Designing the reactor’s core using genetic algorithms

Our new paper on “Novel genetic algorithm for loading pattern optimization based on core physics heuristics” is now online!

Israeli & Gilad, 2018, Ann. Nucl. Energy 118, 35–48.

This study, which was carried out by Ph.D candidate Ella Israeli and her supervisor Dr. Erez Gilad, is of true inter-disciplinary nature in the sense that a combination of expertise in both evolutionary algorithms and nuclear reactor physics is required. This field of research is active and relevant, and has been for many years, but the successful application of modern evolutionary algorithms for solving such problems is only just beginning.

Abstract:

A genetic algorithm based on novel genetic operators is implemented for the problem of nuclear fuel loading pattern optimization. This is achieved using rank selection or tournament selection and novel crossover operator and fitness function constructions, e.g., improved crossover and mutation operators by considering the chromosomes as permutations (which is a specific feature of the loading pattern problem) and the ‘‘stage fitness function” that separates the different objectives of the optimization. Another novel feature of the algorithm is the consideration of the geometric nature of the problem and the desired loading pattern solutions. A new geometric crossover is developed to utilize this geometric knowledge and its implementation exhibits good results. A comprehensive study is performed on the effect of different adaptive mutation strategies on the performances of the algorithm. The new algorithm is implemented and applied to two benchmark problems and used to study the effect of boundary conditions on the symmetry of the obtained best solutions.

Introduction & Background

The majority of nuclear reactors are operated in cycles with periodic complicated and expensive refueling outages. The fuel in the reactor core is not homogeneously burned and usually, a third of the (most depleted) fuel assemblies (FAs) are replaced during refueling. The loaded fresh FAs, together with the remaining depleted FAs, are rearranged to form a new core configuration (loading pattern, or LP). The new core configuration should maximize the energy production until the subsequent refueling outage (long cycle) while still satisfying all safety limitations and operational constraints. The LP optimization problem is of great importance for electric utilities as well as for research reactors operating with limited nuclear fuel repository.

A well-known method used for addressing the optimization problem of in-core fuel management is the evolutionary algorithm, and more specifically the genetic algorithm. It is a tool used to find solutions for complex optimization problems that mimic the evolutionary process seen in nature. It does so by creating a population of non-optimized initial solutions (LPs), choosing the better ones as parents (selection) according to how much they “fit” the optimization purpose, mating (crossover) and mutating them to breed better offspring solutions, just like any breeding process. However, many studies dealing with this problem thus far use basic and traditional implementations of the genetic algorithm, disregard important and relevant problem-related information, such as the geometrical structure of the core, or impose unnecessary restrictions to cut down on algorithm runtime.

For example, almost all studies in this field impose symmetry restrictions on the problem. The main reason for using symmetry constraints is an operational one; the different primary coolant loops of the nuclear power plant must maintain similar thermal-hydraulic conditions (e.g., flow rate, temperature, pressure) during nominal operation, imposing symmetry on the reactor core power production distribution. On the other hand, research reactors (RRs) operating at low power, whether cooled by one or more loops, are free of this operational constraint of symmetry. The same is true for Integral Reactors (IRs) in general, for Small Modular Reactors (SMRs) in particular, and especially for reactor designs characterized by a single coolant loop. Actually, most LPs that use burnt fuel from previous irradiation cycles, in both RRs and NPPs, are always slightly non-symmetric, even for equilibrium cores. Imposing symmetry on the problem eliminates a priori and unjustifiably any (even slightly) non-symmetric LPs which potentially perform better than symmetric ones.

In this work, a genetic algorithm is developed and implemented by using up-to-date selection and crossover operators and novel fitness function constructions (rank selection or tournament selection instead of the traditional roulette wheel selection operator; improved crossover and mutation operators that consider the chromosomes as permutations (which is a specific feature of the LP problem); highly adaptive mutation strategies based on the instantaneous genetic variance of the population; and the “stage fitness function” that separates the different objectives of the optimization for a simpler search). The new algorithm is implemented and applied to two benchmark problems and used to study the effect of boundary conditions on the symmetry of the obtained best solutions, with very good results.

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