الگوریتم بهینه سازی در طرح شبکه ای راکتور آب جوشان (BWR) OPTIMIZATION ALGORITHMS IN BOILING WATER LATTICE DESIGN

Since the inception of nuclear power engineers and scientists have pursued optimal core design; for longer still mathematicians have long sought methods for finding extrema over a large set of points. With the introduction of high-powered computers, numerical methods now exist to approximate and find the optima of complex functions. These algorithms are applicable to any system that can be quantized and weighted; their application to nuclear simulations has led to dramatic advancements in all aspects of reactor design, from the fuel pins to the core loading pattern. Within a core design there are hundreds of independent constrained variables that can be altered, sometimes with drastic physical effect. In an average Boiling Water Reactor (BWR) core there are over four hundred fuel bundles, some reactors containing close to one thousand. Each bundle is composed of an 8-by-8 to 10-by-10 grid of fuel pins that are each filled with hundreds of fuel pellets. These pellets are the lowest level alterable structure for building a reactor core. Assuming just one variable per pellet, there is a preposterously large search space of 1020,594,603 ~ 1 0 10′ unique configurations. For comparison there are approximately 1080 atoms in the observable universe. Therefore without a supercomputer the size of several universes there is no way to ensure the absolutely optimal core design. It is possible to achieve reasonably close approximations using optimization methods, the most popular of which are the genetic algorithm and simulated annealing. These optimization methods work to find the extrema of a single representative function by various iterative processes. To further reduce computational challenge, discrete levels or averages are adopted within bounding limits. There are a near infinite number of factors, enrichments, and densities in reactor cores to consider, however all of these aspects are within the greater structure of a fuel bundle. Creating a simulation of fuel bundle arrangement is a computationally intense process that seriously challenges algorithms. The greedy exhaustive dual binary swaps (GEDBS) method was tested on the level of fuel lattice design within a BWR fuel bundle. The GEDBS is an algorithm which replaces two fuel pins in a lattice with two from an available palette of pin types, measures the configuration and iterates from the result. This method is a more brute force approach than either the genetic algorithm (GA) or simulated annealing (SA). Ultimately the GEDBS will be compared with the effectiveness of SA and GA; this could eventually lead to the creation of even more efficient methods to find maxima and minima. SA, GA, and GEDBS are all proceed by minimizing/maximizing a single function which encompasses all of the relevant variables to the problem. By simplifying a great deal of complexity to a single function the numerical evaluation of a ‘better’ solution can be more readily realized by a computer. This function often becomes stagnant around a local extreme rather than its goal of a global extreme. The amount the algorithm is willing to deviate from its current best value will indicate how large a potential barrier the algorithm can traverse, however with this ability to overcome large potential barriers comes inherent chaos and inefficiency. It is the careful balance of these factors that will prove the ultimate effectiveness of any optimization method. For example a fully exhaustive system that checked every possibility could reach the optimal solution, but still continue processing and check the worst solution in the process. A non-exhaustive pattern would iterate from the current best pattern to differing degrees and not waste computation time checking in the area of the worst responses.