, Nikos D. LagarosAbstractThe application of the performance-based seismic design concept using alternative problem formulations is presentedin this work. The formulations discussed, are implemented within an automated structural design framework using ametaheuristic optimisation algorithm. Such frameworks are able to accommodate any advanced -linear or nonlinear,static or dynamic- analysis procedure and thus replace, the conventional trial-and-error process. The formulationspresented treat the seismic design problem in a deterministic or a probabilistic manner, with one or more objectivesthat represent the initial cost or the cost of future earthquake losses that may occur during the lifetime of a structuralsystem. The implementations presented are all consistent with the performance-based design concept and take intoconsideration the structural response at a number of limit-states, from serviceability to collapse.Keywords: Performance-based design, Reliability-based optimisation, Particle swarm optimization, Pushoveranalysis, Life-cycle cost, Single and multiple objectives.Contents1 Introduction 12 Seismic design problem formulations 22.1 Deterministic design . . . . . . . . . . 22.2 Reliability-based design . . . . . . . . . 22.3 Robust design . . . . . . . . . . . . . . 32.4 Minimum life-cycle cost design . . . . 33 Design objectives 34 Metaheuristic Algorithms 44.1 Particle Swarm Optimization for single-objective problems . . . . . . . . . . . 44.2 Particle Swarm Optimization for multi-objective problems . . . . . . . . . . . 55 The “design” phase 65.1 Outline . . . . . . . . . . . . . . . . . 65.2 Analysis procedures . . . . . . . . . . . 65.2.1 Static pushover analysis . . . . 75.2.2 Nonlinear response historyanalysis . . . . . . . . . . . . . 75.3 Acceptance criteria . . . . . . . . . . . 86 Performance-based earthquake engineering 86.1 Direct calculation of the limit-stateprobabilities . . . . . . . . . . . . . . . 86.2 Monte Carlo Simulation . . . . . . . . 96.3 First Order Reliability Method (FORM) 96.4 The FEMA/SAC method . . . . . . . . 107 Life-Cycle Cost calculation 108 Modelling and Finite Element analysis 119 Numerical Example 1110 Conclusions 121. IntroductionPerformance-based earthquake engineering (PBEE)implies the design, evaluation, construction and main-tenance of engineering facilities in order to meet theobjectives set by the society and the owners/users ofa facility. In the case of earthquakes, the aim is tomake structures having a predictable and reliable per-formance, or in other words, the structures should beable to resist earthquakes with quantifiable confidencein order to assist design engineers to take decisions re-garding the desired performance. Therefore, the modernconceptual approach of seismic structural design is thatstructures should meet multiple performance-based ob-jectives defined for a number of different hazard levelsranging form earthquakes with small intensity and small
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