Swarm intelligence of artificial bees applied to In-Core Fuel Management Optimization

Artificial Bee Colony (ABC) algorithm is a relatively new member of swarm intelligence. ABC tries to simulate the intelligent behavior of real honey bees in food foraging and can be used for solving continuous optimization and multi-dimensional numeric problems. This paper introduces the Artificial Bee Colony with Random Keys (ABCRK), a modified ABC algorithm for solving combinatorial problems such as the In-Core Fuel Management Optimization (ICFMO). The ICFMO is a hard combinatorial optimization problem in Nuclear Engineering which during many years has been solved by expert knowledge. It aims at getting the best arrangement of fuel in the nuclear reactor core that leads to a maximization of the operating time. As a consequence, the operation cost decreases and money is saved. In this study, ABCRK is used for optimizing the ICFMO problem of a Brazilian “2-loop” Pressurized Water Reactor (PWR) Nuclear Power Plant (NPP) and the results obtained with the proposed algorithm are compared with those obtained by Genetic Algorithms (GA) and Particle Swarm Optimization (PSO). The results show that the performance of the ABCRK algorithm is better than or similar to that of other population-based algorithms, with the advantage of employing fewer control parameters.     

Optimization of fuel core loading pattern design in a VVER nuclear power reactors using Particle Swarm Optimization (PSO)

The two main goals in core fuel loading pattern design optimization are maximizing the core effective multiplication factor (K_eff) in order to extract the maximum energy, and keeping the local power peaking factor (P_q) lower than a predetermined value to maintain fuel integrity. In this research, a new strategy based on Particle Swarm Optimization (PSO) algorithm has been developed to optimize the fuel core loading pattern in a typical VVER. The PSO algorithm presents a simple social model by inspiration from bird collective behavior in finding food. A modified version of PSO algorithm for discrete variables has been developed and implemented successfully for the multi-objective optimization of fuel loading pattern design with constraints of keeping P_q lower than a predetermined value and maximizing K_eff. This strategy has been accomplished using WIMSD and CITATION calculation codes. Simulation results show that this algorithm can help in the acquisition of a new pattern without contravention of the constraints.     

Particle Swarm Optimization applied to the nuclear reload problem of a Pressurized Water Reactor

The concept of Swarm Intelligence is based on the ability of individuals to learn with their own experience in a group as well as to take advantage of the performance of other individuals, which are social–collaborative aspects of intelligence. In 1995, Kennedy and Eberhart presented the Particle Swarm Optimization (PSO), a Computational Intelligence metaheuristic technique. Since then, some PSO models for discrete search spaces have been developed for combinatorial optimization, although none of them presented satisfactory results to optimize a combinatorial problem such as the Nuclear Reactor Reload Problem (NRRP). In this sense, we have developed the Particle Swarm Optimization with Random Keys (PSORK) to optimize combinatorial problems. PSORK has been tested for benchmarks to validate its performance and to be compared to other techniques such as Ant Systems and Genetic Algorithms, and in order to analyze parameters to be applied to the NRRP. We also describe and discuss its performance and applications to the NRRP with a survey of the research and development of techniques to optimize the reloading operation of Angra 1 nuclear power plant, located at the Southeast of Brazil.     

A novel multi objective Loading Pattern Optimization by Gravitational Search Algorithm (GSA) for WWER1000 core

In this paper, a novel multi objective optimization algorithm, Gravitational Search Algorithm (GSA), is developed in order to implement in the Loading Pattern Optimization (LPO) of a nuclear reactor core. In recent decades several metaheuristic algorithms or computational intelligence methods have been expanded to optimize reactor core loading pattern. Regarding the coupled behavior of Neutronic and Thermal-Hydraulic (NTH) dynamics in a nuclear reactor core, proper loading pattern of fuel assemblies (FAs) depends on NTH aspects, simultaneously. Thus, obtaining optimal arrangement of FAs, in a core to meet special objective functions is a complex problem. Gravitational Search Algorithm (GSA) is constructed based on the law of Gravity and the notion of mass interactions, using the theory of Newtonian physics and searcher agents are the collection of masses. In this work, for multi objective optimization, the NTH aspects are included in fitness function. Neutronic goals include increasing multiplication factor (K_eff), decreasing of power picking factor (PPF) and flattening of the power density, also thermal–hydraulic (TH) goals include increasing critical heat flux (CHF) and decreasing average of fuel centers temperature. Therefore, at the first step, GSA method is compared with other metaheuristic algorithms on Shekel's Foxholes problem. In the second step for finding the best core pattern and implementation of the objectives listed, GSA algorithm has been performed for case of WWER1000 reactor. For the NTH calculations, PARCS (Purdue advanced reactor core simulator) and COBRA-EN codes are implemented, respectively. The results demonstrate that GSA algorithm have promising performance and can propose for other optimization problems of nuclear engineering field.     

