This study investigates the performance of elitism-integrated Genetic Algorithms (GA) and Differential Evolution (DE) for the in-core fuel management (ICFM) of the Dalat Nuclear Research Reactor (DNRR). An elitist strategy was implemented within both GA and DE frameworks to preserve high-fidelity solutions throughout the evolutionary process. The ICFM problem for the DNRR entails the strategic arrangement of 100 fuel bundles with diverse burnup levels, aiming to maximize fuel utilization while enhancing safety margins. Comprehensive computations were performed to evaluate the sensitivity of the algorithms to the ratio between the elitist archive size (A) and population size (NP). Results demonstrate that elitism significantly bolsters GA performance, with optimal convergence achieved at NP = 30 and an archive size of 25% of NP. Furthermore, the integration of elitism enables DE to utilize larger population sizes effectively, overcoming the inherent limitations of its basic scheme and yielding superior solution quality. Statistical analysis reveals that the DE variant outperforms GA in terms of both convergence rate and solution diversity for DNRR fuel management. Notably, the optimal core configurations identified by both metaheuristics exceeded the performance of the reference core across all primary objectives: extending reactor operation by approximately 1700 hours and reducing the power peaking factor by nearly 4.0%.

This paper presents the sensitivity and uncertainty analysis for the Dalat Nuclear Research Reactor (DNRR) using MCNP6.2 and several data libraries such as ENDF/B-VII.1, ENDF/B-VIII.0, JENDL-4.0 and JENDL-5. Calculations have been performed for the first DNRR core with 88 highly enriched uranium fuel bundles. The effect of the new data libraries on the criticality analysis of the DNRR core has been analyzed based on 24 criticality conditions in comparison with the measurement. The largest discrepancies of the effective multiplication factor, keff, obtained with the four data libraries are −271, −297, −258 and −157 pcm, respectively, compared to the experiments. The values obtained with JENDL-5 are greater than that obtained with the other libraries by about 100 pcm in most cases. The nuclides with the major contributions to the positive sensitivities are U-235, H-1, C-12, Be-9, Al-27 and O-16. Whereas, the most negative sensitivity coefficients are found with the capture reactions of H-1, U-235, Al-27, U-238, B-10, Be-9, Fe-56, O-16 and C-12, and the alpha production of B-10. The highest uncertainties are obtained with the capture and elastic scattering of H-1, and the capture and fission of U-235. Subsequently, Al-27, O-16, Be-9, C-12, Fe-56,and U-238 have remarkable contribution to the uncertainty of the keff. The total uncertainties obtained with the four data libraries are 534.9, 466.6, 429.5 and 379.1 pcm, respectively.

This paper presents a detailed description of a new variant of differential evolution for nuclear reactor refueling optimization problem. This variant combines the elitism strategy with a discrete differential evolution. The elitism strategy allows non-dominated solutions found during the search and stored in the archive to participate in the differential evolution operation. The population size is the same as the archive size, and the number of non-dominated solutions participating in the search at a particular generation is controlled by a specific probability. The proposed method is successfully applied to a nuclear research reactor for its first refueling time to search for optimal loading patterns that both maximize the effective multiplication keff and minimize the power peaking factor PPF of the reactor. The optimal loading patterns can significantly improve the operational time and safety of the reactor compared to the loading pattern used in practice.

This paper investigates the performance of genetic algorithm (GA) with improved selection techniques, i.e. Tournament and Roulette Wheel, applied to in-core fuel management of the Dalat nuclear research reactor (DNRR). Numerical calculations have been performed based on the DNRR core with 100 HEU fuel bundles. The optimal fitness function was chosen to maximize the keff and minimize the power peaking factor. The statistical analysis using Mann-Whitney test shows that the performance of GA with Tournament selection is advantageous over the Roulette Wheel selection in the ICFM problem of the DNRR. The optimal core configurations obtained with the improved GA methods have the keff values greater by about 500 pcm, and the PPF lower by about 4.0% compared to the reference core.

