private static void makeAndSaveProblemDefinition()
{
var pd = new ProblemDefinition();
/* Add a design space descriptor so that optimizatoin
* methods for discrete variables can be used. Here we
* make a very generous discretization, which amounts
* to 2 million steps in each of the 2 design variables. */
var dsd = new DesignSpaceDescription(2);
for (var i = 0; i < 2; i++)
{
dsd[i] = new VariableDescriptor(-5000, 5000, 100.0);
}
pd.Add(dsd);
/* Add three convergence criteria */
pd.Add(new DeltaXConvergence(0.0001));
pd.Add(new MaxAgeConvergence(100, 0.000000001));
pd.Add(new MaxFnEvalsConvergence(50000));
pd.Add(new MaxSpanInPopulationConvergence(1));
/* setting the number of convergence criteria needed is not necessary
* since we will be using the default value of 1. Interesting to un-
* comment the next line and see how it affects the process. */
//pd.NumConvergeCriteriaNeeded = 2;
/* Add the objective function. */
var objfn = new polynomialObjFn();
objfn.Add("x1^2");
objfn.Add("x2^2");
objfn.Add("-2*x1");
objfn.Add("-10*x2");
objfn.Add("26");
/* this is a simple parabola center at {1, 5} */
pd.Add(objfn);
var g1 = new polynomialInequality();
g1.Add("-x1");
g1.Add("x2"); /* this inequality translates to x2 - x1 < 0
* of simply x1 > x2. */
pd.Add(g1);
pd.Add(new double[] { 1500.0, 700.0 });
var stream = new FileStream(filename, FileMode.Create);
pd.SaveProbToXml(stream);
}
// This is the set of valid AGMA gear pitches (in unit of inch^-1).
private static void Main()
{
//var opty = new GradientBasedOptimization();
//var opty = new HillClimbing();
var opty = new GeneticAlgorithm(100);
var numGears = 2 * NumGearPairs;
/* here is the Dependent Analysis. Take a look at the file/class ForceVelocityPositionAnalysis.cs
* and notice that it inherits from IDependent Analysis. By adding this to the optimization method
* (line 122), we are ensuring that it is called for any new decision variables found in the process.*/
var FVPAnalysis = new ForceVelocityPositionAnalysis(numGears, outputTorque, inputSpeed, inputPosition);
opty.Add(FVPAnalysis);
/* here is the objective function, minimize mass. Note that it will hold a reference to the
* ForceVelocityPositionAnalysis so that it can reference it for exact values of diamter. */
opty.Add(new massObjective(FVPAnalysis, gearDensity));
/* here is an inequality constraint for fitting within the box described above. Again, it
* needs to position and diameter information stored in ForceVelocityPositionAnalysis */
opty.Add(new boundingboxConstraint(FVPAnalysis, boxMinX, boxMaxX, boxMinY, boxMaxY, boxMinZ,
boxMaxZ));
/* on and on: stress inequality, output Location, output Speed equalities. Details can be found in
* http://dx.doi.org/10.1115/DETC2009-86780 */
opty.Add(new stressConstraint(FVPAnalysis, Nf, SFB, SFC));
opty.Add(new outputLocationConstraint(FVPAnalysis, locationTol, outputX, outputY, outputZ));
opty.Add(new outputSpeedConstraint(FVPAnalysis, speedTol, outputSpeed));
for (var i = 0; i < NumGearPairs - 1; i++)
{
// each mating gear pair must have the same pitch.
