Algorithm 4.

$m\text{\_}mutation(m,\varphi ,\tau ,P_{i,j},P_{i,j}^{\prime },P_{i,j}^{″},t)$

1:  // This function mutates exactly m positions. The inputs are the number of positions to mutate, sequence, target structure, pair        probabilities, nested pair probabilities, non-nested pair probabilities and the design template, respectively.

2:  mutation_count ← 0

3:  while mutation_count < m do

4:     i ← random(1, length(τ))

5:     if ϕi is a free nucleotide OR mutation_count = = (m − 1) then

6:        ϕ ← mutate_single_nucleotide(ϕ, τ, Pi, j, t)

7:        mutation_count ← mutation_count + 1

8:     end if

9:     if ϕi is not a single nucleotide then

10:        $\varphi \leftarrow mutate\text{\_}basepair(\varphi ,\tau ,P_{i,j}^{\prime },P_{i,j}^{″},t)$

11:        mutation_count ← mutation_count + 2

12:     end if

13:  end while

14:  Return ϕ