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Refactored NSGA2, Non-dominated sorting genetic algorithm, implementation in C based on the code written by Dr. Kalyanmoy Deb.

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This is the Readme file for NSGA-II code.

About this version

Basically this version is a Refactored version of the original code in order to make the code structure more portable. Several changes have been made:

  1. The NSGA2Type type has been defined to carry all the necessary parameters of the NSGA2 algorithm. This will reduce the number of external variables and reduce the possible conflict when it uses within another routine.
  2. Three function has been extracted from the main() function, previously in nsga2r.c.
    1. ReadParamters: Read the parameters through input file or command line
    2. InitNSGA2: Initialize output files, allocate memory, and perform the first generation
    3. NSGA2: Run the generation, save the results and free the allocated memory.
    4. PrintNSGA2Parameters: Print the input parameters.
  3. Two extra void pointers have been provided and passed around to the function that has to call evaluate function. These are helpful when you want to integrate the algorithm to your code (e.g. simulator). Using void *inp and void *out pointer you could pass your simulator parameters around without changing the structure of NSGA2, as long as your objective function knows how to handle the inp and out to produce the objective values.

About the Algorithm

NSGA-II: Non-dominated Sorting Genetic Algorithm - II

Please refer to the following paper for details about the algorithm:

  • Authors: Dr. Kalyanmoy Deb, Sameer Agrawal, Amrit Pratap, T Meyarivan
  • Paper Title: A Fast and Elitist multi-objective Genetic Algorithm: NSGA-II
  • Journal: IEEE Transactions on Evolutionary Computation (IEEE-TEC)
  • Year: 2002
  • Volume: 6
  • Number: 2
  • Pages: 182-197

NOTE

This archive contains routines for plotting the objective data real-time using gnuplot. The code has been written for posix compliant operating systems and uses sta ndard piping method provided by GNU C library. The routines should work on any unix and unix like OS having gnuplot installed and which are posix compliant.

How to compile and run the program

Makefile has been provided for compiling the program on linux (and unix-like) systems. Edit the Makefile to suit your need. By default, provided Makefile attempts to compile and link all the existing source files into one single executable.

Name of the executable produced is: nsga2r

To run the program type: ./nsga2r random_seed or ./nsga2r random_seed < input_data/inp_file.in

Here random_seed is a real number in (0,1) which is used as a seed for random number generator, and "inp_file.in" is the file that stores all the input parameters

About the output files

File Description
initial_pop.out This file contains all the information about initial population.
final_pop.out This file contains the data of final population.
all_pop.out This file contains the data of populations at all generations.
best_pop.out This file contains the best solutions obtained at the end of simulation run.
params.out This file contains the information about input parameters as read by the program.

About the input parameters

Parameter Description
popsize This variable stores the population size (a multiple of 4)
ngen Number of generations
nobj Number of objectives
ncon Number of constraints
nreal Number of real variables
min_realvar[i] minimum value of i^{th} real variable
max_realvar[i] maximum value of i^{th} real variable
pcross_real probability of crossover of real variable
pmut_real probability of mutation of real variable
eta_c distribution index for real variable SBX crossover
eta_m distribution index for real variable polynomial mutation
nbin number of binary variables
nbits[i] number of bits for i^{th} binary variable
min_binvar[i] minimum value of i^{th} binary variable
max_binvar[i] maximum value of i^{th} binary variable
pcross_bin probability of crossover for binary variable
pmut_bin probability of mutation for binary variable
choice option to display the data realtime using gnuplot
obj1, obj2, obj3 index of objectives to be shown on x, y and z axes respectively
angle1, angle2 polar and azimuthal angle required for location of eye

Defining the Test Problem

Edit the source file problemdef.c to define your test problem. Some sample problems (24 test problems from Dr. Deb's book - Multi-Objective Optimization using Evolutionary Algorithms) have been provided as examples to guide you how to define your own objectives and constraints functions. You can also link other source files with the code based on your need. Consider the points below when you are implementing your objective functions.

  1. The code has been written for minimization of objectives (min f_i). If you want to maximize a function, you may use negative of the function value as the objective value.
  2. A solution is said to be feasible if it does not violate any of the constraints. Constraint functions should evaluate to a quantity greater than or equal to zero (g_j >= 0), if the solution has to be feasible. A negative value of constraint means, it is being violated.
  3. If there are more than one constraints, it is advisable (though not mandatory) to normalize the constraint values by either reformulating them or dividing them by a positive non-zero constant.

About the files

Files Descriptions
nsga2.h Header file containing declaration of global variables and functions
rand.h Header file containing declaration of variables and functions for random number generator
allocate.c Memory allocation and deallocation routines
auxiliary.c auxiliary routines (not part of the algorithm)
crossover.c Routines for real and binary crossover
crowddist.c Crowding distance assignment routines
decode.c Routine to decode binary variables
display.c Routine to display the data real-time using gnuplot
dominance.c Routine to perform non-domination checking
eval.c Routine to evaluate constraint violation
fillnds.c Non-dominated sorting based selection
initialize.c Routine to perform random initialization to population members
list.c A custom doubly linked list implementation
merge.c Routine to merge two population into one larger population
mutation.c Routines for real and binary mutation
nsga2r.c Implementation of main function and the NSGA-II framework
problemdef.c Test problem definitions
rand.c Random number generator related routines
rank.c Rank assignment routines
report.c Routine to write the population information in a file
sort.c Randomized quick sort implementation
tourselect.c Tournament selection routine

Please feel free to send questions/comments/doubts/suggestions/bugs etc. to deb@iitk.ac.in

Dr. Kalyanmoy Deb 14th June 2005 http://www.iitk.ac.in/kangal/

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Refactored NSGA2, Non-dominated sorting genetic algorithm, implementation in C based on the code written by Dr. Kalyanmoy Deb.

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