pyMultiobjective

Introduction

A python library for the following Multiobjective Optimization Algorithms or Many Objectives Optimization Algorithms: C-NSGA II (Clustered Non-Dominated Sorting Genetic Algorithm II); CTAEA (Constrained Two Archive Evolutionary Algorithm); GrEA (Grid-based Evolutionary Algorithm); HypE (Hypervolume Estimation Multiobjective Optimization Algorithm); IBEA-FC (Indicator-Based Evolutionary Algorithm with Fast Comparison Indicator); IBEA-HV (Indicator-Based Evolutionary Algorithm with Hypervolume Indicator); MOEA/D (Multiobjective Evolutionary Algorithm Based on Decomposition); NAEMO (Neighborhood-sensitive Archived Evolutionary Many-objective Optimization); NSGA II (Non-Dominated Sorting Genetic Algorithm II); NSGA III (Non-Dominated Sorting Genetic Algorithm III); OMOPSO (Optimized Multiobjective Particle Swarm Optimization); PAES (Pareto Archived Evolution Strategy) with Fast Non-Dominance Sorting); RVEA (Reference Vector Guided Evolutionary Algorithm); SMPSO (Speed-Constrained Multiobjective Particle Swarm Optimization); SMS-EMOA (S-Metric Selection Evolutionary Multiobjective Optimization Algorithm); SPEA2 (Strength Pareto Evolutionary Algorithm 2); U-NSGA III (Unified Non-Dominated Sorting Genetic Algorithm III).

Usage

1. Install

pip install pyMultiobjective

2. Import

# Import NSGA III
from pyMultiobjective.algorithm import non_dominated_sorting_genetic_algorithm_III

# Import Test Functions. Available Test Functions: Dent, DTLZ1, DTLZ2, DTLZ3, DTLZ4, DTLZ5, DTLZ6, DTLZ7, Fonseca-Fleming, Kursawe, Poloni, Schaffer1, Schaffer2, ZDT1, ZDT2, ZDT3, ZDT4, ZDT6, Viennet1, Viennet2, Viennet3 
from pyMultiobjective.test_functions import dent_f1, dent_f2

# OR Define your Own Custom Function. The function input should be a list of values, 
# each value represents a dimenstion (x1, x2, ...xn) of the problem.

# Run NSGA III
parameters = {
	'references': 5,
	'min_values': (-5, -5),
	'max_values': (5, 5),
	'mutation_rate': 0.1,
	'generations': 1500,
	'mu': 1,
	'eta': 1,
	'k': 2, 
	'verbose': True
}
sol = non_dominated_sorting_genetic_algorithm_III(list_of_functions = [dent_f1, dent_f2], **parameters)

# Import Graphs
from pyMultiobjective.util import graphs

# Plot Solution - Scatter Plot
parameters = {
	'min_values': (-5, -5),
	'max_values': (5, 5),
	'step': (0.1, 0.1),
	'solution': sol, 
	'show_pf': True,
	'show_pts': True,
	'show_sol': True,
	'pf_min': True,  # True = Minimum Pareto Front; False = Maximum Pareto Front
	'custom_pf': [], # Input a custom Pareto Front(numpy array where each column is an Objective Function)
	'view': 'browser'
}
graphs.plot_mooa_function(list_of_functions = [dent_f1, dent_f2], **parameters)

# Plot Solution - Parallel Plot
parameters = {
	'min_values': (-5, -5), 
	'max_values': (5, 5), 
	'step': (0.1, 0.1), 
	'solution': sol, 
	'show_pf': True,
	'pf_min': True,  # True = Minimum Pareto Front; False = Maximum Pareto Front
	'custom_pf': [], # Input a custom Pareto Front(numpy array where each column is an Objective Function)
	'view': 'browser'
}
graphs.parallel_plot(list_of_functions = [dent_f1, dent_f2], **parameters)