opty.Add(new samePitch(i * 4 + 1, (i + 1) * 4 + 1));
}
/******** Set up Design Space *************/
/* for the GA and the Hill Climbing, a compete discrete space is needed. Face width and
* location parameters should be continuous though. Consider removing the 800's below
* when using a mixed optimization method. */
var dsd = new DesignSpaceDescription(numGears * 4);
for (var i = 0; i < numGears; i++)
{
dsd[4 * i] = new VariableDescriptor(5, 1000, 1.0); // number of teeth: integers between 5 and 1000
dsd[4 * i + 1] = new VariableDescriptor(ValidPitches); // pitches from AGMA standard
dsd[4 * i + 2] = new VariableDescriptor(0, 50, 800); // face width is between 0 and 50 inches
dsd[4 * i + 3] = new VariableDescriptor(0, 500, 800); //location is either an angle or a length
// a max of 500 inches is generous
}
opty.Add(dsd);
/******** Set up Optimization *************/
/* the following mish-mash is similiar to previous project - just trying to find a
* combination of methods that'll lead to the optimial optimization algorithm. */
//abstractSearchDirection searchDirMethod = new SteepestDescent();
//opty.Add(searchDirMethod);
//abstractLineSearch lineSearchMethod = new ArithmeticMean(0.0001, 1, 100);
//opty.Add(lineSearchMethod);
opty.Add(new LatinHyperCube(dsd, VariablesInScope.BothDiscreteAndReal));
opty.Add(new GACrossoverBitString(dsd));
opty.Add(new GAMutationBitString(dsd));
opty.Add(new PNormProportionalSelection(optimize.minimize, true, 0.7));
//opty.Add(new RandomNeighborGenerator(dsd,3000));
//opty.Add(new KeepSingleBest(optimize.minimize));
opty.Add(new squaredExteriorPenalty(opty, 10));
opty.Add(new MaxAgeConvergence(40, 0.001));
opty.Add(new MaxFnEvalsConvergence(10000));
opty.Add(new MaxSpanInPopulationConvergence(15));
double[] xStar;
Parameters.Verbosity = VerbosityLevels.AboveNormal;
// this next line is to set the Debug statements from OOOT to the Console.
Debug.Listeners.Add(new TextWriterTraceListener(Console.Out));
var timer = Stopwatch.StartNew();
var fStar = opty.Run(out xStar, numGears * 4);
printResults(opty, xStar, fStar, timer);
Console.ReadKey();
}
static void Main()
{
/* first a new optimization method in the form of a genetic algorithm is created. */
var optMethod = new MultiObjectiveGeneticAlgorithm();
/* The objective function is Rosenbrock's banana function again. */
optMethod.Add(new polynomialObjFn
{
Terms = new List <string>
{
"100*x1^4",
"-200*x1^2*x2",
"x1^2",
"-2*x1",
"100*x2^2",
"1"
}
});
optMethod.Add(new RoyalRoads());
/* Now a number of convergerence criteria are added. Again, since these all
* inherit from the abstractConvergence class, the Add method knows to where
* to store them. */
optMethod.Add(new MaxIterationsConvergence(50000)); /* stop after 500 iteration (i.e. generations) */
optMethod.Add(new MaxAgeConvergence(20, 0.000000001)); /*stop after 20 generations of the best not changing */
optMethod.Add(new MaxSpanInPopulationConvergence(100)); /*stop if the largest distance is only one unit. */
optMethod.NumConvergeCriteriaNeeded = 2; /* two of these three criteria are needed to stop the process. */
/* The genetic algorithm is for discrete problems. Therefore we need to provide the optimization algorithm
* and the subsequent generators with the details of the space. The first variable represents the number of
* passes in our fictitious problem. We set the lower bound to 1 and the upper bound to 20. The third argument
* is the delta and since only integers are possible we set this to 1. The second and third variables are
* really continous, but for the purpose of the GA we set a discretization at one-ten-thousandth for the second
* and one-hundredth in the third. Note that you can provide either the delta or the number of steps. Here
* 36,001 steps will make increments of one-hundredth. */
var SpaceDescriptor = new DesignSpaceDescription
{
new VariableDescriptor(-100, 100, 0.0001),
new VariableDescriptor(-100, 100, 0.0001),
new VariableDescriptor(-100, 100, 0.0001)
