PSI - Issue 78

Besim Yukselen et al. / Procedia Structural Integrity 78 (2026) 1943–1950

1948

4. Results The optimisation procedure, using NSGA-II with initial population identification via SIRA, was conducted for RC jacketing as retrofitting technique, with the following settings: (1) the number of generations was limited to 50, (2) parent selection was performed using binary tournament selection based on Pareto rank and crowding distance, (3) simulated binary crossover was used for recombination, and (4) polynomial mutation was applied during the mutation phase. The NSGA-II operations were implemented using the pymoo framework (Blank and Deb 2020). Table 2 summarises the performance of the as- built structure, the “seismic gap only” intervention, and selected Pareto-optimal retrofit solutions generated from both the SIRA-only and SIRA+NSGA-II optimisation schemes. The selected points correspond to the solutions that yield the minimum value for each of the four key objectives: cost, downtime (DT), expected annual loss (EAL), and environmental impact (EI). The as-built configuration exhibits the poorest performance, with an expected annual loss (EAL) of € 9.155 and a mean downtime to re -occupancy of 1.145 days. Even a minimal intervention strategy, such as adding a seismic gap, yields a significant improvement, reducing EAL by 66% (to € 3.085) and downtime by 75% (to 285 days). However, this solution is not code compliant and therefore not a viable standalone retrofit strategy. Table 2: Performance metrics for the as-built, seismic gap only, and Pareto-optimal solutions from SIRA only and SIRA with NSGA II, based on minimum cost, downtime, EAL, and EI.

SIRA-only Pareto

SIRA+NSGA-II Pareto

Seismic Gap Only

EAL Min.

DT Min.

Cost Min.

EI Min.

EAL Min.

DT Min.

Cost Min.

EI Min.

As built

EAL (€)

9155 1145

3085

374

579

567

567

246

392

587

587

Downtime (days)

285

10

5

5

5

5

4

11

11

Cost (€)

- -

- -

176k 106k

73k

73k

119k 140k

68k

68k

EI (tons CO 2 eq)

39

32

14

14

25

39

13

13

It is observed that, for both SIRA-only and SIRA+NSGA II, the solutions that minimise cost or environmental impact are identical within each set, and all optimised solutions have a mean downtime value under two weeks. Minimising the expected annual loss, however, increases installation costs and environmental impact, more than doubling in SIRA only and nearly doubling with NSGA-II, showing the multi-objective approach's improved ability to balance priorities. Figure 3 further illustrates the comparative performance of the retrofit solutions using a parallel coordinates plot. The SIRA-only solutions appear more scattered and limited in scope, particularly in their ability to reduce expected annual loss and downtime simultaneously. In contrast, the SIRA+NSGA-II solutions demonstrate a denser and broader distribution, indicating a more comprehensive exploration of the solution space.

Fig. 3. Parallel coordinates plot comparing SIRA only and SIRA+NSGA II solutions across cost, downtime, EAL, and EI.

Figure 4 presents partial two-dimensional Pareto plots, showing all pairwise combinations among the four key criteria: (1) EAL vs cost, (2) mean downtime for re-occupancy (RO) vs cost, (3) EAL vs EI, and (4) downtime vs EI. SIRA-only solutions (light blue) form a limited and tightly clustered set, whereas SIRA+NSGA-II solutions (red) define a broader and more efficient Pareto frontier. The SIRA+NSGA II front shows clear improvement in both Pareto dominance and distribution. For example, the EAL vs Cost plot demonstrates that SIRA+NSGA-II