zdt4

Problem definition

Objective function
k = @(x) 91 + sum(x(:,2:end).^2,2) - 10*sum(cos(4*pi*x(:,2:end)),2)
h = @(x,y) 1 - real(sqrt(x./y))
f = @(x) [x(:,1), k(x).*h(x(:,1),k(x))]
Optimization settings
o = struct	
% initializing struct

o.d = 10	
% dimension of decision variable

o.lb = [0 -5*ones(1,9)]	
% lower bounds

o.ub = [1 5*ones(1,9)] 	
% upper bounds

Problem properties

dimension objectives smoothness
10 2 0

Optimization example with nsga2

Algorithm options
o.maxit = 250	
% number of iterations 

o.pop = 100	
% number of population
Optimization 
rng(0)	
% for tractability 

[popPos,popFront,popCost,popInfo,traceIt] = nsga2(f,o)	
% running minimization
Animation 
rng(0)
[~,~,~,~,~,info] = nsga2(f,o)
info.plot = 'pareto'
info.animate = true	
% plot animation 

info.animfreq = 10	
% frame frequency 

info.animstart = 80	
% iteration to start animation 

info.yAxisMax = 1.2
optimview('nsga2',info)

References

[1] E. Zitzler, K. Deb, and L. Thiele. "Comparison of Multiobjective Evolutionary Algorithms: Empirical Results", Evolutionary Computation, 8(2):173-195, 2000

Related functions

nsga2 | plot | scatter