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The ICFMO is a prominent problem in Nuclear Engineering studied for more than 40 years. Characteristics such as a large number of feasible solutions, large number of local optima solutions, disconnected feasible regions, high-dimensionality and approximation hazards (Stevens et al., 1995). Its combinatorial characteristics, the lack of derivative i...
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... power. At that time, the shutdown of the NPP is necessary for the reloading operation, when the most burned FAs (approximately 1/3) are exchanged by fresh nuclear FAs. The ICFMO consists in searching for the best reloading pattern of FAs, with an objective function evaluated according to specific criteria and methods of Nuclear Reactor Physics. Fig. 1 depicts the simplified schematic representation of 121 nuclear FAs (view from top) of a PWR NPP such as Angra 1, in the Southeast of Brazil. In practice, flat power distributions (that is, without power peaks that could compromise safety) within the reactor core are desirable therefore the octant symmetry may be used, which reduces the ...
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... the RK approach, for a chromosome C 1 = [0.39 0.12 0.54 0.98 0.41], the decoded corresponding individual (a candidate solution for a five-dimensional combinatorial problem where no repetitions are allowed) would be I 1 = (2, 1, 5, 3, 4), since 0.12 is the lesser number and corresponds to the second allele; 0.39 corresponds to the first allele and so forth. For a chromosome C 2 = [0.08 0.36 0.15 0.99 0.76], the decoded individual would be I 2 = (1, 3, 2, 5, 4). ...
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... 0.54 0.98 0.41], the decoded corresponding individual (a candidate solution for a five-dimensional combinatorial problem where no repetitions are allowed) would be I 1 = (2, 1, 5, 3, 4), since 0.12 is the lesser number and corresponds to the second allele; 0.39 corresponds to the first allele and so forth. For a chromosome C 2 = [0.08 0.36 0.15 0.99 0.76], the decoded individual would be I 2 = (1, 3, 2, 5, 4). If a crossover operation would be performed between the feasible individuals I 1 and I 2 for the SMSP, TSP or ICFMO, with a crossing site between the second and third alleles, the resultant offspring composed of the descending individuals I 3 = (2, 1, 2, 5, 4) and I 4 = (1, 3, 5, 3, 4) would be unfeasible for the TSP and the ICFMO, since I 3 and I 4 are not possible solutions for these problems since there is repetition of elements. ...
Citations
... One industrial problem that demands efficient optimization techniques is the in-core reloading patterns optimization in nuclear reactors [6,7]. In-core reloading is a critical process in nuclear power plants, involving the arrangement of fuel assemblies within the reactor core to ensure optimal power distribution and safe operation. ...
Operation management of nuclear power plants consists of several computationally hard problems. Searching for an in-core fuel loading pattern is among them. The main challenge of this combinatorial optimization problem is the exponential growth of the search space with a number of loading elements. Here we study a reloading problem in a Quadratic Unconstrained Binary Optimization (QUBO) form. Such a form allows us to apply various techniques, including quantum annealing, classical simulated annealing, and quantum-inspired algorithm in order to find fuel reloading patterns for several realistic configurations of nuclear reactors. We present the results of benchmarking the in-core fuel management problem in the QUBO form using the aforementioned computational techniques. This work demonstrates potential applications of quantum computers and quantum-inspired algorithms in the energy industry.
... One industrial problem that demands efficient optimization techniques is the in-core reloading patterns optimization in nuclear reactors [6,7]. In-core reloading is a critical process in nuclear power plants, involving the arrangement of fuel assemblies within the reactor core to ensure optimal power distribution and safe operation. ...
Operation management of nuclear power plants consists of several computationally hard problems. Searching for an in-core fuel loading pattern is among them. The main challenge of this combinatorial optimization problem is the exponential growth of the search space with a number of loading elements. Here we study a reloading problem in a Quadratic Unconstrained Binary Optimization (QUBO) form. Such a form allows us to apply various techniques, including quantum annealing, classical simulated annealing, and quantum-inspired algorithms in order to find fuel reloading patterns for several realistic configurations of nuclear reactors. We present the results of benchmarking the in-core fuel management problem in the QUBO form using the aforementioned computational techniques. This work demonstrates potential applications of quantum computers and quantum-inspired algorithms in the energy industry.
