3.2.2. Chromosome Coding

Throughout the hot-rolling planning model solution with GA, the chromosome was represented by a coding sequence consisting of decimal natural numbers. For a rolling plan, the serial numbers of the slabs represented the genes in the chromosome coding. The chromosome coding could be expressed as the sequence of {a1, a2 ... ai}, in which the chromosome length was the total number *N* of pre-processed slabs. Figure 7 presents a schematic diagram demonstrating the chromosomal coding of the rolling plan, in which, a1, a50 and a100 were the serial numbers of the slabs; A0, A1 and A2 were the slab sequences constituting the rolling units.

**Figure 7.** Schematic diagram of rolling-plan chromosome coding.

#### 3.2.3. Chromosome Decoding

In different chromosomes, the numbers represented the serial numbers of the slabs, while the order of appearance was the order of processing. Figure 8 presents the flowchart of chromosome decoding. The procedure of rolling plan chromosome decoding was as follows:


**Figure 8.** Flow chart of chromosome decoding.