This paper presents a comparative evaluation of the performance of Genetic Algorithm (GA) and Differential Evolution (DE) algorithm applied to in-core fuel management of the DNRR research reactor. Two GA variants corresponding to two selection operators, i.e., tournament (GA1) and roulette wheel (GA2) selections, respectively, with two-point crossover and scramble mutation were implemented for the ICFM problem. A comprehensive survey of the GA control parameters such as population size, crossover-type, mutation probability, and elitist archive size has been conducted to optimize the performance of the GAs. The basic DE was implemented with a standard mutation strategy DE/rand/1/bin. Numerical computations were performed based on the DNRR research reactor core loaded with 100 highly enriched uranium fuel (HEU) bundles for evaluating the performance of the GA and DE algorithms. Two main objectives were included in the fitness function to maximize the fuel cycle length and flatten the power distribution. The performance of the two GA variants and the basic DE was investigated with the same population size, fitness function, and convergence criterion. Each method was performed with 50 independent runs, and the best fitness values were collected for statistical analysis using Kruskal–Wallis and Mann–Whitney tests in comparison among the three methods. The statistical analysis shows that the performance of GA1 with tournament selection and DE are not significantly different and are better than GA2 with roulette wheel selection. DE is stable and efficient in exploring the search space to approach the global optimal solution in most runs. While, GA1 and GA2 were trapped at local optima by about 26% and 38%, respectively. However, the best solutions obtained with GA1 and GA2 after 50 independent runs are better than that obtained with DE in term of fitness values. This suggests an improvement of the basic DE is needed to maintain the potential good solutions during the evolution process.

A discrete differential evolution (DE) method has been applied to the problem of fuel loading pattern optimization of the Dalat Nuclear Research Reactor (DNRR). A classic strategy DE/rand/l/bin was chosen for the mutation of the DE method. Numerical calculations have been performed based on the core configuration of 100 highly enriched uranium (HEU) fuel bundles with various burnup levels. Comparison of the performance between the DE method and a genetic algorithm (GA) was also carried out. The optimal LPs obtained from the two methods are significantly better than the reference core. DE is more advantageous in exploring search space and approaching a global optimum than GA.

This paper presents the analysis of criticality and control rod worth of the Dalat Nuclear Research Reactor (DNRR) using the SRAC and MCNP5 codes. Criticality calculations were conducted for 49 core configurations of the DNRR established experimentally during the startup period. Reactivity worth of the automatic regulating rod was analyzed in comparison with the measurement data. The impact of various nuclear data libraries (ENDF/B and JENDL) on the criticality and control rod worth analysis of the DNRR were also investigated in comparison between the results obtained using the two codes and the measurement data. The results show that the criticality was predicted within 770 pcm for the calculated cases using the two codes with the ENDF/B-VII.0, JENDL-3.3 and JENDL-4.0 libraries. For the working core with 88 fuel bundles, the criticality was predicted with the discrepancy less than 330 pcm compared to the experiments. This implies that the ENDF/B and JENDL libraries are suitable to analyse the criticality of the DNRR core loaded with the Russian VVR-M2 fuel type. Reactivity worth analysis of the AR rod shows the results were in agreement among the three nuclear data libraries with the discrepancy less than 5%. In most cases, the relative discrepancy is less than about 12% compared to the measurements. The largest discrepancy of the integral reactivity worth is about 17%.

This paper presents the determination of the fuel burnup distribution of the Dalat nuclear research reactor (DNRR) using a method of measurements at subcritical conditions. The method is based on the assumption of linear dependence of the reactivity on the burnup of fuel bundles and the measurements at subcritical conditions. The measurements were taken for seven selected fuel bundles in two different measuring sequences. The measured burnup values have also been compared with the calculations for verifying the method and the measurement procedure. The results obtained with the three detectors have a good agreement with each other with a discrepancy less than 1.0%. The errors of the measured burnup values are within 6%. Comparison between the calculated and measured burnup values shows that the discrepancy of the C/E ratio is within 9% compared to unity. The results indicate that the method of measurements at subcritical conditions could be well applied to determine the relative burnup distribution of the DNRR.