};
optMethod.Add(SpaceDescriptor);
/* the genetic algorithm requires some more values to be fully specified. These include initial,
* crossover, and mutation generators, as well as a selector. A Latin Hyper Cube initial sample is
* first created to assure the population covers the space well. */
optMethod.Add(new LatinHyperCube(SpaceDescriptor, VariablesInScope.BothDiscreteAndReal));
/* the typical bit-string approach to mutation and crossover are adopted here. Note that the
* mutation rate (per candidate) is increased to 0.4 from the default of 0.1. Which means that
* 4 in 10 candidates should experience at least one mutation. No new crossover rate is provided
* therefore the default of 1.7 will be used. This means that between two parents there will likely
* be 1.7 locations of crossover between them. */
optMethod.Add(new GAMutationBitString(SpaceDescriptor, 0.4));
optMethod.Add(new GACrossoverBitString(SpaceDescriptor));
/* Finally, the selector is added to the population. This RandomPairwiseCompare is often referred to
* as tournament selection wherein a random selection of two candidates results in the inferior one
* being removed from the population. It requires the optimization direction: are lower values better
* (minimize) or larger (maximize)? */
optMethod.Add(new SkewboidDiversity(optimize.minimize, optimize.minimize));
optMethod.Add(new RandomPairwiseCompare(optimize.minimize));
/* for output statements (points in the code where the SearchIO.output(...) function is called, the
* verbosity is set to 4 which is high. Typical values are between 0 and 4 but higher values (>4)
* may be used, but this will likely cut into the speed of the search process. */
Parameters.Verbosity = VerbosityLevels.AboveNormal;
/* everything is set, we can now run the algorithm and retrieve the f* and x* values. */
double[] xOptimal;
var fOptimal = optMethod.Run(out xOptimal);
/* since we are curious how the process completed we now output some details. */
SearchIO.output("f* = " + fOptimal); /* the 0 indicates that this statement has high priority
* and shouldn't be skipped in printing to the console. */
SearchIO.output("x* = " + xOptimal.MakePrintString());
SearchIO.output("The process converged by criteria: " + optMethod.ConvergenceDeclaredByTypeString);
Console.ReadLine();
}
protected override void Run()
{
Random r = new Random(); //1);
// double[,] desiredPath ={{1.87,8},{2.93,8.46},{2.80,8.41},
// {1.99,8.06},{0.96,7.46},{0,6.71},{-0.77,5.93},{-1.3,5.26},{-1.60,4.81},{-1.65,4.75},{-1.25,5.33},{0,6.71}};
double[,] desiredPath = { { 125, 225 }, { 165.44, 217.76 }, { 189.57, 200.42 }, { 185.89, 178.49 }, { 158.65, 161.92 }, { 109.38, 135.30 }, { 57.997, 101.69 }, { 24.59, 82.07 }, { 0.33, 76.90 }, { -17.03, 91.46 }, { -13.92, 129.10 }, { -0.74, 155.01 }, { 20.73, 180.91 }, { 53.78, 205.65 }, { 88.17, 219.90 } };
double startAngle = 0;
double endAngle = 2 * Math.PI;
double iOmega = 2;
double iAlpha = 0;
MechSimulation sim = new MechSimulation();
//Below is a relation for bounding box and also the first point
double bb_min, bb_max;
// bb_min = StarMath.Min(desiredPath);
// bb_max = StarMath.Max(desiredPath);
//now that min and max are obtained - we will form a bounding box using these max and min values
bb_max = 250;
bb_min = 250;
sim.Graph = seedGraph;
// designGraph testGraph = this.seedGraph;
// ev.c = new candidate(testGraph, 0);
// ev.c = this.seedGraph;
//bounding box - trying to contain the solutions within a particular box
// BoundingBox bb = new BoundingBox(sim, bb_max,bb_min);
// GrashofCriteria cc = new GrashofCriteria(sim, 0);
//adding a new objective function which can be taken by the optimization program
var pathObjFun = new ComparePathWithDesired(seedCandidate, desiredPath, sim);
//initializing the optimization program
var optMethod = new NelderMead();
//var optMethod = new GradientBasedOptimization();
optMethod.Add(new PowellMethod());
optMethod.Add(new DSCPowell(0.00001, .5, 1000));
