## Hajime-Yabumoto-Mori-Yoshikazu

### Problem definition

##### Objective function
`f  = @(x) [x(:,1).^2 - x(:,2), -0.5*x(:,1) - x(:,2) - 1]`
##### Optimization settings
```o = struct	% initializing struct
g1 = @(x) 6.5 - x(:,1)./6 - x(:,2)
g2 = @(x) 7.5 - 0.5*x(:,1) - x(:,2)
g3 = @(x) 30 - 5*x(:,1) - x(:,2)
o.g = @(x) g1(x).*(g1(x)<0) + g2(x).*(g2(x)<0) + g3(x).*(g3(x)<0)	% constraints
o.d = 2	% dimension of decision variable
o.lb = -7	% lower bounds
o.ub = 4	% upper bounds```

### Problem properties

 dimension objectives smoothness 2 2 -

### Optimization example with nsga2

##### Algorithm options
```o.maxit = 40	% 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 = 4	% frame frequency
optimview('nsga2',info)```

#### References

[1] Y. Hajime, N. Yabumoto, Mori and Yoshikazu, "Multiobjective optimization by means of the thermodynamical genetic algorithm", The 4th Int. Conf. on Parallel Problem Solving from Nature, pages 504-512, 1996