Multiobjective Design Optimization of Grillage Systems according to LRFD-AISC

<table><tr><td><table class="algorithm" id="alg2"><tr><td colspan="2"><i>initiliaze solutionSet(population_size), solution (population_size)</i></td></tr><tr><td colspan="2"><i>initiliaze archive </i><i>(archive_size)</i></td></tr><tr><td colspan="2"><i>evaluate solution, evolution </i><svg height="9.3125" id="M21" style="vertical-align:-0.51414pt" version="1.1" viewbox="0 0 26.75 9.3125" width="26.75" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,9.3125)">
<g transform="translate(72,-64.55)">
<text transform="matrix(1,0,0,-1,-67.78,65.11)">
<tspan style="font-size: 12.50px; " x="0" y="0">+</tspan>
<tspan style="font-size: 12.50px; " x="8.5645552" y="0">+</tspan>
</text>
</g>
</g>
</svg></td></tr><tr><td colspan="2"><i>solutionSet.add(solution)</i></td></tr><tr><td colspan="2"><i>while evolution&lt;max_evolution</i>
										{
										</td></tr><tr><td colspan="2">    <i>spea=Spea2Fitness(solutionsSet U archive) </i></td></tr><tr><td colspan="2">    <i>spea.FitnessAssignmanet </i></td></tr><tr><td colspan="2">    <i>archive=spea.enviromantalSelection(archive_size) </i></td></tr><tr><td colspan="2">        <i>if evolution </i>&lt;<i>max_evolution </i>{</td></tr><tr><td colspan="2">        <i>offspring=mutation(crossover(selection(archive))) </i></td></tr><tr><td colspan="2">        <i>evaluate offspring, evolution  </i><svg height="13.575" id="M22" style="vertical-align:-2.26974pt" version="1.1" viewbox="0 0 29.0375 13.575" width="29.0375" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,13.575)">
<g transform="translate(72,-61.14)">
<text transform="matrix(1,0,0,-1,-71.95,63.45)">
<tspan style="font-size: 12.50px; " x="0" y="0">+</tspan>
<tspan style="font-size: 12.50px; " x="8.5645552" y="0">+</tspan>
<tspan style="font-size: 12.50px; " x="17.12911" y="0">}</tspan>
</text>
</g>
</g>
</svg></td></tr><tr><td colspan="2">    <i>solutionSet.add(offspring)</i>}</td></tr><tr><td colspan="2"><i>front </i><svg height="6.1624999" id="M23" style="vertical-align:-0.0pt" version="1.1" viewbox="0 0 10.825 6.1624999" width="10.825" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,6.1625)">
<g transform="translate(72,-67.07)">
<text transform="matrix(1,0,0,-1,-71.95,67.12)">
<tspan style="font-size: 12.50px; " x="0" y="0">=</tspan>
</text>
</g>
</g>
</svg><i>Ranking(archive).getsubfront</i></td></tr></table></td></tr></table>

Advances in Civil Engineering

alg2

Algorithm 2

Algorithm 2: Multiobjective Design Optimization of Grillage Systems according to LRFD-AISC 