This work suggests a method for determining the activities of cylindrical radioactive samples. The self-attenuation factor was applied for providing the self-absorption correction of gamma rays in the sample material. The experimental measurement of a 238U reference sample and the calculation using the MCNP5 code allow obtaining the semi-empirical formulae of detecting efficiencies for the gamma energies ranged from 185 to 1764keV. These formulae were used to determine the activities of the 238U, 226Ra, 232Th, 137Cs and 40K nuclides in the IAEA RGU-1, IAEA-434, IAEA RGTh-1, IAEA-152 and IAEA RGK-1 radioactive standards. The coincidence summing corrections for gamma rays in the 238U and 232Th series were applied. The activities obtained in this work were in good agreement with the reference values.

This paper presents a new approach based on a binary mixed integer coded genetic algorithm in conjunction with the weighted sum method for multi-objective optimization of fuel loading patterns for nuclear research reactors. The proposed genetic algorithm works with two types of chromosomes: binary and integer chromosomes, and consists of two types of genetic operators: one working on binary chromosomes and the other working on integer chromosomes. The algorithm automatically searches for the most suitable weighting factors of the weighting function and the optimal fuel loading patterns in the search process. Illustrative calculations are implemented for a research reactor type TRIGA MARK II loaded with the Russian VVR-M2 fuels. Results show that the proposed genetic algorithm can successfully search for both the best weighting factors and a set of approximate optimal loading patterns that maximize the effective multiplication factor and minimize the power peaking factor while satisfying operational and safety constraints for the research reactor.

In this paper, an investigation on the dependence of the effective multiplication factor, k(eff), on moderator temperature for various thicknesses of the upper beryllium reflector in reactor conditions with different fuel burnups for the Miniature Neutron Source Reactor is carried out. Based on the linear dependence of k(eff) on moderator temperature, an approach to calculate the moderator temperature coefficient of reactivity, (alpha) over bar (T), at different temperatures and its average value, (alpha) over bar (T), in a range of temperatures directly through the moderator temperature is developed. Calculations are performed to evaluate the effect of change in the upper reflector thickness on the moderator temperature coefficient of reactivity for the fresh core and reactor conditions with different fuel burnups. Calculated results indicate that (alpha) over bar (T) increases with the increased beryllium thickness, but decreases with the increasing fuel burnup. Analysis of calculated results provides an additional insight into the relation of the upper reflector thickness, the neutron energy spectrum in the reactor core, and the moderator temperature coefficient of reactivity.

The essential issue in analyzing the activity of 238U in an HPGe detector based gamma spectrometer via 63.3keV line is relating to the strong self-absorption of this weak gamma ray in sample material. The present work suggests a method of the self-absorption corrections for 63.3keV gamma rays by a combination of experimental measurements and Monte Carlo MCNP5 calculations. The effects of sample chemical composition, density and geometry were calculated in terms of self-attenuation factors. The method, developed for a cylindrical sample geometry, accounted for variable sample heights and densities. The analysis of 238U activity was applied for three main soil types in Vietnam, which are grey, alluvial and red soils. The results obtained with the above outlined method were in good agreement with those derived by other methods.

This paper presents results of the evaluated group constants for fuel and other important materials of the Miniature Neutron Source Reactor (MNSR) and the moderator temperature coefficient of reactivity through global reactor calculation. In this study, the group constants were calculated with the WIMSD code and the global reactor calculation is accomplished by the CITATION code. This work also presents a method for evaluation of the moderator temperatures directly through the values of moderator temperature for MNSRs. This method provides simple analytical representation convenient for reactor kinetics calculation and reactor safety assessment.

This work aims at improving the detection efficiency of an HPGe detector based gamma spectrometer for measurements of environmental radioactivity sample. Application of a simple genetic algorithm and the Monte Carlo simulation computer code MCNP5 allows to search for optimal dimensions of the Marinelli beaker typed source geometry that maximizes the detector efficiency for a fixed configuration of the gamma spectrometer. The interested gamma energies are in the range of 255-1926 keV. Optimization calculation was repeated several times to deduce average dimensions of an optimal Marinelli beaker typed sample with a volume of 450 cm(3). Effects of gamma energy, sample chemical composition and sample density on the optimal dimensions were also investigated. Calculated results showed that the effects were negligible. A validated experiment with arrangements using an optimal beaker and three other ones was carried out to verify calculated results. It is shown that experimental and calculated results of the detector efficiency are in a good agreement.