... A number of solution techniques within the realms of mathematical programming, expert-or knowledge-based systems and metaheuristics, have been proposed for solving the ICFMO problem [2,5]. Metaheuristics have, in particular, emerged as the most prominent solution techniques applicable to the problem. ...
... Such an assignment of assemblies is referred to as a fuel reload configuration (or a loading pattern). The ICFMO problem is well known in the field of nuclear engineering and has been a subject of research for many years [1][2][3][4]. Characteristics associated with this problem include its large combinatorial decision space, multiple conflicting, nonlinear objective functions and constraints that generally cannot be expressed in closed form, and computationally expensive function evaluations using a reactor core simulator [5,6]. ...
... Furthermore, in this version of the AMALGAM method, a minimum value for N i t+1 is enforced at 4 as follows. Once N i t+1 has been calculated according to (2), any fractions are rounded to the nearest integer. If any value is smaller than the minimum of 4, that value is increased up to the minimum. ...
This paper is concerned with the problem of constrained multiobjective in-core fuel management optimisation (MICFMO) using, for the first time, a hyperheuristic technique as solution approach. A multiobjective hyperheuristic called the AMALGAM method (an evolutionary-based technique incorporating multiple sub-algorithms simultaneously) is compared to three previously-studied metaheuristics, namely the nondominated sorting genetic algorithm II, the Pareto ant colony optimisation algorithm and the multiobjective optimisation using cross-entropy method, in an attempt to improve upon the level of generality at which MICFMO may be conducted. This solution approach was motivated by a lack of consistent performance by the aforementioned metaheuristics when applied in isolation. Comparisons are conducted in the context of a test suite of several problem instances based on the SAFARI-1 nuclear research reactor. Nonparametric statistical analyses in respect of the optimisation results reveal that the AMALGAM method significantly outperforms the three metaheuristics in the majority of problem instances within the test suite. Additional comparisons are also performed between the proposed AMALGAM method and a randomised (or no-learning) version thereof, as well as a selection choice function-based multiobjective hyperheuristic available in the literature. It is found that the proposed method is superior to the choice function-based algorithm within the context of the MICFMO test suite, and yields results of similar quality when compared to its randomised version. The practical relevance of the hyperheuristic results is further demonstrated by comparing the solutions thus obtained to a reload configuration designed according to the current fuel assembly reload design approach followed at the SAFARI-1 reactor.
... The in-core fuel management optimisation (ICFMO) problem is a nonlinear assignment problem in which an optimal fuel reload configuration (or a loading pattern) is sought for a nuclear reactor core. It is a classical problem in the field of nuclear engineering and has been studied for several decades [1]. Fresh and partially burnt fuel assemblies from an available set have to be assigned to loading positions in a reactor core in such a way that the resulting configuration optimises reactor performance, while also ensuring that operational constraints are satisfied. ...
... Techniques involving mathematical programming and expert/ knowledge-based systems were utilised during the early years of research [2]. More recently, however, metaheuristic techniques, such as simulated annealing, tabu search, evolutionary algorithms and swarm intelligence algorithms, have been applied to ICFMO [1]. Research has also been aimed towards reducing the computational cost of function evaluations associated with ICFMO. ...
... The eight metaheuristics were implemented within the MA-TLAB software suite [34]. All calculations in this study were 1 A utility function represents a decision maker's preferences in explicit mathematical form such that the function provides a complete ordering in the objective space [22]. performed on an ® Intel Core™ i7-2720QM computer (2.20 GHz) with 8.00 GB of RAM, running a 64-bit Windows 7 Professional operating system. ...
