PSI - Issue 78

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

1946

consequence functions were adopted (e.g.,(Cardone 2016; Cardone et al. 2019)). The reconstruction cost was set at €2.064.000, assuming a unit cost of €1.720/m². In turn, downtime was estimated using the framework developed by (Molina Hutt et al. 2022), implemented via the TREADS tool. The downtime objective has been defined as the mean estimated time to reach re-occupancy following a seismic event corresponding to a 475-year return period. Repair time consequences were derived from the work of (Mucedero et al. 2025), allowing for consistent and literature informed estimation across different retrofitting strategies. 2.2. Non-dominated sorting genetic algorithm II The Non-dominated Sorting Genetic Algorithm II (NSGA-II) (Deb et al. 2002) is a widely used evolutionary algorithm for multi-objective optimisation. Each candidate represents an individual solution, encoded as a vector of design variables that correspond to the problem's dimensions. The encoding can be described in different formats, such as binary strings, real numbers, or other appropriate encoding methods. NSGA-II begins with an initial population that is typically generated randomly or through space-filling methods, such as Latin Hypercube Sampling (LHS). However, in the context of retrofitting design optimisation, given the solution space size for computational ease, biased or informed initialisation strategies can be employed to seed the population with feasible or near feasible designs. This can accelerate convergence by guiding the search toward promising regions of the design space while maintaining diversity across the population. Once initialised, NSGA-II follows an iterative process of non-dominated sorting, organising individuals into Pareto fronts based on dominance relations, and calculating a crowding distance metric to maintain diversity. Parent selection employs binary tournament selection using a crowded-comparison operator that prioritises high-quality and diverse solutions. Variation operators, such as simulated binary crossover and polynomial mutation, generate offspring. The combined parent-offspring population is re-ranked, and the best individuals are chosen for the next generation. This elitist approach retains top solutions while exploring new trade-offs, concluding when a set number of generations or convergence criteria are met, yielding a diverse set of Pareto-optimal solutions.

Fig. 1. General workflow of non-dominated sorting genetic algorithm II.

2.3. Biased initialisation with stochastic iterative retrofitting algorithm To identify a computationally efficient initial population while ensuring that the candidate solutions are feasible or nearly feasible, the Stochastic Iterative Retrofitting Algorithm (SIRA) (Figure 2), developed and employed in earlier studies (Yukselen et al. 2025a; 2025b), was adopted. SIRA ensures that the initial population used in the optimisation process includes retrofitting schemes that satisfy code requirements. The algorithm is based on how retrofitting decisions are commonly made in practice, typically guided by observed performance deficiencies and engineering judgment. A conventional approach involves identifying structural members that fail to meet performance criteria specified by the code and intervening iteratively until full compliance is achieved. However, in practice, engineers rarely retrofit all non-compliant members simultaneously. Instead, they tend to select a subset of members to intervene, often informed by principles such as maintaining structural regularity. While this decision-making process is difficult to formalise through fixed rules, SIRA captures the underlying logic through a stochastic mechanism. In doing so, it translates the uncertainty associated with subjective engineering judgment, known as epistemic uncertainty, into randomness that can be managed within the algorithm, referred to as aleatory uncertainty. At the beginning of the SIRA procedure, a probability value, P, is defined. This value represents the likelihood that a failing member will be retrofitted. The algorithm first evaluates the as-built condition of the structure and