Time Intervals for Maintenance of Offshore Structures Based on Multiobjective Optimization

<table>Pareto front with 12 optimal solutions considering solution <svg height="11.6875" id="M141" style="vertical-align:-0.20473pt" version="1.1" viewbox="0 0 11.425 11.6875" width="11.425" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
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</svg> for the first time interval for maintenance and a set of solutions  selected (<svg height="11.8375" id="M142" style="vertical-align:-3.27605pt" version="1.1" viewbox="0 0 13.925 11.8375" width="13.925" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
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t81.5 29.5q49 0 82 -27q45 -39 45 -123v-185q0 -60 35 -60q18 0 36 11zM275 84v156q-12 -6 -49 -23t-41 -19q-31 -14 -46 -31t-15 -43q0 -35 22.5 -55.5t48.5 -20.5q19 0 42 10.5t38 25.5z" id="x61"></path></g>
<g transform="matrix(.012,-0,0,-.012,7.525,11.775)"><path d="M412 140l28 -9q0 -2 -35 -131h-373v23q112 112 161 170q59 70 92 127t33 115q0 63 -31 98t-86 35q-75 0 -137 -93l-22 20l57 81q55 59 135 59q69 0 118.5 -46.5t49.5 -122.5q0 -62 -29.5 -114t-102.5 -130l-141 -149h186q42 0 58.5 10.5t38.5 56.5z" id="x32"></path></g>
</svg>, <svg height="16.3125" id="M143" style="vertical-align:-3.27605pt" version="1.1" viewbox="0 0 15.1 16.3125" width="15.1" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,12.162)"><path d="M152 404l81 35q23 10 41 10q81 0 139 -61.5t58 -149.5q0 -107 -74.5 -178.5t-176.5 -71.5q-71 0 -147 36v555q0 48 -9.5 59.5t-56.5 15.5v23q79 10 145 35v-308zM152 374v-258q0 -20 6 -35q7 -19 30 -37t58 -18q63 0 99.5 50t36.5 137q0 82 -43.5 131t-108.5 49
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<g transform="matrix(.012,-0,0,-.012,8.7,16.25)"><path d="M412 140l28 -9q0 -2 -35 -131h-373v23q112 112 161 170q59 70 92 127t33 115q0 63 -31 98t-86 35q-75 0 -137 -93l-22 20l57 81q55 59 135 59q69 0 118.5 -46.5t49.5 -122.5q0 -62 -29.5 -114t-102.5 -130l-141 -149h186q42 0 58.5 10.5t38.5 56.5z" id="x32"></path></g>
</svg>, <svg height="11.8375" id="M144" style="vertical-align:-3.27605pt" version="1.1" viewbox="0 0 13.65 11.8375" width="13.65" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,7.7)"><path d="M390 111l17 -21q-34 -45 -80 -73.5t-89 -28.5q-91 0 -146 62t-55 147q0 118 101 195q74 57 149 57h1q59 0 90 -27q16 -14 16 -30q0 -15 -12 -29t-21 -14q-8 0 -19 11q-44 41 -101 41q-52 0 -87.5 -42.5t-35.5 -117.5q0 -49 15 -87t39 -58t49 -30t48 -10q33 0 60.5 12
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<g transform="matrix(.012,-0,0,-.012,7.25,11.775)"><path d="M412 140l28 -9q0 -2 -35 -131h-373v23q112 112 161 170q59 70 92 127t33 115q0 63 -31 98t-86 35q-75 0 -137 -93l-22 20l57 81q55 59 135 59q69 0 118.5 -46.5t49.5 -122.5q0 -62 -29.5 -114t-102.5 -130l-141 -149h186q42 0 58.5 10.5t38.5 56.5z" id="x32"></path></g>
</svg>, <svg height="16.3125" id="M145" style="vertical-align:-3.27605pt" version="1.1" viewbox="0 0 15.4375 16.3125" width="15.4375" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,12.162)"><path d="M517 51v-25q-101 -18 -155 -38v65l-61 -36q-50 -29 -78 -29q-68 0 -126.5 58t-58.5 155q0 103 77 175.5t180 72.5q36 0 67 -12v143q0 48 -11.5 58.5t-65.5 14.5v25q79 9 156 34v-597q0 -38 7.5 -48t36.5 -13zM362 85v275q-35 51 -103 51q-20 0 -40.5 -8.5t-42 -28
