ES Recombination

In ES, we can also do recombination to combine information from multiple parents to produce a new child solution.

• I don’t really understand the point of this tbh. Isn’t this just a fucking genetic algorithm now. I guess mutation is the main operator in ES and recombination is the main operator in GA or some bullshit

Intermediate (arithmetic) recombination

The child is a weighted average of parents, common for real-valued vectors. Example (multiple parents):

$$y=\sum _{k=1}^{\mu }{w}_k{x}^{(k)},\sum _{k=1}^{\mu }{w}_k=1$$

Example (two parents):

$$y=\alpha x^{(1)}+(1-\alpha )x^{(2)},\alpha \in [0,1]$$

• This is literally just arithmetic crossover wtf

Discrete recombination

The child copies values directly from parents.

$$y_i=\{\begin{array}{ll}{x}_i^{(1)},& \text{w.p. }1/2\\ x_i^{(2)},& \text{w.p. }1/2\end{array}$$

Global discrete:

$$y=\{\begin{array}{ll}{x}^{(1)}& \text{w.p. }1/2\\ x^{(2)}& \text{w.p. }1/2\end{array}$$

Global Discrete Recombination

Choose the parent once and then copy the entire vector.