Add benchmark results

README.md

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+# EMOA
+
+Benchmarks of Evolutionary multi-objective optimization algorithms (EMOA) on Real-world Multi-objective
+Optimization Problem Suite.
+
+## Quick Start
+
+Creating the environment：
+
+```
+conda create -n pymoo python=3.8
+conda activate pymoo
+pip install -U pymoo
+```
+
+Change the test problem in `main.py`
+
+```
+python main.py
+```
+
+## Benchmark
+
+> population size: 100
+> number of generations: 200
+
+#### CRE-2-3-1
+
+Time (s):
+CTAEA 6.297407865524292
+NSGA2 9.709688425064087
+NSGA3 13.19536280632019
+
+![](images/CRE-2-3-1.png)
+
+#### CRE-2-4-2
+
+Time (s):
+CTAEA 5.5211687088012695
+NSGA2 8.863621950149536
+NSGA3 12.693290948867798
+
+#### CRE-2-4-3
+
+Time (s):
+CTAEA 5.683619022369385
+NSGA2 9.352391481399536
+NSGA3 13.239986419677734
+
+![](images/CRE-2-4-3.png)
+
+#### CRE-2-7-4
+
+Time (s):
+CTAEA 6.6659016609191895
+NSGA2 10.643601417541504
+NSGA3 14.66565227508545
+
+![](images/CRE-2-7-4.png)
+
+#### CRE-2-4-5
+
+Time (s):
+CTAEA 5.434146165847778
+NSGA2 10.283865928649902
+NSGA3 15.255037069320679
+
+![](images/CRE-2-4-5.png)

main.py

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+from cProfile import label
+from pymoo.algorithms.moo.nsga2 import NSGA2
+from pymoo.algorithms.moo.ctaea import CTAEA
+from pymoo.algorithms.moo.nsga3 import NSGA3
+
+from pymoo.factory import  get_reference_directions
+from pymoo.optimize import minimize
+
+from pymoo.visualization.scatter import Scatter
+from reproblem import *
+
+import time
+
+# Define the problem
+problem = CRE25() # CRE21() CRE22() CRE23() CRE24() CRE25()
+
+ref_dirs = get_reference_directions("das-dennis", 2, n_partitions=64)
+
+# Define Algorithms
+nsga_2_alg = NSGA2(pop_size=100)
+nsga_3_alg = NSGA3(pop_size=100, ref_dirs=ref_dirs)
+ctaea_alg  = CTAEA(ref_dirs=ref_dirs)
+
+# C-TAEA
+start = time.time()
+res_ctaea = minimize(problem,
+               ctaea_alg,
+               ('n_gen', 200),
+               seed=1,
+               verbose=False)
+end = time.time()
+print('CTAEA', end - start)
+
+# NSGA-II
+res_nsga_2 = minimize(problem,
+               nsga_2_alg,
+               ('n_gen', 200),
+               seed=1,
+               verbose=False)
+end = time.time()
+print('NSGA2', end - start)
+
+# NSGA-III
+res_nsga_3 = minimize(problem,
+               nsga_3_alg,
+               ('n_gen', 200),
+               seed=1,
+               verbose=False)
+end = time.time()
+print('NSGA3', end - start)
+
+# Plot the results
+plot = Scatter(title="Approximated Pareto fronts of the CRE2-4-5", legend=True)
+
+plot.add(res_ctaea.F, facecolor="none", edgecolor="blue", label="C-TAEA")
+plot.add(res_nsga_2.F, facecolor="none", edgecolor="red", label="NSGA-II")
+plot.add(res_nsga_3.F, facecolor="none", edgecolor="yellow", label="NSGA-III")
+
+plot.show()

nsga-ii-re.py

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-from pymoo.algorithms.moo.nsga2 import NSGA2
-from pymoo.algorithms.moo.ctaea import CTAEA
-from pymoo.algorithms.moo.nsga3 import NSGA3
-
-from pymoo.factory import  get_reference_directions
-from pymoo.optimize import minimize
-
-from pymoo.visualization.scatter import Scatter
-from reproblem import *
-
-problem = CRE22()
-ref_dirs = get_reference_directions("das-dennis", 2, n_partitions=64)
-
-algorithm = NSGA2(pop_size=100)
-algorithm = NSGA3(pop_size=92,
-                  ref_dirs=ref_dirs)
-# IBEA
-algorithm = CTAEA(ref_dirs=ref_dirs)
-
-res = minimize(problem,
-               algorithm,
-               ('n_gen', 200),
-               seed=1,
-               verbose=False)
-
-plot = Scatter()
-plot.add(problem.pareto_front(), plot_type="line", color="black", alpha=0.7)
-plot.add(res.F, facecolor="none", edgecolor="red")
-plot.show()