Simultaneous Model Selection,Robust Data Reconciliation and Outlier Detection with Swarm Intelligence in a Thermal Reactor Power calculation

Data Reconciliation (DR) and Gross Errors Detection (GED) are techniques of increasing interest in Nuclear Power Plants and used in order to keep Mass and Energy balance into account. These Techniques have been extensively studied in Chemical and Petrochemical Industry due to its benefits, which include closing the mass and energy balance and the yield of promising financial results. Many techniques were developed to solve Data Reconciliation and Outlier Detection, some of them use, for example, Quadratic Programming, Lagrange Multipliers, Mixed-Integer NonLinear Programming and others use Evolutionary Algorithms like Genetic Algorithms (GA) and Particle Swarm Optimization (PSO). Nowadays, Robust Statistics is also increasing in interest and it is being used in order to surpass some methods limitation, e.g., assuming that the errors are Normally Distributed, which does not always reflects real problems situation. In this paper we present a novel method to perform simultaneously: (a) the tuning of the Hampel’s Three Part Redescending Estimator (HTPRE) constants; (b) the Robust Data Reconciliation and (c) the Gross Error Detection. The automatic tuning procedure is based on the minimization of the Robust Akaike Criteria and the Particle Swarm Algorithm is used as a global optimization method. Simulations were made considering a nonlinear process commonly used as a benchmark by several authors and also in calculating the Thermal Reactor Power based on a simplified example. The results show the potential use of the technique even in an on-line Process to solve Data Reconciliation and Gross Error Detection problem and do not need a separate procedure to tune first redescending estimator and later perform the DR and GED method.     

A class-based search for the in-core fuel management optimization of a pressurized water reactor

The In-Core Fuel Management Optimization (ICFMO) is a prominent problem in nuclear engineering, with high complexity and studied for more than 40 years. Besides manual optimization and knowledge-based methods, optimization metaheuristics such as Genetic Algorithms, Ant Colony Optimization and Particle Swarm Optimization have yielded outstanding results for the ICFMO. In the present article, the Class-Based Search (CBS) is presented for application to the ICFMO. It is a novel metaheuristic approach that performs the search based on the main nuclear characteristics of the fuel assemblies, such as reactivity. The CBS is then compared to the one of the state-of-art algorithms applied to the ICFMO, the Particle Swarm Optimization. Experiments were performed for the optimization of Angra 1 Nuclear Power Plant, located at the Southeast of Brazil. The CBS presented noticeable performance, providing Loading Patterns that yield a higher average of Effective Full Power Days in the simulation of Angra 1 NPP operation, according to our methodology.     

A Metropolis algorithm combined with Nelder–Mead Simplex applied to nuclear reactor core design

A hybridization of the recently introduced Particle Collision Algorithm (PCA) and the Nelder–Mead Simplex algorithm is introduced and applied to a core design optimization problem which was previously attacked by other metaheuristics. The optimization problem consists in adjusting several reactor cell parameters, such as dimensions, enrichment and materials, in order to minimize the average peak-factor in a three-enrichment-zone reactor, considering restrictions on the average thermal flux, criticality and sub-moderation. The new metaheuristic performs better than the genetic algorithm, particle swarm optimization, and the Metropolis algorithms PCA and the Great Deluge Algorithm, thus demonstrating its potential for other applications.     

PWR fuel management optimization using continuous particle swarm intelligence

The objective of nuclear fuel management is to minimize the cost of electrical energy generation subject to operational and safety constraints. In the present work, a core reload optimization package using continuous version of particle swarm optimization, CRCPSO, which is a combinatorial and discrete one has been developed and mapped on nuclear fuel loading pattern problems. This code is applicable to all types of PWR cores to optimize loading patterns. To evaluate the system, flattening of power inside a WWER-1000 core is considered as an objective function although other variables such as K_eff along power peaking factor, burn up and cycle length can be included. Optimization solutions, which improve the safety aspects of a nuclear reactor, may not lead to economical designs. The system performed well in comparison to the developed loading pattern optimizer using Hopfield along SA and GA.     

