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<h1>Optimization Component</h1>

<table>
	<th colspan=2>Visualize Optimization Trajectory using Excel</th>
	<tr>
		<td>Description:</td>
		<td>These models demonstrate the use of the Optimization component along with the excel component.
		Running these models will bring up an Excel worksheet that displays the trajectory of the optimizer
		in the design space. For example, one can notice that LSGRG moves along the constraint looking for an
		improved design in QuadraticHoleProblem.

		<p>
		Use the technique editor, either in the design gateway or the runtime gateway, to change the optimization
		technique.
		</td>
	</tr>
	<tr>
		<td>Models:</td>
		<td>
			<li><a href="MultivalleyProblem.zmf">MultivalleyProblem.zmf</a> - Minimizing an objective function
					that has multiple local minima.</li>
			<li><a href="DiscontinuousDomainProblem.zmf">DiscontinuousDomainProblem.zmf</a> - Minimizing a linear function
					in a domain that is not continuous.</li>
			<li><a href="QuadraticHoleProblem.zmf">QuadraticHoleProblem.zmf</a> - Minimizing a quadratic function
					in a domain that has a hole.</li>
			<li><a href="IsolatedMultipeakProblem.zmf">IsolatedMultipeakProblem.zmf</a> - Maximizing an objective
					in a domain that consists of isolated islands.</li>

		</td>
	</tr>
	<tr>
		<td>Illustrated components:</td>
		<td>Optimization, Excel</td>
	</tr>
	<tr>
		<td>Other illustrated features:</td>
		<td>Run grading - in the history table and all graphs, infeasible points are highlighted in red,
			and the best point is highlighted in green.
		</td>
	</tr>
	<tr>
		<td>Simcodes needed:</td>
		<td>None</td>
	</tr>
	<tr>
		<td>Support files needed:</td>
		<td>None</td>
	</tr>
</table>
<br>
<p>
<table>
	<th colspan=2>Optimization - Downhill Simplex Technique</th>
	<tr>
		<td>Description:</td>
		<td>This model demonstrates the use of the Optimization component with the Downhill Simplex optimization
			technique plugin to optimize a cantilever beam. The optimization problem is defined as
			follows:
			<ul>
			    <li>Design Variables (10):
			    <ul>
					<li>Height of the beam at 5 locations
					<li>Width of the beam at 5 locations
			    </ul>
			    <li>Constraints (11):
				<ul>
					<li>Aspect ratio of the beam at 5 locations
					<li>Stress of the beam at 5 locations
					<li>Deflection of the tip of the beam
				</ul>
			    <li>Objective:
				<ul>
					<li>Minimize Volume
				</ul>
			</ul>
		</td>
	</tr>
	<tr>
		<td>Model:</td>
		<td><a href="CantBeamDownhillSimplex.zmf">CantBeamDownhillSimplex.zmf</a></td>
	</tr>
	<tr>
		<td>Illustrated components:</td>
		<td>Optimization, Calculator</td>
	</tr>
	<tr>
		<td>Other illustrated features:</td>
		<td>Run grading - in the history table and all graphs, infeasible points are highlighted in red,
			and the best point is highlighted in green.
		</td>
	</tr>
	<tr>
		<td>Simcodes needed:</td>
		<td>None</td>
	</tr>
	<tr>
		<td>Support files needed:</td>
		<td>None</td>
	</tr>
</table>
<br>
<p>
<table>
	<th colspan=2>Optimization - Evol Technique</th>
	<tr>
		<td>Description:</td>
		<td>This model demonstrates the use of the Optimization component with the Evol optimization
			technique plugin to optimize a cantilever beam. The optimization problem is defined as
			follows:
			<ul>
			    <li>Design Variables (10):
			    <ul>
					<li>Height of the beam at 5 locations
					<li>Width of the beam at 5 locations
			    </ul>
			    <li>Constraints (11):
				<ul>
					<li>Aspect ratio of the beam at 5 locations
					<li>Stress of the beam at 5 locations
					<li>Deflection of the tip of the beam
				</ul>
			    <li>Objective:
				<ul>
					<li>Minimize Volume
				</ul>
			</ul>
		</td>
	</tr>
	<tr>
		<td>Model:</td>
		<td><a href="CantBeamEvol.zmf">CantBeamEvol.zmf</a></td>
	</tr>
	<tr>
		<td>Illustrated components:</td>
		<td>Optimization, Calculator</td>
	</tr>
	<tr>
		<td>Other illustrated features:</td>
		<td>Run grading - in the history table and all graphs, infeasible points are highlighted in red,
			and the best point is highlighted in green.