// optMethod.Add(new GoldenSection(0.001,300));
optMethod.Add(new ArithmeticMean(0.001, 0.1, 300));
//adding simulation
optMethod.Add(sim);
//adding objective function to this optimization routine
optMethod.Add(pathObjFun);
//we are removing this since we do not have a merit function defined
optMethod.Add(new squaredExteriorPenalty(optMethod, 1.0));
// optMethod.Add(bb);
// optMethod.Add(cc);
// convergence
optMethod.Add(new MaxIterationsConvergence(100));
// optMethod.Add(new DeltaXConvergence(0.01));
optMethod.Add(new ToKnownBestFConvergence(0.0, 0.1));
optMethod.Add(new MaxSpanInPopulationConvergence(0.01));
var n = 6;
var dsd = new DesignSpaceDescription();
var minX = StarMath.Min(StarMath.GetColumn(0, desiredPath));
var maxX = StarMath.Max(StarMath.GetColumn(0, desiredPath));
var minY = StarMath.Min(StarMath.GetColumn(1, desiredPath));
var maxY = StarMath.Max(StarMath.GetColumn(1, desiredPath));
var delta = maxX - minX;
minX -= delta;
maxX += delta;
delta = maxY - minY;
minY -= delta;
maxY += delta;
for (int i = 0; i < n; i++)
{
if (i % 2 == 0)
{
dsd.Add(new VariableDescriptor(minX, maxX));
}
else
{
dsd.Add(new VariableDescriptor(minY, maxY));
}
}
// dsd.Add(new VariableDescriptor(0,300));
var LHC = new LatinHyperCube(dsd, VariablesInScope.BothDiscreteAndReal);
var initPoints = LHC.GenerateCandidates(null, 100);
//for each initPoints - generate the fstar value
//generating random x,y values
//double[] x0 = new double[8];
//for (int i = 0; i < x0.GetLength(0); i++) //since I am going to assign ground pivots as they are
// x0[i] = 100*r.NextDouble();
//sim.calculate(x0);
// double[] xStar;
// double fStar = optMethod.Run(out xStar, x0);
//// double fStar = optMethod.Run(out xStar, 8);
double[] fStar1 = new double[initPoints.Count];
List <double[]> xStar1 = new List <double[]>();
for (int i = 0; i < fStar1.GetLength(0); i++)
{
double[] x0 = new double[n];
x0 = initPoints[i];
double[] xStar;
double fStar = optMethod.Run(out xStar, x0);
fStar1[i] = fStar;
xStar1.Add(xStar);
SearchIO.output("LHC i: " + i);
}
int xstarindex;
SearchIO.output("fStar Min=" + StarMath.Min(fStar1, out xstarindex), 0);
SearchIO.output("Xstar Values:" + xStar1[xstarindex]);
SearchIO.output("***Converged by" + optMethod.ConvergenceDeclaredByTypeString, 0);
SearchIO.output("Rerunning with new x values", 0);
// var optMethod1 = new GradientBasedOptimization();
// optMethod1.Add(new FletcherReevesDirection());
// // optMethod1.Add(new ArithmeticMean(0.001, 0.1, 300));
// optMethod1.Add(new GoldenSection(0.001, 300));
// optMethod1.Add(sim);
// optMethod1.Add(pathObjFun);
// optMethod1.Add(new squaredExteriorPenalty(optMethod, 1.0));
//// optMethod1.Add(new MaxIterationsConvergence(100));
// optMethod1.Add(new ToKnownBestFConvergence(0.0, 0.1));
// // optMethod.Add(new MaxSpanInPopulationConvergence(0.01))
// double[] xStar2;
// double fStar2 = optMethod1.Run(out xStar2, xStar1[xstarindex]);
// SearchIO.output("New Fstar = " + fStar2, 0);
//double xstarmin, xstarmax;
//xstarmax = StarMath.Max(xStar1[xstarindex]);
//xstarmin = StarMath.Min(xStar1[xstarindex]);
//var dsd1 = new DesignSpaceDescription();
//dsd1.Add(new VariableDescriptor(xstarmin, xstarmax));
//var LHC1 = new LatinHyperCube(dsd1, VariablesInScope.BothDiscreteAndReal);
//var initPoints1 = LHC.GenerateCandidates(null, 100);
//double[] fstar1 = new double[initPoints1.Count];
//List<double[]> xstar_second = new List<double[]>();
//for (int i = 0; i < fstar1.GetLength(0); i++)
//{
// double[] x0 = new double[n];
// x0 = initPoints[i];
// double[] xStar;
// double fStar = optMethod.Run(out xStar, x0);
// fstar1[i] = fStar;
// xstar_second.Add(xStar);
// SearchIO.output("LHC i: " + i);
//}
//SearchIO.output("New fStar = " + StarMath.Min(fstar1), 0);
//SearchIO.output("***Converged by" + optMethod.ConvergenceDeclaredByTypeString, 0);
}
static void Main()
{
Parameters.Verbosity = VerbosityLevels.AboveNormal;
// this next line is to set the Debug statements from OOOT to the Console.
