标题： 基于光学硬件求解距离优化问题 显示英文标题

标题： Solving Distance-Based Optimization Problems Using Optical Hardware

摘要： 我们提出了一种使用光学计算硬件解决基于距离的优化问题的实用方法。 目标是通过测量距离与点坐标平方欧几里得距离之间的加权平方差来最小化能量函数。 通过将坐标表示为复数，我们将优化问题映射到光学场中，从而可以通过规范变换（CT）方法或基于增益的分岔（GBB）方法进行求解。 为了进一步提高CT方法的性能，我们引入了两种技术：异步更新和陡峭梯度。 CT和GBB方法都可以有效地解决基于距离的问题，并且适用于各种光学硬件平台。 我们的光学实现受到最近在组合优化模拟光学计算方面的进展启发，突显了其在高维环境中高效且可扩展问题解决的潜力。 显示英文摘要

摘要： We present a practical approach to solving distance-based optimization problems using optical computing hardware. The objective is to minimize an energy function defined as the weighted sum of squared differences between measured distances and the squared Euclidean distances of point coordinates. By representing coordinates as complex numbers, we map the optimization problem onto optical fields, enabling its solution through either the canonical transformation (CT) method or the gain-based bifurcation (GBB) method. To further enhance the performance of the CT method, we introduce two techniques: asynchronous update and steepened gradient. Both the CT and GBB methods can effectively solve the distance-based problem and are adaptable to various optical hardware platforms. Our optical implementation is inspired by recent progress in analog optical computing for combinatorial optimization, highlighting its promise for efficient and scalable problem-solving in high-dimensional settings.