## 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

#### Resources

zdt4 optimization source code