		</td>
	</tr>
	<tr>
		<td>Simcodes needed:</td>
		<td>None</td>
	</tr>
	<tr>
		<td>Support files needed:</td>
		<td>None</td>
	</tr>
</table>
<br>
<p>
<table>
	<th colspan=2>Optimization - LSGRG Technique</th>
	<tr>
		<td>Description:</td>
		<td>This model demonstrates the use of the Optimization component with the LSGRG optimization
			technique plugin to optimize a cantilever beam. The optimization problem is defined as
			follows:
			<ul>
			    <li>Design Variables (10):
			    <ul>
					<li>Height of the beam at 5 locations
					<li>Width of the beam at 5 locations
			    </ul>
			    <li>Constraints (11):
				<ul>
					<li>Aspect ratio of the beam at 5 locations
					<li>Stress of the beam at 5 locations
					<li>Deflection of the tip of the beam
				</ul>
			    <li>Objective:
				<ul>
					<li>Minimize Volume
				</ul>
			</ul>
		</td>
	</tr>
	<tr>
		<td>Model:</td>
		<td><a href="CantBeamLSGRG.zmf">CantBeamLSGRG.zmf</a></td>
	</tr>
	<tr>
		<td>Illustrated components:</td>
		<td>Optimization, Calculator</td>
	</tr>
	<tr>
		<td>Other illustrated features:</td>
		<td>Run grading - in the history table and all graphs, infeasible points are highlighted in red,
			and the best point is highlighted in green.
		</td>
	</tr>
	<tr>
		<td>Simcodes needed:</td>
		<td>None</td>
	</tr>
	<tr>
		<td>Support files needed:</td>
		<td>None</td>
	</tr>
</table>
<br>
<p>
<table>
	<th colspan=2>Optimization - MISQP Technique</th>
	<tr>
		<td>Description:</td>
		<td>This model demonstrates the use of the Optimization component with the MISQP optimization
			technique plugin to optimize a Bolt-Nut-Plate joint. This problem has one integer and two
			real design	variables defined as follows:
			<ul>
			    <li>Design Variables (3):
			    <ul>
					<li>Diameter of the bolt, integer
					<li>Thickness of the plates, real, and
					<li>Tightening torque
			    </ul>
			    <li>Constraints (6):
				<ul>
					<li>Stresses on the bolt (tensile, shear, fatigue and thread)
					<li>The plates should not seperate.
					<li>Force on the bolt.
				</ul>
			    <li>Objective:
				<ul>
					<li>Maximize the ratio of plate thickness to bolt diameter
				</ul>
			</ul>
		</td>
	</tr>
	<tr>
		<td>Model:</td>
		<td><a href="NutBoltMISQP.zmf">NutBoltMISQP.zmf</a></td>
	</tr>
	<tr>
		<td>Illustrated components:</td>
		<td>Optimization, Calculator, Script</td>
	</tr>
	<tr>
		<td>Other illustrated features:</td>
		<td>Run grading - in the history table and all graphs, infeasible points are highlighted in red,
			and the best point is highlighted in green.
