Wednesday, June 28, 2017

Multi-Objective Genetic Programming in Java


Genetic Programming Framework that supports Multi-Objective Optimization


Add the following dependency to your POM file:


The sample code belows show tree-gp based multi-objective optimization which minimizes the following two objectives:
  1. the mean square errors in predicting the "Mexican Hat" symbolic regression problem
  2. the average tree depth of the tree-gp program generated.
List<Observation> data = Tutorials.mexican_hat();
TupleTwo<List<Observation>, List<Observation>> split_data = CollectionUtils.split(data, 0.9);
List<Observation> trainingData = split_data._1();
List<Observation> testingData = split_data._2();

NSGPII tgp = NSGPII.defaultConfig();
tgp.setVariableCount(2); // the number of variables is equal to the input dimension of an observation in the "data" list
tgp.setCostFunction((CostFunction) (solution, mogpgpConfig) -> {
 List<Observation> observations = gpConfig.getObservations();
 double error = 0;
 for(Observation observation : observations){
    error += Math.pow(observation.getOutput(0) - observation.getPredictedOutput(0), 2.0);

 double cost1 = error;
 double cost2 = solution.averageTreeDepth();

 return Arrays.asList(cost1, cost2);

tgp.setDisplayEvery(2); // diplay the iteration result for every 2 iterations
NondominatedPopulation pareto_front =;
System.out.println("pareto_front: " + pareto_front.size());
The number of variable of a tree-gp program is set by calling NSGPII.setVariableCount(...), the number of variables is equal to the input dimension of the problem to be solved. In the case of "Mexican Hat" symbolic regression, the input is (x, y), therefore,the number of variables is 2.
The cost evaluator computes two objectives. The first objective is the training cost of a tree-gp 'program' on the 'observations' (which is the symbolic regression trainingData), the second objective is the average depth of the tree-gp 'program'.

Test the programs in the pareto front obtained from the TreeGP evolution

Once the pareto front for the MOGP is obtained, we can access each solution in the pareto front, just like the code below:
MOOGPSolution solution = (MOOGPSolution)pareto_front.get(0);
Solution program = solution.getGp();
These two line returns the tree-gp program associated with the first solution on the pareto-front obtained.
Calling program.mathExpression() will returns the math expression representing the gp program, a sample of which is shown below:
Trees[0]: 1.0 - (if(1.0 < if(1.0 < 1.0, if(1.0 < v0, 1.0, 1.0), if(1.0 < (v1 * v0) + (1.0 / 1.0), 1.0 + 1.0, 1.0)), 1.0, v0 ^ 1.0))
The best program in the TreeGP population obtained from the training in the above step can then be used for prediction, as shown by the sample code below:
for(Observation observation : testingData) {
 double predicted = observation.getPredictedOutput(0);
 double actual = observation.getOutput(0);"predicted: {}\tactual: {}", predicted, actual);

Display the Pareto Front

The following code shows how to display the pareto front generated from MOGP:
 List<TupleTwo<Double, Double>> pareto_front_data = pareto_front.front2D();

ParetoFront chart = new ParetoFront(pareto_front_data, "Pareto Front for MO-GP");

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