Shuffled Frog Leaping Algorithm for Preemptive Project Scheduling Problems with Resource Vacations Based on Patterson Set

Algorithm 1

Decoding procedure for a feasible schedule 𝑞.

Step  1. Initialize, set 𝑡(𝑖,ℎ)=0 (𝑖=1,2,…,𝑁 (including two dummy nodes), ℎ=1,2,…,𝑑_𝑖), 𝐹={1}, 𝑗=1;

Step  2. If |𝐹|≤𝑁,𝑗=𝑗+1 and go to Step  3; else Stop;

Step  3. Choose the 𝑗th element 𝑞(𝑗) in 𝑞;

Step  4. Set 𝐸𝑆(𝑞(𝑗))=max{𝑡(𝑏,𝑑_𝑏)∣𝑏∈𝑃_𝑞(𝑗)}+1, if |𝑃_𝑞(𝑗)|≠0; else ES(q(j)) = 0;

Step  5. Set ℎ=1 and 𝑡(𝑞(𝑗),ℎ)=min{𝑡∣𝐸𝑆(𝑞(𝑗))≤𝑡,𝑟_{𝑞(𝑗)𝑘}≤𝑅_𝑘−∑_{𝑚∈𝐶(𝑡)}𝑟_𝑚𝑘,𝑘=1,2,…,𝑀};

Step  6. Set ℎ=ℎ+1;

Step  7. If ℎ≤𝑑_𝑞(𝑗),𝑡(𝑞(𝑗),ℎ)=min{𝑡∣𝑡(𝑞(𝑗),ℎ−1)≤𝑡,𝑟_{𝑞(𝑗)𝑘}≤𝑅_𝑘−∑_{𝑚∈𝐶(𝑡)}𝑟_𝑚𝑘,𝑘=1,2,…,𝑀} then go to Step  6; else go to

   Step  8;

Step  8. 𝐹=𝐹∪𝑞(𝑗), go to Step  2.