Multistart Simulated Annealing applied to a Reduced Scale Thermo-Hydraulic Loop of a Pressurized Water Reactor core

In this paper we investigate the reduced scale design of a third generation Pressurized Water Reactor core, with single phase flow under natural circulation, based on the Loss-of-Fluid Test facility. Recent works approach this issue applying metaheuristics such as Genetic Algorithms and Particle Swarm Optimization. Both approaches have, as a drawback, the high computational time to obtain an acceptable solution. Here, we propose an alternative method when computational time is critical. We approach the problem applying a Multistart Simulated Annealing method in order to obtain an acceptable solution in a lower computational time. Our results indicate a 98.7% computational time improvement over the state-of-the-art Particle Swarm Optimization method. Moreover, the Multistart Simulated Annealing results are 1.36% better than state-of-the-art Particle Swarm Optimization method. Thus, Multistart SA shows promising results and is a suitable method when time is critical.     

Identification of nuclear power plant transients using the Particle Swarm Optimization algorithm

In order to help nuclear power plant operator reduce his cognitive load and increase his available time to maintain the plant operating in a safe condition, transient identification systems have been devised to help operators identify possible plant transients and take fast and right corrective actions in due time. In the design of classification systems for identification of nuclear power plants transients, several artificial intelligence techniques, involving expert systems, neuro-fuzzy and genetic algorithms have been used. In this work we explore the ability of the Particle Swarm Optimization algorithm (PSO) as a tool for optimizing a distance-based discrimination transient classification method, giving also an innovative solution for searching the best set of prototypes for identification of transients. The Particle Swarm Optimization algorithm was successfully applied to the optimization of a nuclear power plant transient identification problem. Comparing the PSO to similar methods found in literature it has shown better results.     

Application of minimum plutonium criteria at EOC to optimize the fuel loading pattern in VVER-1000 reactors

Most of the strategies yet implemented to optimal fuel loading pattern design in nuclear power reactors, are based on maximizing the core effective multiplication factor (K_eff) to extract maximum energy and lowering the local power peaking factor (P_q) from a predetermined value. However, a new optimization criterion could be of interest, aiming at maximum burn-up of the plutonium content in fuel assemblies, i.e., minimization of remaining plutonium in spent fuel at the end of cycle (EOC). In this research, we developed a new strategy for optimal fuel core loading pattern of a VVER-1000 reactor, based on multi-objective optimization: lowering the P_q, maximization of the K_eff and minimization of remaining plutonium (Pu) in fuels at EOC. This strategy has been implemented considering exact calculations of fuel burn-up during the equilibrium cycle using WIMSD and CITATION calculation codes. We used the genetic algorithm to find the optimum fuel loading pattern. Simulation results show that this strategy can reduce the remaining Pu of the fuels at EOC while considering limitations on core power peaking and multiplication factor.     

New genetic algorithms (GA) to optimize PWR reactors: Part II: Simultaneous optimization of loading pattern and burnable poison placement for the TMI-1 reactor

In this paper, the GARCO–PSU (Genetic Algorithm Reactor Code Optimization–Pennsylvania State University) code simultaneously optimizes the core loading pattern (LP) and the burnable poison (BP) placement in a pressurized water reactor (PWR). The LP optimization and BP placement optimization are interconnected, but it is difficult to solve the combined problem due to its large size. Separating the problem into two sequential steps provides a practical way to solve the problem. However, the result of this method alone may not develop the real optimal solution. GARCO–PSU achieves solving the LP optimization and BP placement optimization simultaneously by developing an innovative genetic algorithm (GA). The classical representation of the genotype has been modified to incorporate in-core fuel management basic knowledge. GARCO has three modes; the first mode optimizes the LP only, the second mode optimizes the LP and BP placement in sequence. The third mode, which optimizes the LP and BP placement simultaneously, is described in this paper. GARCO, as stated in Part I, can be applied to all types of PWR core structures having different geometries with an unlimited number of fuel assembly (FA) types in the inventory.     

