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