In this paper, the topic of constrained multiobjective in-core fuel management optimisation (MICFMO) using metaheuristics is considered. Several modern and state-of-the-art metaheuristics from different classes, including evolutionary algorithms, local search algorithms, swarm intelligence algorithms, a probabilistic model-based algorithm and a harmony search algorithm, are compared in order to determine which approach is most suitable in the context of constrained MICFMO. A test suite of sixteen optimisation problem instances, based on the SAFARI-1 nuclear research reactor, has been established for the comparative study. The suite is partitioned into three classes, each consisting of problem instances having a different number of objectives, but subject to the same stringent constraint set. The effectiveness of a multiplicative penalty function constraint handling technique is also compared with the constrained-domination technique from the literature. The different optimisation approaches are compared in a nonparametric statistical analysis. The analysis reveals that multiplicative penalty function constraint handling is a competitive alternative to constrained-domination, and seems to be particularly effective in the context of bi-objective optimisation problems. In terms of the metaheuristic solution comparison, it is found that the nondominated sorting genetic algorithm II (NSGA-II), the Pareto ant colony optimisation (P-ACO) algorithm and the multiobjective optimisation using cross-entropy method (MOOCEM) are generally the best-performing metaheuristics across all three problem classes, along with the multiobjective variable neighbourhood search (MOVNS) in the bi-objective problem class. Furthermore, the practical relevance of the metaheuristic results is demonstrated by comparing the solutions thus obtained to the current SAFARI-1 reload configuration design approach.
... Various solution techniques have been proposed for solving the ICFMO problem during this time. These techniques include mathematical programming methods, expert/knowledge-based systems and, more recently, metaheuristics such as simulated annealing, tabu search, evolutionary and swarm intelligence algorithms (Meneses et al., 2010). Metaheuristics are approximate solution techniques designed specifically for obtaining high-quality solutions to optimisation problems within reasonable computation times. ...
... Metaheuristic techniques are well-suited for optimisation problems exhibiting the above-mentioned properties, and have succesfully been applied to ICFMO (Meneses et al., 2010). Recently, a metaheuristic called harmony search (HS) (Geem et al., 2001) has also been applied to ICFMO (Schlünz et al., 2012;Poursalehi et al., 2013b) and was found to yield competitive results when compared to a Hopfield neural network/simulated annealing hybrid method and a genetic algorithm. ...
The in-core fuel management optimisation (ICFMO) problem is the problem of finding an optimal fuel reload configuration for a nuclear reactor core. ICFMO may involve the pursuit of a single or multiple objectives, while satisfying several constraints. Very little multiobjective ICFMO research involving the fundamental notion of Pareto optimality has, however, been performed. In this paper, a unified methodology is proposed for the modelling and solution of single- and multiobjective ICFMO problems, be they constrained or unconstrained. With this methodology, ICFMO problems incorporating a variety of objectives and/or constraints may be modelled and solved rapidly, thus providing a cycle-to-cycle optimisation decision support capability for nuclear reactors. An augmented Chebyshev scalarising objective function is incorporated in the methodology for modelling any number of objectives, while an additive penalty function handles potential constraints. Furthermore, an adapted harmony search algorithm is used to solve a given ICFMO problem. The algorithm is able to yield a single solution or a nondominated set of solutions as result (depending on the number of objectives in a problem). The applicability of the methodology is demonstrated by solving (approximately) a variety of ICFMO test problems for the SAFARI-1 nuclear research reactor. The results indicate that the methodology may be used as an effective decision support tool for reactor operators tasked with designing reload configurations from cycle to cycle.
... A number of solution techniques have been proposed for solving the ICFMO problem, such as mathematical programming methods, expert/knowledge-based systems, simulated annealing, evolutionary algorithms, swarm intelligence algorithms and tabu search [4]. Although some research has been directed towards multiobjective ICFMO, most of these approaches involve the use of linear weighted sum aggregations of the objectives (see e.g. ...