Trace.Listeners.Add(new TextWriterTraceListener(Console.Out));
/* first a new optimization method in the form of a genetic algorithm is created. */
var optMethod = new GeneticAlgorithm(100);
/* then an objective function and constraints are added. Since these inherit from
* type OptimizationToolbox.objectiveFunction and OptimizationToolbox.inequality
* the Add function knows where to store them so that they will be invoked by the
* fitness evaluation section of the GA. */
optMethod.Add(new efficiencyMeasurement());
//optMethod.Add(new lessThanManifoldVolume());
/* GA's cannot explicitly handle inequalities, so a merit function must be added
* so that the fitness evaluation knows how to combine the constraint with the
* objective function. */
//optMethod.Add(new squaredExteriorPenalty(optMethod, 50));
/* Now a number of convergerence criteria are added. Again, since these all
* inherit from the abstractConvergence class, the Add method knows to where
* to store them. */
optMethod.Add(new ToKnownBestFConvergence(0.0, 0.5));
optMethod.Add(new MaxIterationsConvergence(50000)); /* stop after 500 iteration (i.e. generations) */
optMethod.Add(new MaxAgeConvergence(20, 0.000000001)); /*stop after 20 generations of the best not changing */
optMethod.Add(new MaxSpanInPopulationConvergence(100)); /*stop if the largest distance is only one unit. */
optMethod.NumConvergeCriteriaNeeded = 2; /* two of these three criteria are needed to stop the process. */
/* The genetic algorithm is for discrete problems. Therefore we need to provide the optimization algorithm
* and the subsequent generators with the details of the space. The first variable represents the number of
* passes in our fictitious problem. We set the lower bound to 1 and the upper bound to 20. The third argument
* is the delta and since only integers are possible we set this to 1. The second and third variables are
* really continous, but for the purpose of the GA we set a discretization at one-ten-thousandth for the second
* and one-hundredth in the third. Note that you can provide either the delta or the number of steps. Here
* 36,001 steps will make increments of one-hundredth. */
var SpaceDescriptor = new DesignSpaceDescription
{
new VariableDescriptor(1, 20, 1.0),
new VariableDescriptor(0, 100, 0.0001),
new VariableDescriptor(-180, 180, 36000)
};
optMethod.Add(SpaceDescriptor);
/* the genetic algorithm requires some more values to be fully specified. These include initial,
* crossover, and mutation generators, as well as a selector. A Latin Hyper Cube initial sample is
* first created to assure the population covers the space well. */
optMethod.Add(new LatinHyperCube(SpaceDescriptor, VariablesInScope.BothDiscreteAndReal));
/* the typical bit-string approach to mutation and crossover are adopted here. Note that the
* mutation rate (per candidate) is increased to 0.4 from the default of 0.1. Which means that
* 4 in 10 candidates should experience at least one mutation. No new crossover rate is provided
* therefore the default of 1.7 will be used. This means that between two parents there will likely
* be 1.7 locations of crossover between them. */
optMethod.Add(new GAMutationBitString(SpaceDescriptor, 0.4));
optMethod.Add(new GACrossoverBitString(SpaceDescriptor));
/* Finally, the selector is added to the population. This RandomPairwiseCompare is often referred to
* as tournament selection wherein a random selection of two candidates results in the inferior one
* being removed from the population. It requires the optimization direction: are lower values better
* (minimize) or larger (maximize)? */
optMethod.Add(new RandomPairwiseCompare(optimize.minimize));
/* for output statements (points in the code where the SearchIO.output(...) function is called, the
* verbosity is set to 4 which is high. Typical values are between 0 and 4 but higher values (>4)
* may be used, but this will likely cut into the speed of the search process. */
Parameters.Verbosity = VerbosityLevels.AboveNormal;
// this next line is to set the Debug statements from OOOT to the Console.
Trace.Listeners.Add(new TextWriterTraceListener(Console.Out));
var timer = Stopwatch.StartNew();
/* everything is set, we can now run the algorithm and retrieve the f* and x* values. */
double[] xOptimal;
var fOptimal = optMethod.Run(out xOptimal);
printResults(optMethod, xOptimal, fOptimal, timer);
}
