## Chakong-Haimes

### Problem definition

##### Objective function
```f = @(x) [(x(:,1)-2).^2 + (x(:,2)-1).^2 + 2,...
9*x(:,1) - (x(:,2)-1).^2]```
##### Optimization settings
```o = struct	% initializing struct
g1 = @(x) 225 - sum(x.^2,2)
g2 = @(x) 10 - x(:,1) + 3*x(:,2)
o.g = @(x) g1(x).*(g1(x)<0) + g2(x).*(g2(x)<0)	% constraints
o.d = 2	% dimension of decision variable
o.lb = -20	% lower bounds
o.ub = 20	% upper bounds```

### Problem properties

 dimension objectives smoothness 2 2 -

### Optimization example with nsga2

##### Algorithm options
```o.maxit = 40	% 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
info.animfreq = 2	% frame frequency
optimview('nsga2',info)```

#### References

[1] V. Chankong, Y.Y. Haimes, "Multiobjective Decision Making Theory and Methodology", Elsevier Science, New York, 1983

#### Resources

Chakong-Haimes optimization source code