切伦科夫望远镜阵列的多目标遗传算法优化
Multi-Objective Genetic Algorithm Optimisation for an Array of Cherenkov Telescopes
摘要：
我们已经构思并实现了一个多目标遗传算法（GA）代码的成像大气切伦科夫望远镜（IACTs）阵列的优化。该算法将一系列成本函数（度量）作为输入，每个成本函数描述优化的不同目标（例如有效面积、角分辨率等），所有这些都用望远镜在平面上的相对位置来表示。该算法的输出是一个家庭的几何安排，对应于数组优化问题的解决方案的完整的集合，并根据相对权重给予每个（可能是冲突的）优化的对象彼此不同。由于该算法与并行优化一起工作，它允许尽可能多的成本函数，并可以将约束条件，如阵列的预算（成本上限）和地形的拓扑限制，如无法安装望远镜的地理事故。它还允许不同类型的望远镜（混合阵列），并且每种类型的望远镜的数量可以被视为要优化的参数-例如，受每种类型的成本或感兴趣的能量范围的约束。该算法快速收敛到优化解（如果与单个配置的完整蒙特卡罗模拟的时间相比），其目的是提供一种工具来研究可能几何形状的完整参数空间，并帮助设计复杂的阵列。它并不取代详细的蒙特卡罗研究，但旨在指导它。在这里显示的数组的例子中，我们已经使用了简单的启发式表达式描述IAC技术的基本原理作为度量，但这些输入函数可以根据给定的实验所需的详细或复杂。
英文摘要：
We have conceived and implemented a multi-objective genetic algorithm (GA) code for the optimisation of an array of Imaging Atmospheric Cherenkov Telescopes (IACTs). The algorithm takes as input a series of cost functions (metrics) each describing a different objetive of the optimisation (such as effective area, angular resolution, etc.), all of which are expressed in terms of the relative position of the telescopes in the plane. The output of the algorithm is a family of geometrical arrangements which correspond to the complete set of solutions to the array optimisation problem, and differ from each other according to the relative weight given to each of the (maybe conflicting) objetives of the optimisation. Since the algorithm works with parallel optimisation it admits as many cost functions as desired, and can incorporate constraints such as budget (cost cap) for the array and topological limitations of the terrain, like geographical accidents where telescopes cannot be installed. It also admits different types of telescopes (hybrid arrays) and the number of telescopes of each type can be treated as a parameter to be optimised - constrained, for example, by the cost of each type or the energy range of interest. The purpose of the algorithm, which converges fast to optimised solutions (if compared to the time for a complete Monte Carlo Simulation of a single configuration), is to provide a tool to investigate the full parameter space of possible geometries, and help in designing complex arrays. It does not substitute a detailed Monte Carlo study, but aims to guide it. In the examples of arrays shown here we have used as metrics simple heuristic expressions describing the fundamentals of the IAC technique, but these input functions can be made as detailed or complex as desired for a given experiment.
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