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<g transform="matrix(.012,-0,0,-.012,9.038,16.25)"><path d="M412 140l28 -9q0 -2 -35 -131h-373v23q112 112 161 170q59 70 92 127t33 115q0 63 -31 98t-86 35q-75 0 -137 -93l-22 20l57 81q55 59 135 59q69 0 118.5 -46.5t49.5 -122.5q0 -62 -29.5 -114t-102.5 -130l-141 -149h186q42 0 58.5 10.5t38.5 56.5z" id="x32"></path></g>
</svg>, <svg height="11.8375" id="M146" style="vertical-align:-3.27605pt" version="1.1" viewbox="0 0 13.6875 11.8375" width="13.6875" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,7.7)"><path d="M380 106l15 -22q-42 -52 -87 -74t-76 -22q-89 0 -142 62t-53 151q0 103 66 175q67 73 146 73h1q61 0 105.5 -46.5t44.5 -105.5q0 -16 -4.5 -22.5t-18.5 -9.5q-54 -10 -262 -17q1 -95 46 -143.5t104 -48.5q61 0 115 50zM225 412q-35 0 -64.5 -32.5t-40.5 -90.5q83 0 170 3
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<g transform="matrix(.012,-0,0,-.012,7.287,11.775)"><path d="M412 140l28 -9q0 -2 -35 -131h-373v23q112 112 161 170q59 70 92 127t33 115q0 63 -31 98t-86 35q-75 0 -137 -93l-22 20l57 81q55 59 135 59q69 0 118.5 -46.5t49.5 -122.5q0 -62 -29.5 -114t-102.5 -130l-141 -149h186q42 0 58.5 10.5t38.5 56.5z" id="x32"></path></g>
</svg>, <svg height="16.3125" id="M147" style="vertical-align:-3.27605pt" version="1.1" viewbox="0 0 11.4875 16.3125" width="11.4875" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,12.162)"><path d="M54 437h47v21q0 48 11 83q23 72 77 118q55 46 110 53q53 -3 79 -34q13 -16 5 -35q-5 -13 -19 -24t-27 3q-37 37 -81 37q-34 0 -53 -29q-24 -37 -23 -153v-40h118q5 -7 1.5 -21t-11.5 -19h-108v-287q0 -55 13 -67t73 -18v-25h-236v26q49 5 60 16.5t11 60.5v294h-70l-4 11z
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<g transform="matrix(.012,-0,0,-.012,5.1,16.25)"><path d="M412 140l28 -9q0 -2 -35 -131h-373v23q112 112 161 170q59 70 92 127t33 115q0 63 -31 98t-86 35q-75 0 -137 -93l-22 20l57 81q55 59 135 59q69 0 118.5 -46.5t49.5 -122.5q0 -62 -29.5 -114t-102.5 -130l-141 -149h186q42 0 58.5 10.5t38.5 56.5z" id="x32"></path></g>
</svg>, and <svg height="12.725" id="M148" style="vertical-align:-3.98578pt" version="1.1" viewbox="0 0 14.4125 12.725" width="14.4125" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,7.7)"><path d="M463 437l5 -8q-21 -38 -45 -51l-57 3q30 -35 30 -88q0 -76 -52.5 -118t-122.5 -42q-24 0 -51 5q-30 -21 -30 -42q0 -16 16 -27t47 -11q19 0 54 0.5t52 0.5q36 0 65.5 -8t53.5 -36t24 -74q0 -77 -75 -137.5t-174 -60.5q-79 0 -126 37.5t-48 84.5q0 32 24 56q21 21 83 70
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<g transform="matrix(.012,-0,0,-.012,8.012,12.663)"><path d="M412 140l28 -9q0 -2 -35 -131h-373v23q112 112 161 170q59 70 92 127t33 115q0 63 -31 98t-86 35q-75 0 -137 -93l-22 20l57 81q55 59 135 59q69 0 118.5 -46.5t49.5 -122.5q0 -62 -29.5 -114t-102.5 -130l-141 -149h186q42 0 58.5 10.5t38.5 56.5z" id="x32"></path></g>
</svg>) for the second interval for maintenance<i>. </i></table>

Mathematical Problems in Engineering

fig11

Figure 11

Figure 11: Time Intervals for Maintenance of Offshore Structures Based on Multiobjective Optimization 