Optimization of depleted uranium loading in fresh core of large sized Indian PHWR by evolutionary algorithm

Pressurised Heavy Water Reactors (PHWRs) are based on Natural Uranium (NU) fuel and heavy water as moderator and coolant. At the beginning of reactor life of PHWR, if all NU bundles are loaded, the power peaking is high and full power cannot be drawn. In order to draw full power, it is possible to flatten the power in fresh core by loading some depleted uranium (DU) (or Thorium) bundles. The determination of the best possible locations of DU bundles which maximize economy and preserve safety is a constrained combinatorial optimization problem. This paper presents optimization of DU bundle distribution in the fresh core of the 700 MWe PHWR. An evolutionary technique based on Estimation of Distribution Algorithm (EDA) is used to determine the optimum DU loading pattern. The best suitable locations for DU bundles are determined using EDA. In order to meet some additional constraints, some additional DU bundles are placed at 11th and 12th bundle locations in few channels. These channels are selected manually. The overall aim of the optimization is to maximize K-effective and get 100% full power without violating safety parameters such as maximum permissible bundle power, channel power peaking factor and permitted reactivity worth in shut-down system. The optimum configuration is explicitly presented.     

DERMAGA – An alternative tool to generate random patterned-channel-age in CANDU fuel management analyses part I: Method development

In any reactor physics analysis, the instantaneous power distribution in the reactor core of any power reactor, including CANDU-type reactor, can be calculated when the actual bundle-wise burnup distribution is known. Considering the fact that CANDU utilizes the on-power refuelling to compensate for the reduction in reactivity due to fuel burnup, in the CANDU fuel management analysis, snapshots of power and burnup distributions can be obtained by simulating and tracking reactor operation over an extended period using various tools such as the *SIMULATE module of the reactor fuelling simulation program (RFSP) code. However, for some studies, such as an evaluation of a conceptual design of a next generation CANDU reactor, the preferred approach to obtain a snapshot of the power distribution in the core is based on the patterned-channel-age model implemented in the *INSTANTAN module of the RFSP code. The objective of this approach is to obtain a representative snapshot of core conditions quickly. Presently such patterns could be generated by a program called RANDIS which is implemented within the *INSTANTAN module. Presented in this paper is an alternative approach to derive the patterned-channel-age model where an optimization algorithm is utilized to find patterns which produce representative power distributions in the core. In the present analysis, the genetic algorithm (GA) technique has been successfully utilized to find a quasi-optimal patterned-channel-age. This paper is Part I of a two-part paper which highlights the development of this alternative method for generating patterned-channel-ages.     

Balancing exploration and exploitation in differential evolution via variable scaling factors: An application to practical problems

Some optimization problems in the field of nuclear engineering, as for example the incore nuclear fuel management and a nuclear reactor core design, are highly multimodal, requiring techniques that overcome local optima, exploring the search space and promoting the exploitation of its most promising areas. The differential evolution algorithm (DE) relies mainly on the mechanism of mutation, where an individual is perturbed using the weighted difference (with the so-called “scaling factor” F) between two randomly chosen individuals. DE's canonical version employs a constant value of F. However, this parameter should be variable in order to balance the exploration and exploitation of the search space. In this work, we test some variable scaling factors from the literature and present the novel exponential scaling factor. These methods are applied to two problems: the aforementioned core design and the turbine balancing problem, which is an NP-hard (i.e. intrinsically harder than those that can be solved in nondeterministic polynomial time) combinatorial optimization problem that can be used to assess the potential of an algorithm to be applied to fuel management optimization. DE with variable scaling factors perform well in both problems, showing potential to be used in other nuclear science and engineering optimization problems.     

Optimization of refueling cycle length by an enhanced PSO with novel mutation operator

In this paper, a new method for optimizing the fuel arrangement in a WWER-1000 reactor core during refueling cycle is presented. Finding the best configuration corresponding to the desired pattern, an enhanced PSO with a Novel Mutation operator is applied. WIMS and PARCS (Purdue Advanced Reactor Core Simulator) codes are used to calculate the neutronics cross sections and multiplication factor of core with corresponded power peaking factors (PPFs) during burn up cycles, respectively. Cross sections and burn up during cycle length were calculated by WIMS code, then core parameters were calculated by PARCS and finally hybridization of intelligent PSO (Particle Swarm Optimization) method and novel mutation were used to obtain optimal arrangement. The purposed algorithm is based on increasing burn up value and refueling cycle length and by keeping power peaking factor in safe margins. In this way, neutronic parameters of the reactor during operation cycle from BOC (Begin Of Cycle) to EOC (End Of Cycle), were calculated. Implementation of this algorithm has been done in MATLAB. In this case, Bushehr WWER-1000 NPP reactor was studied. The comparison between results and Final Safety Analysis Report (FSAR) data shows good agreement.     

