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<a name = "hj-top"> </a><table class = "table1" id = "table11"><tr><td><table class = "DocHeader"><tr><td class = "DocHeader1" colspan = "2"><h1>Introduction to Discrete Sizing</h1></td></tr><tr><td class = "DocHeader4" colspan = "2"/></tr><tr><td class = "DocHeader3" colspan = "2"><table class = "DocThemeIntro" id = "table12"><tr><td class = "Intro1Only"><p class = "header"><p class = "abstract">
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This section introduces the concept of discrete sizing, along with the possible approaches for it. </span>

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<p>This page discusses: </p><ul><li><a href = "#tso-c-usr-sizing-discrete-introduction__tso-c-usr-sizing-Discrete-need" id = "toc_rg" title = "">Need for Discrete Sizing Methods </a></li><li><a href = "#tso-c-usr-sizing-discrete-introduction__tso-c-usr-sizing-Discrete-approach" id = "toc_rg" title = "">Possible Approaches</a></li></ul>
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<div class = "section" id = "tso-c-usr-sizing-discrete-introduction__tso-c-usr-sizing-Discrete-need"><h2 class = "title sectiontitle">Need for Discrete Sizing Methods </h2>


<p>Standardization is a very important part of most manufacturing and fabrication processes. In most
                cases, fabricators use certain fixed sizes of sheets and thus the equipment and
                processes are calibrated to work efficiently for these set of sizes. Using a
                gradient-based optimization method like CSA (Convex Separable Approximations) the
                output from the optimizer is usually continuous and sometimes impossible to produce
                without precision equipment. Also a lot of time must be spent on designing new
                fixtures and calibrating the processes for the optimized sizes. A solution to the
                above problems is the discrete sizing optimization. </p>
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<div class = "section" id = "tso-c-usr-sizing-discrete-introduction__tso-c-usr-sizing-Discrete-approach"><p><map name = "FPMap1"><area href = "#hj-top" title = "Back to Top" shape = "rect" coords = "416, 0, 435, 10"/></map><span class = "itemsprite"/></p><h2 class = "title sectiontitle">Possible Approaches</h2>

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<th class = "entry" id = "tso-c-usr-sizing-discrete-introduction__tso-c-usr-sizing-Discrete-approach__entry__1">Discrete Optimization</th>
<th class = "entry" id = "tso-c-usr-sizing-discrete-introduction__tso-c-usr-sizing-Discrete-approach__entry__2">Heuristic Methods</th>
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<td class = "entry" headers = "tso-c-usr-sizing-discrete-introduction__tso-c-usr-sizing-Discrete-approach__entry__1">These are a family of mathematically consistent methods that work toward
                                    finding discrete global solutions. However, they are not
                                    computationally efficient and impossible to use for industrial
                                    scale models.</td>
<td class = "entry" headers = "tso-c-usr-sizing-discrete-introduction__tso-c-usr-sizing-Discrete-approach__entry__2">A heuristic is any approach to problem solving that uses techniques that
                                    are meaningful from an engineering point of view but are not
                                    guaranteed to be mathematically correct. In context of sizing
                                    optimization with discrete design variables heuristics are used
                                    to modify a gradient-based optimization algorithm that is based
                                    on continuous design variables to enforce their values to be
                                    discrete by the end of the optimization process. </td>
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<p> A heuristic scheme is implemented to ensure computational efficiency and compatibility.</p>

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