发表机构
Università di Parma; Sapienza Università di Roma; Università degli Studi di Padova（帕尔马大学; 罗马第一大学; 帕多瓦大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对混合整数二次分式优化问题，提出基于Dinkelbach参数化重构的精确算法，结合分支定界和变量邻域搜索启发式，数值实验表明优于通用精确算法。
AI 中文摘要
我们研究具有二元和连续箱约束变量的混合整数二次分式优化问题。目标函数是两个二次函数的比值，这种结构在投资组合选择、信号处理和数据分析中自然出现。我们提出了一种基于Dinkelbach参数化重构的精确算法。在每次Dinkelbach迭代中，分式问题被替换为一个具有箱约束的非凸混合整数二次子问题。该子问题通过专门的branch-and-bound求解器全局求解。为了加速外层方案，我们使用变量邻域搜索启发式算法为Dinkelbach方案提供初始可行解。该启发式算法在连续局部搜索和二元空间探索阶段之间交替进行，在二元空间探索阶段中，可行当前解的连续变量被固定。数值结果表明，所提出的方法优于基于Dinkelbach参数化重构的通用精确算法。
英文摘要
We study mixed-integer quadratic fractional optimization problems with binary and continuous box-constrained variables. The objective is the ratio of two quadratic functions, a structure that arises naturally in portfolio selection, signal processing, and data analytics. We propose an exact algorithm based on Dinkelbach's parametric reformulation. At each Dinkelbach iteration, the fractional problem is replaced by a nonconvex mixed-integer quadratic subproblem with box constraints. This subproblem is solved globally by a specialized branch-and-bound solver. To accelerate the outer scheme, we use a Variable Neighborhood Search heuristic to provide an initial feasible solution to the Dinkelbach scheme. The heuristic alternates between continuous local searches and a binary-space exploration phase in which the continuous variables of a feasible incumbent are fixed. Numerical results show that the proposed approach outperforms general-purpose exact algorithms based on Dinkelbach's parametric reformulation.
