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Special Section Papers

# Novel Genetic Algorithms for Loading Pattern Optimization Using State-of-the-Art Operators and a Simple Test Case

[+] Author and Article Information
Ella Israeli

The Unit of Nuclear Engineering,
Ben-Gurion University of the Negev,
Beer-Sheva 84105, Israel
e-mail: ellaisra@post.bgu.ac.il

The Unit of Nuclear Engineering,
Ben-Gurion University of the Negev,
Beer-Sheva 84105, Israel

1Corresponding author.

Manuscript received October 30, 2016; final manuscript received December 26, 2016; published online May 25, 2017. Assoc. Editor: Ilan Yaar.

ASME J of Nuclear Rad Sci 3(3), 030901 (May 25, 2017) (10 pages) Paper No: NERS-16-1150; doi: 10.1115/1.4035883 History: Received October 30, 2016; Revised December 26, 2016

## Abstract

Novel genetic algorithms (GAs) are developed by using state-of-the-art selection and crossover operators, e.g., rank selection or tournament selection instead of the traditional roulette (fitness proportionate (FP)) selection operator and novel crossover and mutation operators by considering the chromosomes as permutations (which is a specific feature of the loading pattern (LP) problem). The algorithm is applied to a representative model of a modern pressurized water reactor (PWR) core and implemented using a single objective fitness function (FF), i.e., keff. The results obtained for some reference cases using this setup are excellent. They are obtained using a tournament selection operator with a linear ranking (LR) selection probability method and a new geometric crossover operator that allows for geometrical, rather than random, swaps of gene segments between the chromosomes and control over the sizes of the swapped segments. Finally, the effect of boundary conditions (BCs) on the symmetry of the obtained best solutions is studied and the validity of the “symmetric loading patterns” assumption is tested.

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## Figures

Fig. 1

A random LP representative of some first generation of an evolutionary process

Fig. 2

A schematic layout of core #1 fuel assemblies typical initial LP. Fuel type 1/2/3 represent 3.1/2.4/1.6 w/o 235U enrichment, respectively.

Fig. 3

A rough estimation (pre-GA) for the highest keff core LP for core #1 (Sec. 2.3). The different locations in the core indicate the different enrichment levels of the FAs, with central (peripheral) locations indicating higher (lower) enrichment.

Fig. 4

Algorithm flow chart

Fig. 5

The core vector data structure

Fig. 6

Top—the original cores and the mapping of the chromosome to the core. Bottom—the corresponding chromosomes, with each fuel type, e. g., I, II, III, represented by different shade. The cell randomly chosen for crossover is marked with bold border in the upper panel. The randomly chosen neighborhood size is 3 × 3. Segment parts that are not in the core are omitted.

Fig. 7

The cores after segments swap. Notice that the number of FAs of each type is not preserved.

Fig. 8

Cells outside the selected segment are chosen to switch fuel type, in order to restore the original fuel inventory

Fig. 9

The chosen cells are repositioned into the appropriate fuel type, resulting in two “legal” offspring cores

Fig. 10

The LP with the highest keff value produced by the GA algorithm with void BCs

Fig. 11

keff as a function of maximum expVal with RW

Fig. 12

LPs generated from optimizations with different parameter sets, all with maximum expVal = 1.8, alongside the evolution of their (lighter shades represent the maximum and minimum keff of each generation, whereas dark black represents the mean) and population variance

Fig. 13

The variance of the population as a function of generation number for different maximum expVal values (m) with RW selection

Fig. 14

keff as a function of tournament size for different maximum expVal values

Fig. 15

keff versus recGen. recGen values are 1, 30, 50, 70, 100, and 200.

Fig. 16

The LP with the highest keff value produced by the GA algorithm with reflective BCs

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