Optimization Example-03-Point on Surface Video
This example shows the process of setting up Optimo for single objective optimization. The objective of this example is to find a point on a surface with the minimum Z value. The parametric variables are X and Y of the points.
The user can modify population number, lower and upper limits of optimization variables, and the number of objectives (it is one for the single objective optimization).
The “NSGA-II.InitialSolutionList” node creates a list of random numbers (the size of which is the population size) for each variable (initial population list) within the specified range. The population list includes a placeholder for fitness function results which will be assigned when the fitness function results are evaluated. The number of variables can be changed by adding or removing an index to the Lower Limits and Upper Limits Lists node (both upper and lower limits must have the same number of indices).
The output of the “NSGA_II.InitialSolutionList” node is a list of lists of variables and objectives. Optimo is designed in a way that the user can modify the fitness functions without needing to change to the whole process or to write any script. A list of variables can be taken from the initial list of populations and can be used as an input to the defined fitness functions. Objective functions can be added and removed, but the “number of objectives” input must match the number of objective functions. In the latest version of Optimo the list of fitness values are calculated by applying fitness function to initial population list using "Function.Apply" node.
In the point on surface fitness function custom node, the two lists of variables created by InitialSolutionList are used as X and Y values to create a range of points on the XY plane.
Then they are projected to the surface by shooting rays toward the surface. The Z values of the intersection points are gathered as the result of the fitness function.
The “NSGA-II.AssignFitnessFunction” node assigns the fitness function values to the population list.
The Dynamo graph below is contained inside the “NSGA_II Function” custom node. The function of this node is to run the NSGA II algorithm recursively to generate the specified number of generations. The first input to this custom node, “init” is a list containing two elements. The first element in the list is the counter that controls the number of iterations. The Fitness Function gets fed into the “NSGA_II Function” custom node as an input along with the lowerLimits and upperLimits.
The GenerationAlgorithm creates a new population based on the previous generation. This new generation is then evaluated with the same fitness functions, and the fitness function results overwrite the objectives’ values in this new generation. The “NSGA_II.Sorting” node takes the previous generation as well as the current generation, and ranks them in the equally optimal solution front based on their fitness (best results first).
The “LoopWhile” node is essentially running in the “NSGA_II Function” node recursively. The number of loops depends on the iteration number inserted into LoopCompleteionCheck as an input. The init input gets incremented by one in each loop, and once init reaches the same value as completionCheck, the loop ends and the Dynamo program continues. The LoopBody input is the output from the NSGA_II function (it becomes the input for the recursive call to the NSGA_II Function node).
The results from optimization process are shows as point on the face of the selected surface. The final results are exported to a csv file as well.