Reloading pattern optimization of VVER-1000 reactors (in transient cycles) using imperialist competitive algorithm

In this paper, the Imperialist Competitive Algorithm was for the first time used for reloading pattern optimization of Bushehr's VVER-1000 reactor in the second cycle. Since the diversity of loadable fuels in the reactor core is at its highest level in the second cycle as compared to other operational cycles, it was decided to test optimization calculations in the most complicated state. To estimate the fuel compositions remained from the first cycle, and to precisely calculate the objective parameters of each of the arrangements examined in the optimization process, a program was designed based on the coupling of WIMS-D5B and CITATION-LDI2 codes in the neutronic section and the WERL code in the thermohydraulic part. The process of reloading pattern optimization was carried out in two states. In the first state, it was tried to obtain an arrangement with the maximum effective multiplication factor and the safe maximum power peaking factor. The objective of the second state was to obtain a reloading pattern with the flattest distribution of radial power peaking factor. In both of the optimization states, to ensure the optimality and safety of the proposed arrangements during the cycle, the behavior of thermo-neutronic parameters of the reactor core in the second cycle was studied through time-dependent calculations. The comparison between the results of this study and the arrangement proposed by the Russian contractor for a similar VVER-1000 reactor (Balakovo) revealed that the objective parameters of the arrangement proposed in this research provide more optimality. Finally, considering the innovative use of the imperialist competitive algorithm for optimizing reactor's reloading pattern and in view of the high speed of this algorithm, the present research can seemingly be a new step toward optimization of reloading patterns of nuclear reactors.     

Multiobjective fuel management optimization for self-fuel-providing LMFBR using genetic algorithms

One of the conceptual options under consideration for the future of nuclear power is the long-term development without fuel reprocessing. This concept is based on a reactor that requires no plutonium reprocessing for itself, and provides high efficiency of natural uranium utilization, so called Self-Fuel-Providing LMFBR (SFPR). Several design considerations were previously given to this reactor type which, however, suffer from some problems connected with insufficient power flattening, large reactivity swings during burnup cycles, and peak fuel burnup being significantly higher than recent technology experience, which is about 18% for U-10 wt%Zr metallic fuel to be considered. Yet, the mentioned core parameters demonstrate high sensitivity to the fuel management strategy selected for the reactor. Therefore, the aim of this study is to develop a practical tool for the improvement of the core characteristics by fuel management optimization, which is based on advanced optimization techniques such as Genetic Algorithms (GA). The calculation results obtained by a simplified reactor model can serve as estimates of achievable values for mentioned core parameters, which are necessary to make decisions at the preliminary optimization stage.     

Optimization of Refueling Scheme of Fast Reactor Core by Means of Man Machine Interactive Method

A computer system for performing quick survey and optimization has been developed to aid in-core fuel management of sodium cooled fast reactors. The method utilizes the conversational mode of computer operation, to perform on-line computation, display of results and acceptance of commands, thus permitting rapid exchange of information between the machine and the person in charge. To improve the overall efficiency of the system as problem-solver, an algorithm is introduced to provide for automated shuffling to determine the fuel loading patterns of successive cycles. This algorithm serves to model the refueling and shuffling arrangement after a prescribed optimized standard core pattern according to the extent of burnup of each fuel sub-assembly.

The proposed system is applied to problems of: (1) straightforward simulation of fuel performance in given in-core fuel management programs, covering core and radial blanket refueling and control rod positioning, (2) optimization, and (3) modification of in-core fuel management programs.

Several numerical examples are treated, to confirm the applicability of this conversational-mode problem-solving system to in-core fuel management.     

A new approach to the use of genetic algorithms to solve the pressurized water reactor's fuel management optimization problem

A Genetic Algorithm (GA) based system, coupling the computer codes GENESIS 5.0 and ANC through the interface ALGER has been developed aiming at pressurized water reactor's (PWR) fuel management optimization. An innovative codification, the List Model (LM), has been incorporated into the system. LM avoids the use of heuristic crossover operators and only generates valid nonrepetitive loading patterns in the reactor core. The LM has been used to solve the Traveling Salesman Problem (TSP). The results got for a benchmark problem were very satisfactory, in terms of precision and computational costs. The GENESIS/ALGER/ANC system has been successfully tested in optimization studies for Angra 1 power plant reloads.