		</td>
	</tr>
	<tr>
		<td>Simcodes needed:</td>
		<td>None</td>
	</tr>
	<tr>
		<td>Support files needed:</td>
		<td>None</td>
	</tr>
</table>
<br>
<p>
<table>
	<th colspan=2>Optimization - MMFD Technique</th>
	<tr>
		<td>Description:</td>
		<td>This model demonstrates the use of the Optimization component with the MMFD optimization
			technique plugin to optimize a cantilever beam. The optimization problem is defined as
			follows:
			<ul>
			    <li>Design Variables (10):
			    <ul>
					<li>Height of the beam at 5 locations
					<li>Width of the beam at 5 locations
			    </ul>
			    <li>Constraints (11):
				<ul>
					<li>Aspect ratio of the beam at 5 locations
					<li>Stress of the beam at 5 locations
					<li>Deflection of the tip of the beam
				</ul>
			    <li>Objective:
				<ul>
					<li>Minimize Volume
				</ul>
			</ul>
		</td>
	</tr>
	<tr>
		<td>Model:</td>
		<td><a href="CantBeamMMFD.zmf">CantBeamMMFD.zmf</a></td>
	</tr>
	<tr>
		<td>Illustrated components:</td>
		<td>Optimization, Calculator</td>
	</tr>
	<tr>
		<td>Other illustrated features:</td>
		<td>Run grading - in the history table and all graphs, infeasible points are highlighted in red,
			and the best point is highlighted in green.
		</td>
	</tr>
	<tr>
		<td>Simcodes needed:</td>
		<td>None</td>
	</tr>
	<tr>
		<td>Support files needed:</td>
		<td>None</td>
	</tr>
</table>
<br>
<p>
<table>
	<th colspan=2>Optimization - NCGA Technique</th>
	<tr>
		<td>Description:</td>
		<td>This model demonstrates the use of the Optimization component with the NCGA multi-objective
			genetic algorithm optimization technique plugin to optimize a cantilever beam. The optimization
			problem is defined as follows:
			<ul>
			    <li>Design Variables (10):
			    <ul>
					<li>Height of the beam at 5 locations
					<li>Width of the beam at 5 locations
			    </ul>
			    <li>Constraints (11):
				<ul>
					<li>Aspect ratio of the beam at 5 locations
					<li>Stress of the beam at 5 locations
					<li>Deflection of the tip of the beam
				</ul>
			    <li>Objectives (2):
				<ul>
					<li>Minimize Volume
					<li>Minimize Stress1 (stress in the first section of the beam)
				</ul>
			</ul>
			To review the trade-off between the two objectives:
			<ol>
				<li>A scatter plot template is created in this example displaying the trade-off between the two
					objectives.
				<li>After execution, select the Data Analysis tab in the Runtime Gateway.
				<li>Click the Options button near the bottom of the gateway and check Show Pareto Points Only.
				<li>The scatter plot will then show the Pareto front Stress1 versus Volume.
			</ol>
		</td>
	</tr>
	<tr>
		<td>Model:</td>
		<td><a href="CantBeamNCGA.zmf">CantBeamNCGA.zmf</a></td>
	</tr>
	<tr>
		<td>Illustrated components:</td>
		<td>Optimization, Calculator</td>
	</tr>
	<tr>
		<td>Other illustrated features:</td>
		<td>
			<ul>
				<li>Run grading - in the history table and all graphs, infeasible points are highlighted in red,
					Pareto points are highlighted in blue, and the best point is highlighted in green.
				<li>Data Analysis tools:  EDM (Engineering Data Mining) including display of Pareto optimal points,
					2D Scatter plot viewer for evaluating trade-offs between multiple objectives
			</ul>
		</td>
	</tr>
	<tr>
		<td>Simcodes needed:</td>
		<td>None</td>
	</tr>
	<tr>
		<td>Support files needed:</td>
		<td>None</td>
	</tr>
</table>
<br>
<p>
<table>
	<th colspan=2>Optimization - NLPQL Technique</th>
	<tr>
		<td>Description:</td>
		<td>This model demonstrates the use of the Optimization component with the NLPQL optimization
			technique plugin to optimize a cantilever beam. The optimization problem is defined as
			follows:
			<ul>
			    <li>Design Variables (10):
			    <ul>
					<li>Height of the beam at 5 locations
					<li>Width of the beam at 5 locations
			    </ul>
			    <li>Constraints (11):
				<ul>
					<li>Aspect ratio of the beam at 5 locations
					<li>Stress of the beam at 5 locations
					<li>Deflection of the tip of the beam
				</ul>
			    <li>Objective:
				<ul>
					<li>Minimize Volume
				</ul>
			</ul>
		</td>
	</tr>
	<tr>
		<td>Model:</td>
		<td><a href="CantBeamNLPQL.zmf">CantBeamNLPQL.zmf</a></td>
	</tr>
	<tr>
		<td>Illustrated components:</td>
		<td>Optimization, Calculator</td>
	</tr>
	<tr>
		<td>Other illustrated features:</td>
		<td>Run grading - in the history table and all graphs, infeasible points are highlighted in red,
			and the best point is highlighted in green.
