text: ## 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.
explanation: The document contains multiple sections, each discussing different topics related to optimization and mathematical problems. 
  
  1. The first section is a brief introduction with a play on words about "cuckoo search" and mentions a potential series of papers.
  2. The second section references two academic papers that critique and discuss the topic of metaphor-based metaheuristics in optimization.
  3. The third section introduces a mathematical problem involving a series where each element represents the number of times a specific value occurs in the series. This section includes a question about the series and provides an example.
  4. The fourth section discusses a constraint involving the sum of the K largest elements of a vector and how to formulate this constraint mathematically.
  
  The document contains multiple questions and answers related to mathematical problems.
distilabel_metadata.content: Evaluate the user given text extract and determine if it contains a math question and optionally and answer to this question.
  
  Output rules:
  
  1. Briefly describe the document and mention if it contains a question or a question and answer.
  2. Finalize the output with: Label: no-question,question,question-and-answer,multiple-question,multiple-question-and-answer
distilabel_metadata.role: system
distilabel_metadata.content: ## 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.
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The document contains multiple sections, each discussing different topics related to optimization and mathematical problems. 
  
  1. The first section is a brief introduction with a play on words about "cuckoo search" and mentions a potential series of papers.
  2. The second section references two academic papers that critique and discuss the topic of metaphor-based metaheuristics in optimization.
  3. The third section introduces a mathematical problem involving a series where each element represents the number of times a specific value occurs in the series. This section includes a question about the series and provides an example.
  4. The fourth section discusses a constraint involving the sum of the K largest elements of a vector and how to formulate this constraint mathematically.
  
  The document contains multiple questions and answers related to mathematical problems.
  
  Label: multiple-question-and-answer