Binh-Korn

Problem definition

Objective function
```f = @(x) [4*sum(x.^2,2), ...
sum((x-5).^2,2)]```
Optimization settings
```o = struct	% initializing struct
g1 = @(x) 25 - (x(:,1)-5).^2 - x(:,2).^2
g2 = @(x) (x(:,1)-8).^2 + (x(:,2)+3).^2 - 7.7
o.g = @(x) g1(x).*(g1(x)<0) + g2(x).*(g2(x)<0)	% constraints
o.d = 2	% dimension of decision variable
o.lb = [0 0]	% lower bounds
o.ub = [5 3]	% upper bounds```

Problem properties

 dimension objectives smoothness 2 2 0

Optimization example with nsga2

Algorithm options
```o.maxit = 6	% number of iterations
o.pop = 40	% 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
optimview('nsga2',info)```

References

[1] Binh, T. and U. Korn, "MOBES: A multiobjective evolution strategy for constrained optimization problems. In Proceedings of the third international Conference on Genetic Algorithms (Mendel97), ", Brno, Czech Republic, pp. 176-182, 1997