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1. Getting started
   1. Specifying the objective functions
   2. Calling the optimizer

Welcome to the MOBOpt wiki!

MOBOpt stands for Multi-Objective Bayesian Optimization

Based on the mono-objective optimizer available at Bayesian Optimization

Getting started

Specifying the objective functions

In order to use the MOBOpt package it is necessary to specify a function that is going to be optimized.

def objective(x):
    """ Objective functions to be optimized

    Input: x --> 1-D np.array with NParam elements
    """
    ...
    return np.array(f1(x), f2(x), ..., f_NObj(x))

Where x is a np.array with the arguments of the objectives, NParam is the dimensionality of the search space, fi is the i-th of the NObj different objectives.

Calling the optimizer

To use the optimizer, it is necessary to instantiate a MOBayesianOpt object.

import mobopt as mo

Optimizer = mo.MOBayesianOpt(target=objective,
                             NObj=NObj,
                             pbounds=bounds)

The required arguments are:

1. target: the function to be optimized;
2. NObj: the number of objective functions;
3. pbounds: numpy array with shape (NParam, 2) specifying the bounds for the variables in the search space, where NParam is the dimensionality of the search space;

It is necessary to call the method initialize which probes the objective functions the first random initial points necessary to initialize the method. The parameter init_points specifies how many random points will be calculated.

Optimizer.initialize(init_points=2)

And finally, the maximize method will actually run the optimization algorithm, it requires the argument n_iter which defines the number of iterations of the method (effectively the number of calls of the objective function)

front, pop = Optimizer.maximize(n_iter=NIter)

The maximize method returns two variables:

• front: np.array of shape (nPts, NObj), with the Pareto Front of the problem (results in objective space)
• pop: np.array of shape (nPts, NParam), with the Pareto Set of the problem (results in search space)

In both cases nPts represent the number of points in the Pareto Front.