		</td>
	</tr>
	<tr>
		<td>Simcodes needed:</td>
		<td>None</td>
	</tr>
	<tr>
		<td>Support files needed:</td>
		<td>None</td>
	</tr>
</table>
<br>
<p>
<table>
	<th colspan=2>Optimization - NSGA-II Technique</th>
	<tr>
		<td>Description:</td>
		<td>This model demonstrates the use of the Optimization component with the NSGA-II multi-objective
			genetic algorithm optimization technique plugin to optimize a cantilever beam. The optimization
			problem is defined as follows:
			<ul>
			    <li>Design Variables (10):
			    <ul>
					<li>Height of the beam at 5 locations
					<li>Width of the beam at 5 locations
			    </ul>
			    <li>Constraints (11):
				<ul>
					<li>Aspect ratio of the beam at 5 locations
					<li>Stress of the beam at 5 locations
					<li>Deflection of the tip of the beam
				</ul>
			    <li>Objectives (2):
				<ul>
					<li>Minimize Volume
					<li>Minimize Stress1 (stress in the first section of the beam)
				</ul>
			</ul>
			To review the trade-off between the two objectives:
			<ol>
				<li>A scatter plot template is created in this example displaying the trade-off between the two
					objectives.
				<li>After execution, select the Data Analysis tab in the Runtime Gateway.
				<li>Click the Options button at the bottom of the gateway, and check the Show Pareto Points Only option.
				<li>The scatter plot on the right will then show the Pareto front Stress1 versus Volume.
			</ol>
		</td>
	</tr>
	<tr>
		<td>Model:</td>
		<td><a href="CantBeamNSGA2.zmf">CantBeamNSGA2.zmf</a></td>
	</tr>
	<tr>
		<td>Illustrated components:</td>
		<td>Optimization, Calculator</td>
	</tr>
	<tr>
		<td>Other illustrated features:</td>
		<td>
			<ul>
				<li>Run grading - in the history table and all graphs, infeasible points are highlighted in red,
					Pareto points are highlighted in blue, and the best point is highlighted in green.
				<li>Data Analysis tools:  EDM (Engineering Data Mining) including display of Pareto optimal points,
					2D Scatter plot viewer for evaluating trade-offs between multiple objectives
			</ul>
		</td>
	</tr>
	<tr>
		<td>Simcodes needed:</td>
		<td>None</td>
	</tr>
	<tr>
		<td>Support files needed:</td>
		<td>None</td>
	</tr>
</table>
<br>
<p>
<table>
	<th colspan=2>Optimization - Multi-Objective Particle Swarm Optimization Technique</th>
	<tr>
		<td>Description:</td>
		<td>This model demonstrates the use of the Optimization component with the Multi-Objective Particle Swarm optimization
			technique plugin to optimize a cantilever beam. The optimization problem is defined as
			follows:
			<ul>
			    <li>Design Variables (10):
			    <ul>
					<li>Height of the beam at 5 locations
					<li>Width of the beam at 5 locations
			    </ul>
			    <li>Constraints (11):
				<ul>
					<li>Aspect ratio of the beam at 5 locations
					<li>Stress of the beam at 5 locations
					<li>Deflection of the tip of the beam
				</ul>
			    <li>Objective:
				<ul>
					<li>Minimize Volume
					<li>Minimize Stress1 (stress in the first section of the beam)
				</ul>
			</ul>
		</td>
	</tr>
	<tr>
		<td>Model:</td>
		<td><a href="CantBeamParticleSwarm.zmf">CantBeamParticleSwarm.zmf</a></td>
	</tr>
	<tr>
		<td>Illustrated components:</td>
		<td>Optimization, Calculator</td>
	</tr>
	<tr>
		<td>Other illustrated features:</td>
		<td>Run grading - in the history table and all graphs, infeasible points are highlighted in red,
			and the best point is highlighted in green.