# Plot Solution - Andrews Plot
parameters = {
	'min_values': (-5, -5), 
	'max_values': (5, 5), 
	'step': (0.1, 0.1), 
	'solution': sol, 
	'normalize': True,
	'size_x': 15,
	'size_y': 15,
	'show_pf': True, 
	'pf_min': True, # True = Minimum Pareto Front; False = Maximum Pareto Front
	'custom_pf': [] # Input a custom Pareto Front(numpy array where each column is an Objective Function)
}
graphs.andrews_plot(list_of_functions = [dent_f1, dent_f2], **parameters)

# Import Performance Indicators. Available Performance Indicators: GD, GD+, IGD, IGD+, Maximum Spread, Spacing and Hypervolume
from pyMultiobjective.util import indicators

parameters = {
	'min_values': (-5, -5), 
	'max_values': (5, 5), 
	'step': (0.1, 0.1), 
	'solution': sol, 
	'pf_min': True, # True = Minimum Pareto Front; False = Maximum Pareto Front
	'custom_pf': [] # Input a custom Pareto Front(numpy array where each column is an Objective Function)
}
gd   = indicators.gd_indicator(list_of_functions = [dent_f1, dent_f2], **parameters)
gdp  = indicators.gd_plus_indicator(list_of_functions = [dent_f1, dent_f2], **parameters)
igd  = indicators.igd_indicator(list_of_functions = [dent_f1, dent_f2], **parameters)
igdp = indicators.igd_plus_indicator(list_of_functions = [dent_f1, dent_f2], **parameters)
ms   = indicators.ms_indicator(list_of_functions = [dent_f1, dent_f2], **parameters)
sp   = indicators.sp_indicator(list_of_functions = [dent_f1, dent_f2], **parameters)

print('GD   = ', gd)
print('GDP  = ', gdp)
print('IGD  = ', igd)
print('IGDP = ', igdp)
print('MS   = ', ms)
print('SP   = ', sp)


parameters = {
	'solution': sol, 
	'n_objs': 2,
	'ref_point': [], # A Reference Point. If empty, an arbitrary Reference Point will be Used
}
hypervolume = indicators.hv_indicator(**parameters)
print('Hypervolume = ', hypervolume)

3. Try it in Colab

• C-NSGA II ( Colab Demo ) ( Original Paper )
• CTAEA ( Colab Demo ) ( Original Paper )
• GrEA ( Colab Demo ) ( Original Paper )
• HypE ( Colab Demo ) ( Original Paper )
• IBEA-FC ( Colab Demo ) ( Original Paper )
• IBEA-HV ( Colab Demo ) ( Original Paper )
• MOEA/D ( Colab Demo ) ( Original Paper )
• NAEMO ( Colab Demo ) ( Original Paper )
• NSGA II ( Colab Demo ) ( Original Paper )
• NSGA III ( Colab Demo ) ( Original Paper )
• OMOPSO ( Colab Demo ) ( Original Paper )
• PAES ( Colab Demo ) ( Original Paper )
• RVEA ( Colab Demo ) ( Original Paper )
• SMPSO ( Colab Demo ) ( Original Paper )
• SMS-EMOA ( Colab Demo ) ( Original Paper )
• SPEA2 ( Colab Demo ) ( Original Paper )
• U-NSGA III ( Colab Demo ) ( Original Paper )

4. Test Functions

• Dent ( Paper ) ( Pareto Front ) ( Plot )
• DTLZ1 ( Paper ) ( Pareto Front ) ( Plot )
• DTLZ2 ( Paper ) ( Pareto Front ) ( Plot )
• DTLZ3 ( Paper ) ( Pareto Front ) ( Plot )
• DTLZ4 ( Paper ) ( Pareto Front ) ( Plot )
• DTLZ5 ( Paper ) ( Pareto Front ) ( Plot )
• DTLZ6 ( Paper ) ( Pareto Front ) ( Plot )
• DTLZ7 ( [ Paper ](https://doi.org/10.1109/CEC.2002.100