Simultaneous and multi-criteria optimization of TS requirements and maintenance at NPPs

One of the main concerns of the nuclear industry is to improve the availability of safety-related systems at nuclear power plants (NPPs) to achieve high safety levels. The development of efficient testing and maintenance has been traditionally one of the different ways to guarantee high levels of systems availability, which are implemented at NPP through technical specification and maintenance requirements (TS&M). On the other hand, there is a widely recognized interest in using the probabilistic risk analysis (PRA) for risk-informed applications aimed to emphasize both effective risk control and effective resource expenditures at NPPs. TS&M-related parameters in a plant are associated with controlling risk or with satisfying requirements, and are candidate to be evaluated for their resource effectiveness in risk-informed applications. The resource versus risk-control effectiveness principles formally enter in optimization problems where the cost or the burden for the plant staff is to be minimized while the risk or the availability of the safety equipment is constrained to be at a given level, and vice versa. Optimization of TS&M has been found interesting from the very beginning. However, the resolution of such a kind of optimization problem has been limited to focus on only individual TS&M-related parameters (STI, AOT, PM frequency, etc.) and/or adopting an individual optimization criterion (availability, costs, plant risks, etc.). Nevertheless, a number of reasons exist (e.g. interaction, similar scope, etc.) that justify the growing interest in the last years to focus on the simultaneous and multi-criteria optimization of TS&M. In the simultaneous optimization of TS&M-related parameters based on risk (or unavailability) and cost, like in many other engineering optimization problems, one normally faces multi-modal and non-linear objective functions and a variety of both linear and non-linear constraints. Genetic algorithms (GAs) have proved their capability to solve these kinds of problems, although GAs are essentially unconstrained optimization techniques that require adaptation for the intended constrained optimization, where TS&M-related parameters act as the decision variables. This paper encompasses, in Section 2, the problem formulation where the objective function is derived and constraints that apply in the simultaneous and multi-criteria optimization of TS&M activities based on risk and cost functions at system level. Fundamentals of a steady-state GA (SSGA) as an optimization method is given in Section 3, which satisfies the above requirements, paying special attention to its use in constrained optimization problems. A simple case of application is provided in Section 4, focussing on TS&M-related parameters optimization for a stand-by safety-related system, which demonstrates how the SSGA-based optimization approach works at the system level, providing practical and complete alternatives beyond only mathematical solutions to a particular parameter. Finally, Section 5 presents our conclusions.