Documentation of ranking
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[FitnV, RankV] = ranking(ObjV, RankOpt, SUBPOP, Goals, Chrom, ShareOpt);
RANK-based fitness assignment, single and multi objective, linear and nonlinear
This function performs single and multi objective ranking of objective values.
Linear and nonlinear distribution of the fitness values is possible.
Sharing between MO individuals (search space) and objective values (solution space)
Syntax: [FitnV, RankV] = ranking(ObjV, RankOpt, SUBPOP, Goals, Chrom, ShareOpt)
This function ranks individuals represented by their associated
cost, to be *minimized*, and returns a column vector FitnV
containing the corresponding individual fitnesses. For multiple
subpopulations the ranking is performed separately for each
subpopulation. Different size of every subpopulation and multiple
strategies are supported.
Single and multi-objective ranking are supported. For multi-objective
ranking the respective option must be set. Then PARETO ranking is
performed and (if provided) Goals are used.
The implementation follows in large parts the standard way of PARETO ranking
and goal attainment. For a good description have a look at many of the papers
of Carlos Fonseca (including his dissertation), for instance:
Fonseca, C. M.: Multiobjective Genetic Algorithms with Application to Control
Engineering Problems. Ph.D. Thesis, Department of Automatic Control and
Systems Engineering, University of Sheffield, Sheffield, U.K., 1995.
If individuals and ShareOpt are provided, sharing in search or solution space
is performed. The default method is sharing in search space. The switch to
sharing in solution space can be done at the end of the file inside the source
code (see ShareMethod).
For multiple objetives single objective ranking can be enforced. Then only
the first objective value ObjV(:,1) is used. The remaining objective values
ObjV(:,2:end) are ignored.
ObjV - Column vector/matrix containing the objective values of the
individuals in the current population (cost values).
if a matrix, multiobjective ranking assumed (at the moment
only singleobjective ranking - however, this is transparent)
each row corresponds to the objective value/s of one individual
RankOpt - (optional) If RankOpt is a scalar in [1, 2] linear ranking is
assumed and the scalar indicates the selective pressure.
If RankOpt is a 2 or 3 element vector:
RankOpt(1): SP - scalar indicating the selective pressure
RankOpt(2): RM - ranking method
RM = 0: linear ranking
RM = 1: non-linear ranking
RankOpt(3): RMO - single/multi objective ranking
RMO = 0: single objective ranking (even for multiple
objective values, first objective value
ObjV(:,1) is only used for ranking)
RMO > 0: multi objective ranking
If RankOpt is omitted or NaN, linear ranking, a selective
pressure of 2 and single objective ranking are assumed.
When RankOpt contains multiple rows (as many as subpopulations),
each row contains the parameters for one subpopulation.
If RankOpt is a vector with length(RankOpt) > 3 it containes
the fitness to be assigned to each rank. Then it should have
at least the length of the longest subpopulation (or as many
entries as rows in ObjV). Usually RankOpt is monotonously
decreasing. Rank 1 is the best individual!
SUBPOP - (optional) Vector/scalar containing number of individuals
per subpopulation/number of subpopulations
if omitted or NaN, 1 subpopulation is assumed
Goals - (optional) Row vector containing objective function goals for
multiobjective Pareto-ranking. Individuals who satisfy goals
are preferred in a Pareto fashion against these who do not
To satisfy a goal the respective objective value must be smaller
or equal to the Goal value.
Chrom - (optional) Column Vector/Matrix of Chromosomes needed for fitness
sharing in Individual space. If omitted or NaN no sharing in
individual space is performed
ShareOpt - (optional) 2-row-matrix, first row contains parameter for sharing
in individual space, second row for sharing in objective space.
ShareOpt(:, 1): ShareSigma, minimum cluster size for the spaces
ShareOpt(:, 2): ShareAlpha, penalty factor for single faults
ShareOpt(:, 3): ShareBeta , penalty factor for summarized faults
If omitted or NaN ShareAlpha and ShareBeta are set to 1.
If ShareSigma is omitted or NaN sharing of applied space is not possible
see geamain2 for the calculation of the ShareOpt parameters
FitnV - Column vector containing the fitness values of the
individuals in the current population.
RankV - Column vector containing the (Pareto-) Rank of the
Individuals in the current population
% It is assumed in the first examples, that the variable objv contains a
% column of objective values.
% This performs linear ranking with standard selective pressure, all objv
% are taken from individuals in one population
% The same as above, however, the objv are from 4 subpopulations
>> ranking(objv, , 4)
% Use linear ranking with selective pressure 1.5
>> ranking(objv, [1.5])
% Use non-linear ranking with selective pressure 1.5
>> ranking(objv, [1.5, 1])
% Use different strategies for every of the three subpopulation. The
% first subpop works with nonlinear ranking and SP=1.5, the second uses
% nonlinear ranking with SP=2.5 and the third linear ranking with SP=1.5.
>> ranking(objv, [1.5 1; 2.5 1; 1.5 0], 3)
% Similar to above, ranking method is computed internally. If SP > 2,
% nonlinear ranking is used, else linear ranking,
% the different size of each subpopulation is given directly
>> ranking(objv, [1.5; 2.5; 1.5], [11 23 16])
% multiple objectives per individual: the variable MObjv contains an
% array of objective values.
>> MObjv = [1 2 3; 1.5 2.5 3.5; 1 3 5; 2 1.4 8];
% Perform multi-objective ranking with linear ranking and selective
% pressure of 1.6, no sharing performed
>> ranking(MObjv, [1.6 0 1])
% Similar to above with different selective pressure for each subpopulation
% and goals defined
>> ranking(MObjv, [1.6 0 1; 1.2 0 1; 1.8 0 1; 1.4 0 1], 4, [1.6 2.9 4.2])
% MO ranking with sharing, Chrom and ShareOpt are needed
>> ranking(MObjv, [1.6 0 1; 1.2 0 1; 1.8 0 1; 1.4 0 1], 4, [1.6 2.9 4.2], [1 2; 1 3; 1 4; 1 5],[10; 1])
% Perform this ranking once with ShareMethod=0 (sharing between individuals)
% and once with ShareMethod=1 (sharing between objective values) and compare
% the fitness values (ShareMethod must be set in the source code)
See also: selection, compdiv, rankgoal, rankshare
This document is part of version 3.8
GEATbx: Genetic and Evolutionary Algorithm Toolbox for use with Matlab -
The Genetic and Evolutionary Algorithm Toolbox is not public domain
© 1994-2006 Hartmut Pohlheim, All Rights Reserved,