*3.4. Optimization Procedure*

The ISA algorithm is applied to find the optimal solution of the constrained multiobjective function shown in (4) and (5). The input variable is the maintenance activity

(*XMA(s, j)*) performed for each road section *s* and for treatment *j*. then the PCR of each section in a specific year is updated as in (9). The initialization of PCR, according to the constraints, is shown in the pseudo-code in Figure 2. The optimization procedure is applied for a number of sections and for a specified number of years, as shown in the pseudo-code in Figure 3.

$$PCR(\mathbf{s}, t) = PCR(\mathbf{s}, t - 1) + X\_{MA}(\mathbf{s}, t) \tag{9}$$

**Figure 2.** Pseudo-code of PCR initialization.

**Figure 3.** Pseudo-code of the application of the ISA algorithm for PMMS problem.
