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

Erez Gilad

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

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

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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Turinsky, P. J. , 2005, “ Nuclear Fuel Management Optimization: A Work in Progress,” Nucl. Technol., 151(1), pp. 3–8.
Turinsky, P. J. , Keller, P. M. , and Abdel-Khalik, H. S. , 2005, “ Evolution of Nuclear Fuel Management and Reactor Operational Aid Tools,” Nucl. Eng. Technol., 37(1), pp. 79–90.
Holland, J. H. , 1975, Adaptation in Natural and Artificial Systems, University of Michigan Press, Ann Arbor, MI.
Goldberg, D. E. , 1989, Genetic Algorithms in Search, Optimization and Machine Learning, 1st ed., Addison-Wesley Longman Publishing, Boston, MA.
Parks, G. T. , 1996, “ Multiobjective PWR Reload Core Design by Nondominated Genetic Algorithm Search,” Nucl. Sci. Eng., 124(1), pp. 178–187.
Haibach, B. V. , and Feltus, M. A. , 1997, “ A Study on the Optimization of Integral Fuel Burnable Absorbers Using the Genetic Algorithm Based Cigaro Fuel Management System,” Ann. Nucl. Energy, 24(6), pp. 439–448. [CrossRef]
Parks, G. T. , and Miller, I. , 1998, Selective Breeding in a Multiobjective Genetic Algorithm, Springer, Berlin, pp. 250–259.
Chapot, J. L. C. , Silva, F. C. D. , and Schirru, R. , 1999, “ A New Approach to the Use of Genetic Algorithms to Solve the Pressurized Water Reactor's Fuel Management Optimization Problem,” Ann. Nucl. Energy, 26(7), pp. 641–655. [CrossRef]
Toshinsky, V. G. , Sekimoto, H. , and Toshinsky, G. I. , 1999, “ Multiobjective Fuel Management Optimization for Self-Fuel-Providing LMFBR Using Genetic Algorithms,” Ann. Nucl. Energy, 26(9), pp. 783–802. [CrossRef]
Toshinsky, V. G. , Sekimoto, H. , and Toshinsky, G. I. , 2000, “ A Method to Improve Multiobjective Genetic Algorithm Optimization of a Self-Fuel-Providing LMFBR by Niche Induction Among Nondominated Solutions,” Ann. Nucl. Energy, 27(5), pp. 397–410. [CrossRef]
Hongchun, W. , 2001, “ Pressurized Water Reactor Reloading Optimization Using Genetic Algorithms,” Ann. Nucl. Energy, 28(13), pp. 1329–1341. [CrossRef]
Gang, P. , Feng, P. , and Rong, F. , 2002, “ Application of Genetic Algorithm in Research and Test Reactor Core Loading Pattern Optimization,” PHYSOR 2002, Seoul, Korea, Paper No. 8A-03.
Erdogan, A. , and Geckinli, M. , 2003, “ A PWR Reload Optimisation Code (XCore) Using Artificial Neural Networks and Genetic Algorithms,” Ann. Nucl. Energy, 30(1), pp. 35–53. [CrossRef]
Pereiraa, C. M. , and Lapa, C. M. , 2003, “ Coarse-Grained Parallel Genetic Algorithm Applied to a Nuclear Reactor Core Design Optimization Problem,” Ann. Nucl. Energy, 30(5), pp. 555–565. [CrossRef]
Ortiz, J. J. , and Requena, I. , 2004, “ An Order Coding Genetic Algorithm to Optimize Fuel Reloads in a Nuclear Boiling Water Reactor,” Nucl. Sci. Eng., 146(1), pp. 88–98.
Alim, F. , Ivanov, K. , and Levine, S. H. , 2008, “ New Genetic Algorithms (GA) to Optimize PWR Reactors Part I: Loading Pattern and Burnable Poison Placement Optimization Techniques for PWRs,” Ann. Nucl. Energy, 35(1), pp. 93–112. [CrossRef]
Alim, F. , Ivanov, K. , Yilmaz, S. , and Levine, S. H. , 2008, “ New Genetic Algorithms (GA) to Optimize PWR Reactors Part II: Simultaneous Optimization of Loading Pattern and Burnable Poison Placement for the TMI-1 Reactor,” Ann. Nucl. Energy, 35(1), pp. 113–120. [CrossRef]
Khoshahval, F. , Minuchehr, H. , and Zolfaghari, A. , 2011, “ Performance Evaluation of PSO and GA in PWR Core Loading Pattern Optimization,” Nucl. Eng. Des., 241(3), pp. 799–808. [CrossRef]
Rahmania, Y. , Pazirandeh, A. , Ghofrani, M. B. , and Sadighi, M. , 2013, “ Using a Combination of Weighting Factors, Genetic Algorithm and Ant Colony Methods to Speed up the Reloading Pattern Optimization of VVER-1000 Reactors,” Transactions of the Conference Safety Assurance of NPP With WWER Vol. 1, V. Mokhov, S. Sorokin, S. Titova, and E. Serdobintseva, eds., JSC OKB GIDROPRESS, Podolsk, Russia.
Zameer, A. , Mirza, S. M. , and Mirza, N. M. , 2014, “ Core Loading Pattern Optimization of a Typical Two-Loop 300 MWe PWR Using Simulated Annealing (SA), Novel Crossover Genetic Algorithms (GA) and Hybrid GA(SA) Schemes,” Ann. Nucl. Energy, 65, pp. 122–131. [CrossRef]
Mitsubishi Heavy Industries, Ltd., 2013, “APWR Design Control Document (DCD),” Mitsubishi Heavy Industries, Ltd., Tokyo, Japan, Tier 2, Chap. 4, Rev. 4.
Grundmann, U. , Rohde, U. , and Mittag, S. , 2000, “ DYN3D–Three-Dimensional Core Model for Steady State and Transient Analysis of Thermal Reactors,” PHYSOR 2000, Pittsburgh, PA, Paper No. 155.
Stammler, R. J., 2003, “HELIOS Methods,” Studsvik Scandpower, Kjeller, Norway.


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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.

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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.

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Fig. 1

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

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Fig. 4

Algorithm flow chart

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Fig. 5

The core vector data structure

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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.

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Fig. 7

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

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Fig. 8

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

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Fig. 9

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

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Fig. 10

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

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Fig. 11

keff as a function of maximum expVal with RW

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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

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Fig. 13

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

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Fig. 14

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

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Fig. 15

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

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Fig. 16

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



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