optimobo 0.1.5

Solve multi-objective problems using Bayesian optimisation.

OptiMOBO

Solve bi-objective multi-objective problems using multi-objective bayesian optimisation (MOBO).

This repo contains implementations of two MOBO methods. They are designed to solve bi-objective minimisation problems, constraints are not supported. The methods include:

• Mono-surrogate. This uses a single model to optimise. Objective vectors are aggregated into a single scalar value and a Gaussian process is built upon the scalarised values.
• Multi-surrogate. This method uses multiple models. One model for each objective. Multi-objective acquisition functions are used to identify new sample points.

The two methods are written as two classes MultiSurrogateOptimiser and MonoSurrogateOptimiser. They are designed to solve problems that inherit from the Problem class presented in the library pymoo.

Examples

The following code defines a bi-objective problem, MyProblem, and uses multi-surrogate Bayesian optimisation (utilising Tchebicheff aggregation as an acquisition function) to solve.

import numpy as np
from optimisers import MultiSurrogateOptimiser
from pymoo.core.problem import ElementwiseProblem

class MyProblem(ElementwiseProblem):

    def __init__(self):
        super().__init__(n_var=2,
                         n_obj=2,
                         xl=np.array([-2,-2]),
                         xu=np.array([2,2]))

    def _evaluate(self, x, out, *args, **kwargs):
        f1 = 100 * (x[0]**2 + x[1]**2)
        f2 = (x[0]-1)**2 + x[1]**2
        out["F"] = [f1, f2]

problem = MyProblem()
optimi = MultiSurrogateOptimiser(problem, [0,0], [700,12])
out = optimi.solve(n_iterations=100, display_pareto_front=True, n_init_samples=20, sample_exponent=3, acquisition_func=Tchebicheff([0,0],[700,12]))

Will return a Pareto set approximation:

For the multi-objective benchmark problem DTLZ5:

from pymoo.problems import get_problem
problem = get_problem("dtlz5", n_obj=2, n_var=5)
optimi = MultiSurrogateOptimiser(problem, [0,0], [1.3,1.3])
out = optimi.solve(n_iterations=100, display_pareto_front=True, n_init_samples=20, sample_exponent=3, acquisition_func=Tchebicheff([0,0],[1.3,1.3])) 

Will return:

The output results is a tuple containing:

• Solutions on the Pareto front approximation.
• The corresponding inputs to the solutions on the Pareto front.
• All evaluated solutions.
• All inputs used in the search.

Key Features

Mono and multi-surrogate:

Two optimisers based on differing methods.

Choice of acquisition/aggragation functions:

In mono-surrogate MOBO, scalarisation functions are used to aggregate objective vectors in a single value that can be used by the optimsier. In multi-surrogate MOBO, scalarisation functions are used as convergence measures to select sample points. This package contains 10 scalarisation functions that can be used in the above mentioned contexts. Options Include:

• Weighted Sum
• Tchebicheff
• Modified Tchebicheff
• Augmented Tchebicheff
• Weighted Norm
• Weighted Power
• Weighted Product
• PBI
• IPBI
• Exponential Weighted Criterion

They are written so they can be used in any context.

Experimental Parameters

Various experimental parameters can be customised.

Requirements

• numpy
• scipy
• pygmo
• pymoo