanmoy, et al. "A fast and elitist multiobjective genetic algorithm: NSGA-II." IEEE transactions on evolutionary computation 6.2 (2002): 182-197.
<a href="http://repository.ias.ac.in/83498/1/2-a.pdf">[pdf]</a>
</small>
</div>
</section>
<section>
<h2>NSGA-II Overview</h2>
<br/>
<img src="../imgs/nsgaii.png" width="40%" height="auto">
<br/>
<img src="../imgs/crowding_distance_gr.png" width="55%" height="auto">
<br/>
<div class="textbox"><small>
Deb, Kalyanmoy, et al. "A fast and elitist multiobjective genetic algorithm: NSGA-II." IEEE transactions on evolutionary computation 6.2 (2002): 182-197.
<a href="http://repository.ias.ac.in/83498/1/2-a.pdf">[pdf]</a>
</small>
</div>
</section>
<section>
<h2>Problems with Pareto</h2>
<br/>
<img src="../imgs/problem_with_pareto.png" width="60%" height="auto">
<br/>
<br/>
<div class="textbox"><small>
Ishibuchi, Hisao, and Hiroyuki Sato. "Evolutionary many-objective optimization."
<a href="https://dl.acm.org/doi/proceedings/10.1145/3205651">Proceedings of the Genetic and Evolutionary Computation Conference Companion.</a> 2019.
</small>
</div>
</section>
<section>
<h2>Many-objective optimization</h2>
<br/>
<img src="../imgs/pareto_num_solutions.png" width="60%" height="auto">
<br/>
<br/>
<div class="textbox"><small>
Ishibuchi, Hisao, and Hiroyuki Sato. "Evolutionary many-objective optimization."
<a href="https://dl.acm.org/doi/proceedings/10.1145/3205651">Proceedings of the Genetic and Evolutionary Computation Conference Companion.</a> 2019.
</small>
</div>
</section>
<section>
<h2>Exercise 1</h2>
<br/>
<div class="textbox">
Explore some applications of MOEAs.
<br/>
Choose an article and discuss in your group what the problem is and what the different objectives are.
<br/>
<ul>
<li><a href="http://www.human-competitive.org/sites/default/files/harper-paper.pdf">Explaining quantum correlations through evolution of causal models</a></li>
<li><a href="http://www.human-competitive.org/sites/default/files/sarro-petrozziello-harman-paper.pdf">Multi-objective Software Effort Estimation</a></li>
<li><a href="https://www.cse.unr.edu/~mingli/papers/tsg0313.pdf">Multi-Objective Optimal Energy Consumption Scheduling in Smart Grids</a></li>
<li><a href="http://www.dmi.unict.it/mpavone/nc-cs/materiale/lupita-cec07.pdf">Applications of Multi-Objective Evolutionary Algorithms in Economics and Finance: A Survey</a></li>
<li><a href="http://en.etsmtl.ca/ETS/media/ImagesETS/Labo/LIVIA/Publications/2004/NNassif_NAFIPS_2004.pdf">Evolutionary Algorithms for Multi-Objective Optimization in HVAC System Control Strategy</a></li>
</ul>
</div>
</section>
</div>
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Evolutionary Computation by Dennis G. Wilson, Yuri Lavinas, Paul Templier
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<a href="https://github.com/d9w/evolution/">https://github.com/d9w/evolution/</a>
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