#?Program?Name:?NSGA-II.py
#?Description:?This?is?a?python?implementation?of?Prof.?Kalyanmoy?Deb‘s?popular?NSGA-II?algorithm
#?Author:?Haris?Ali?Khan?
#?Supervisor:?Prof.?Manoj?Kumar?Tiwari

#Importing?required?modules
import?math
import?random
import?matplotlib.pyplot?as?plt

#First?function?to?optimize
def?function1（x）:
????value?=?-x**2
????return?value

#Second?function?to?optimize
def?function2（x）:
????value?=?-（x-2）**2
????return?value

#Function?to?find?index?of?list
def?index_of（alist）:
????for?i?in?range（0len（list））:
????????if?list[i]?==?a:
????????????return?i
????return?-1

#Function?to?sort?by?values
def?sort_by_values（list1?values）:
????sorted_list?=?[]
????while（len（sorted_list）!=len（list1））:
????????if?index_of（min（values）values）?in?list1:
????????????sorted_list.append（index_of（min（values）values））
????????values[index_of（min（values）values）]?=?math.inf
????return?sorted_list

#Function?to?carry?out?NSGA-II‘s?fast?non?dominated?s