NSGA-III

NSGA-III

Citation Author(s):
Luis Felipe
Ariza Vesga
Universidad Nacional de Colombia
Submitted by:
luis ariza
Last updated:
Tue, 04/23/2019 - 22:34
DOI:
10.21227/f5g3-0088
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Abstract: 

This paper presents a fast and open source extension based on the NSGA-II code stored in the repository of the Kanpur Genetic Algorithms Laboratory (KanGAL) and the adjustment of the selection operator. It slightly modifies existing well-established genetic algorithms for many-objective optimization called the NSGA-III, the adaptive NSGA-III (A-NSGA-III), and the efficient adaptive NSGA-III,  (A$^2$-NSGA-III). The proposed method is tested on a range of benchmark problems and showcases notable performance improvement. NSGA-II and NSGA-III are frequently employed as a reference for a comparative evaluation of new evolutionary algorithms. However, the latter is proprietary and many researchers have been forced to implement it from scratch with lower performance. Our NSGA-III variations consider static and dynamic reference points where individuals in the first front are contemplated to obtain extreme points that are neither negatives nor repeated. Those algorithms resolve binary and real, constrained and non-constrained Multi-Objective and Many-objective problems. Additionally, when efficient adaptive NSGA-III is employed to solve the Car-Side Impact problem and the Water problem, we find not only visually well-distributed solutions, but also in terms of the Hyper-volume metric compared to the A-NSGA-III and the NSGA-III.

Instructions: 

This is the Readme file for NSGA-III, A-NSGA-III and A^2-NSGA-III codes. A NSGA-II extension from Kanpur the Genetic Algorithms Laboratory (KanGAL). The NSGA-III, A-NSGA-III and A^2-NSGA-III extension was coded by Luis Felipe Ariza Vesga. Email: lfarizav@gmail.com   About the Algorithm -------------------------------------------------------------------------- NSGA-II: Non-dominated Sorting Genetic Algorithm - II and NSGA-III: Non-dominated Sorting Genetic Algorithm - III   Please refer to the following papers 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   Authors: Dr. Kalyanmoy Deb, and H. Jain Paper Title: An Evolutionary Many-Objective Optimization Algorithm Using Reference-Point-Based Nondominated Sorting Approach, Part I: Solving Problems With Box Constraints Journal: IEEE Transactions on Evolutionary Computation (IEEE-TEC) Year: 2014 Volume: 18 Number: 4 Pages: 577-601   Authors: Dr. Kalyanmoy Deb, and H. Jain Paper Title: An Evolutionary Many-Objective Optimization Algorithm Using Reference-Point Based Nondominated Sorting Approach, Part II: Handling Constraints and Extending to an Adaptive Approach Journal: IEEE Transactions on Evolutionary Computation (IEEE-TEC) Year: 2014 Volume: 18 Number: 4 Pages: 602-622   Authors: Dr. Kalyanmoy Deb, and H. Jain Paper Title: An Improved Adaptive Approach for Elitist Nondominated Sorting Genetic Algorithm for Many-Objective Optimization Journal: COIN Report Number 2013014 Year: 2013   ---------------------------------------------------------------------------     --------------------------------------------------------------------------- NOTE: This archive contains routines for ploting the objective data realtime using gnuplot. The code has been written for posix compliant operating systems and uses standard 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 Here random_seed is a real number in (0,1) which is used as a seed for random number generator. You can also store all the input data in a text file and use a redirection operator to give the inputs to the program in a convenient way. You may use the following syntax: ./nsga2r random_seed <inp_file.in, where "inp_file.in" is the file that stores all the input parameters ---------------------------------------------------------------------------     About the output files --------------------------------------------------------------------------- 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 containts 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 --------------------------------------------------------------------------- adaptive_nsga: 2 --> A^2 NSGA-III, 1 --> A NSGA-III, 0 --> NSGA-III" popsize: This variable stores the population size (a multiple of 4) ngen: Number of generations nobj: Number of objectives ncon: Number of inequality constraints neqcon: Number of equality 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 define your own objective and constraint functions. You can also link other source files with the code depending on your need. Following points are to be kept in mind while writing objective and constraint functions. 1. The code has been written for minimization of objectives (min f_i). If you want to maximize a function, you may use negetive 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 negetive 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 --------------------------------------------------------------------------- global.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 realtime using gnuplot dominance.c: Routine to perofrm 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 referencepoints.c: Reference points implementation metris.c: Inverted Generational Distace (IGD) ---------------------------------------------------------------------------   Please feel free to send questions/comments/doubts/suggestions/bugs etc. to deb@iitk.ac.in about NSGA-II to   Dr. Kalyanmoy Deb 14th June 2005 http://www.iitk.ac.in/kangal/   --------------------------------------------------------------------------- Please feel free to send questions/comments/doubts/suggestions/bugs etc about NSGA-III A-NSGA-III and A^2-NSGA-III to   Luis Felipe Ariza Vesga 17th Apr 2019 lfarizav@unal.edu.co lfarizav@gmail.com Some videos on Youtube: https://www.youtube.com/channel/UCMgWIVOV9bJtIfIxQOYhOuw 

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[1] Luis Felipe Ariza Vesga, "NSGA-III", IEEE Dataport, 2019. [Online]. Available: http://dx.doi.org/10.21227/f5g3-0088. Accessed: May. 22, 2019.
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author = {Luis Felipe Ariza Vesga },
publisher = {IEEE Dataport},
title = {NSGA-III},
year = {2019} }
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Luis Felipe Ariza Vesga. (2019). NSGA-III. IEEE Dataport. http://dx.doi.org/10.21227/f5g3-0088
Luis Felipe Ariza Vesga, 2019. NSGA-III. Available at: http://dx.doi.org/10.21227/f5g3-0088.
Luis Felipe Ariza Vesga. (2019). "NSGA-III." Web.
1. Luis Felipe Ariza Vesga. NSGA-III [Internet]. IEEE Dataport; 2019. Available from : http://dx.doi.org/10.21227/f5g3-0088
Luis Felipe Ariza Vesga. "NSGA-III." doi: 10.21227/f5g3-0088