Bai bao nay trinh bay kết quả đanh gia hằng số nhom đối với nhien liệu va cac vật liệu quan trọng trong vung hoạt của lo phản ứng hạt nhân MNSR va hệ số nhiệt độ chất lam chậm của độ phản ứng của lo phản ứng nay thong qua tinh toan toan lo. Trong nghien cứu nay, hằng số nhom được tinh toan bằng chương trinh WIMSD va tinh toan toan lo được thực hiện bằng chương trinh CITATION. Cong trinh nay cũng trinh bay một phương phap đanh gia hệ số nhiệt độ chất lam chậm của độ phản ứng tại cac nhiệt độ khac nhau va gia trị trung binh của no trong một khoảng nhiệt độ trực tiếp thong qua gia trị của nhiệt độ chất lam chậm đối với lo phản ứng loại MNSR. Phương phap nay cung cấp một biểu dien toan học thuận lợi cho cac tinh toan động học va đanh gia an toan lo phản ứng hạt nhân.

This article presents results obtained from a research into an application of simulated annealing method to the in-core fuel reloading pattern optimization for a research reactor. The decision variable of the optimization problem is a fuel reloading pattern for the next cycle after the present cycle finishes. The objective function maximizes the effective multiplication factor keff at the beginning of cycle while it is established to include an important safety paramater – the power peaking factor, in search process. A procedure for searching the optimal solutions was formed and a computer code was developed in the Fortran language running on PCs. Nuclear safety parameters for the optimization problem are provided from the results of the multigroup neutron diffusion theory computation program CITATION. A sample calculation was performed to find the optimal fuel reloading patterns for the second cycle of the Dalat research reactor and the results are presented in this article.

This article presents results from an application of a genetic algorithm (GA) to the fuel reload optimization for a research reactor. In this work, we proposed an improved model of the problem and a new coding procedure for the GA to automatically search for optimal fuel loading patterns most suitable for the research reactor. The model consists of an objective function, which maximizes the effective multiplication factor and minimizes the power peaking factor, and operational and safety constraints. The new coding procedure is used to handle a constraint on the limited number of fuel shuffles in a refueling operation. The GA works with an elitist selection based on the elitism strategy and the roulette wheel spin method, a modified one-point crossover and a simple mutation. A computer program was developed in FORTRAN 90 running on a Pentium III personal computer to perform illustrative calculations for a research reactor type TRIGA MARK II. Results from illustrative calculations show that the GA can successfully search for the optimal loading patterns, which can be employed to establish a simple refueling scheme for the reactor with a limited number of fuel shuffles in a practical refueling operation.

Trong thời gian gần đây việc mo hinh hoa hệ phổ kế gamma dung detector ban dẫn sieu tinh khiết HPGe bằng phương phap Monte Carlo cho kết quả kha phu hợp với thực nghiệm khi hiệu chỉnh tối ưu cac thong số detector. Cong trinh nay phân tich ảnh hưởng của cac thong số detector len hiệu suất của no đối với detector HPGe GC1518 của hang Canberra Industries, Inc. đặt tại Trung tâm Hạt nhân TP Hồ Chi Minh. Tam thong số detector đa được khảo sat tren cơ sở cac gia trị va dung sai của chung do nha sản xuất cung cấp. Tinh toan theo chương trinh MCNP4C2 cho thấy rằng, trong 8 thong số đo chỉ co bề day lớp germanium bất hoạt co ảnh hưởng đang kể đến hiệu suất detector. Như vậy bề day lớp germanium bất hoạt được coi la thong số quan trọng nhất khi hiệu chỉnh cac thong số detector để lam phu hợp giữa tinh toan Monte Carlo với thực nghiệm.