The in-core fuel management optimisation (ICFMO) problem has been studied for several decades. Very little research has, however, been aimed at multiobjective optimisation involving the fundamental notion of Pareto optimality. In this paper, the recently developed multiobjective optimisation using the cross-entropy method (MOO CEM) algorithm is applied to a multiobjective ICFMO problem for the first time. A derivation of the MOO CEM algorithm is presented for ICFMO, along with a constraint handling technique. The algorithm
is applied to a biobjective test problem for the SAFARI-1 nuclear research reactor. The Pareto set approximated by the algorithm is compared to solutions obtained by typical operational reload strategies. The results indicate that the MOO CEM algorithm for multiobjective ICFMO is a robust and efficient method which is able to obtain a good spread of trade-off solutions. The method may therefore greatly aid in the decision making of a reactor operator tasked with designing reload configurations.
... These characteristics, as well as the multiobjective and combinatorial nature of the problem, clearly demonstrate that the CFROP is a difficult, ill-structured problem to solve. A number of solution techniques have been proposed in order to solve the problem, such as mathematical programming methods, expert systems, simulated annealing, evolutionary algorithms, swarm intelligence algorithms and tabu search [6]. However, the overwhelming majority of CFROP research has been orientated towards power reactors. ...
The core fuel reload optimisation problem (CFROP) refers to the problem of finding an optimal fuel loading configuration for a nuclear reactor core. The CFROP is typically multiobjective, nonlinear, discrete and combinatorial in nature. In this paper, a mathematical formulation of the CFROP for the SAFARI-1 nuclear research reactor is presented. The multiple objectives applicable to SAFARI-1 are aggregated into a single objective function. A harmony search algorithmwith a dimensionality reduction procedure is proposed as a solution technique for solving the problem approximately. The algorithm has been implemented on a personal computer and applied to solve the CFROP for a historic SAFARI-1 core. Fuel loading configurations that improve upon the historically chosen configuration were obtained by the algorithm. The results show that the solution approach has the capability of proposing good fuel loading configurations to assist the operators of SAFARI-1.
... These algorithms have distinct characteristics that might be interesting in different situations. Table 5shows results for the algorithms presented in literature based on data provided by Meneses et al. (2010). All these approaches were developed in the same conditions of the QEA presented in section 6. ...
Nuclear Reactor Reload Optimization Problem (NRROP), which focuses on the economics and safety of the Nuclear Power Plant (NPP), is a classical problem in Nuclear Engineering that has been studied for more than 40 years. For decades, the NRROP was carried out by specialists that used their knowledge and experience to build configurations of the reactor core aiming at fulfilling the safety regulations of the NPP. Since the1980s, however, researchers have proposed metaheuristics optimization to automate this process. Recently, new researches have shown that Quantum Inspired Evolutionary Algorithms are among the best alternatives to deal with optimization problems in Nuclear Engineering. In the present work, Quantum Evolutionary Algorithm (QEA) is used for optimizing the NRROP of a Brazilian “2-loop” Pressurized Water Reactor (PWR) Nuclear Power Plant, Angra 1. The main goal of this research is to show the performance of QEA to solve the NRROP compared with its classical counterpart, the Genetic Algorithm (GA). In addition, manual reload and other optimization methods are also used to demonstrate the feasibility of QEA to solve cycle 7 of Angra 1. The performance of QEA, such as search ability and fast convergence, is better than GA and compatible with other Quantum Inspired Evolutionary Algorithms presented in the literature.
In the in-core fuel management optimisation (ICFMO) problem, a fuel reload configuration is sought which optimises the performance of a nuclear reactor, while also satisfying prescribed operational constraints. ICFMO has been studied for several decades, initially as single-objective optimisation problems but in recent years also as multiobjective optimisation problems. Several of the multiobjective ICFMO approaches adopted in the literature, however, exhibit serious shortcomings or drawbacks, and very little research has been performed to address or overcome them. In this paper, we present a brief overview of the various multiobjective ICFMO approaches found in the literature. We also provide a commentary on what we believe to be the most important shortcomings and drawbacks in these approaches and, concurrently, present our suggestions for addressing them. The workability of these suggestions are demonstrated by their application to two test problems for the SAFARI-1 research reactor. The results indicate that our suggested approaches are indeed feasible for multiobjective ICFMO problems. The aim of this paper is to encourage further research toward multiobjective ICFMO via the inclusion of sound principles from the field of operations research.