		</td>
	</tr>
	<tr>
		<td>Simcodes needed:</td>
		<td>None</td>
	</tr>
	<tr>
		<td>Support files needed:</td>
		<td>None</td>
	</tr>
</table>
<br>
<p>
<table>
	<th colspan=2>Optimization - Pointer Technique</th>
	<tr>
		<td>Description:</td>
		<td>This model demonstrates the use of the Optimization component with the Pointer optimization
			technique plugin to optimize a cantilever beam. The optimization problem is defined as
			follows:
			<ul>
			    <li>Design Variables (10):
			    <ul>
					<li>Height of the beam at 5 locations
					<li>Width of the beam at 5 locations
			    </ul>
			    <li>Constraints (11):
				<ul>
					<li>Aspect ratio of the beam at 5 locations
					<li>Stress of the beam at 5 locations
					<li>Deflection of the tip of the beam
				</ul>
			    <li>Objective:
				<ul>
					<li>Minimize Volume
				</ul>
			</ul>
		</td>
	</tr>
	<tr>
		<td>Model:</td>
		<td><a href="CantBeamPointer.zmf">CantBeamPointer.zmf</a></td>
	</tr>
	<tr>
		<td>Illustrated components:</td>
		<td>Optimization, Calculator</td>
	</tr>
	<tr>
		<td>Other illustrated features:</td>
		<td>Run grading - in the history table and all graphs, infeasible points are highlighted in red,
			and the best point is highlighted in green.
		</td>
	</tr>
	<tr>
		<td>Simcodes needed:</td>
		<td>None</td>
	</tr>
	<tr>
		<td>Support files needed:</td>
		<td>None</td>
	</tr>
</table>
<br>
<p>
<table>
	<th colspan=2>Optimization - Stress Ratio Technique</th>
	<tr>
		<td>Description:</td>
		<td>These models demonstrate the use of the Optimization component along with the Stress Ratio optimization
		technique plugin to optimized an idealized structure.  The algorithm assumes an inverse relationship between
		design variable and associated constraints and modifies the design variable based on the value of the critical
		associated constraint.  Therefore, a naming convention is used to associate constraints and design variables.  For
		example, constraints Stress1AtZone1, Stress2AtZone1, and Stress3AtZone1 are associated
		with design variable ThicknessAtZone1.  The optimization problem is defined as follows:
			<ul>
			    <li>Design Variables (5):
			    <ul>
					<li>Structural thickness in 5 zones
			    </ul>
			    <li>Constraints (15):
				<ul>
					<li>Stress at three locations within each of the 5 zones
				</ul>
			    <li>Objective:
				<ul>
					<li>Minimize Volume
				</ul>
			</ul>
		</td>
	</tr>
	<tr>
		<td>Models:</td>
		<td>
			<li><a href="StressRatioExample.zmf">StressRatioExample.zmf</a> - Stress Ratio optimization where design variables
					and constraints are Isight scalar parameters.</li>
			<li><a href="StressRatioArraysExample.zmf">StressRatioArraysExample.zmf</a> - Stress Ratio optimization where design
					variables and constraints are elements of Isight array parameters.</li>
		</td>
	</tr>
	<tr>
		<td>Illustrated components:</td>
		<td>Optimization, Calculator</td>
	</tr>
	<tr>
		<td>Other illustrated features:</td>
		<td>Run grading - in the history table and all graphs, infeasible points are highlighted in red,
			and the best point is highlighted in green.
		</td>
	</tr>
	<tr>
		<td>Simcodes needed:</td>
		<td>None</td>
	</tr>
	<tr>
		<td>Support files needed:</td>
		<td>None</td>
	</tr>
</table>

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