## Monday, November 28, 2022

### Cuckoo search is a bit cuckoo

Excuses for the lame title.

This could be the start of a very extended series of papers.

### References

1. Christian L. Camacho-Villalón, Marco Dorigo, Thomas Stützle, An analysis of why cuckoo search does not bring any novel ideas to optimization, Computers & Operations Research, Volume 142, 2022, https://www.sciencedirect.com/science/article/pii/S0305054822000442.
2. Aranha, C., Camacho Villalón, C.L., Campelo, F. et al. Metaphor-based metaheuristics, a call for action: the elephant in the room. Swarm Intell 16, 1–6 (2022)

## Tuesday, November 22, 2022

### A strange series

In [1] a question is posed about a somewhat strange series. Let $$i \in \{ 0,\dots,n\}$$. Then we require:

• $$\color{darkred}x_i \in \{0,1,2,\dots\}$$,
• $$\color{darkred}x_i$$ is equal to the number of times the value $$i$$ occurs in the series. In mathematical terms, one could say: $\color{darkred}x_i = |\{j:\color{darkred}x_j=i\}|$ (here $$|S|$$ is the cardinality of the set $$S$$).

An example for $$n=4$$ is:

index  0 1 2 3 4
value  2 1 2 0 0

## Tuesday, November 8, 2022

### sum of K largest

Consider a vector of variables $$\color{darkred}x_i$$. We want to impose the constraint: $\text{sum of K largest \color{darkred}x_i} \le 0.5\sum_i \color{darkred}x_i$ I.e. the sum of the largest $$K$$ values are less than half of the total. Sometimes this is expressed mathematically as $\sum_{i=1}^K \color{darkred}x_{[i]} \le 0.5\sum_i \color{darkred}x_i$ where $$\color{darkred}x_{[i]}$$ is an ordered version of $$\color{darkred}x_i$$ with $$\color{darkred}x_{[1]}\ge\color{darkred}x_{[2]} \ge \color{darkred}x_{[3]} \dots$$. There are several formulations for this constraint, all of them interesting, I think.