The many-to-many assignment problem (M- MAP), and the CPU/FPGA scheduling problem are two correlated issues in the field of combinatorial optimization. The framework for Kernighan Lin-driven logarithmic barrier approach (KD-LBA) is made to solve the many-to-many assignment problem. KD-LBA is a deterministic technique, which initiates to achieve the globally optimal solutions for MMAP using logarithmic barrier function-based gradient descent technique. Then, the obtained solution is optimized further using the Kernighan Lin-based local search method. Successive Kernighan Lin-driven logarithmic barrier approach (Successive KD-LBA) is also proposed to sort the issue of scheduling in a CPU/FPGA heterogeneous system. It solves the CPU/ FPGA scheduling problem by transforming it into an MMAP. KD-LBA outperforms the state-of-art methods in terms of convergence speed for MMAPs with a group size greater than 40. Successive KD-LBA presents novel scheduling solutions for the CPU/FPGA scheduling problem as compared to the existing works, regarding average makespan and computation time.

多对多分配问题（M-MAP）和 CPU/FPGA 调度问题是组合优化领域中的两个相关问题。Kernighan Lin 驱动的对数障碍方法 (KD-LBA) 的框架旨在解决多对多分配问题。KD-LBA 是一种确定性技术，它开始使用基于对数障碍函数的梯度下降技术来实现 MMAP 的全局最优解。然后，使用基于 Kernighan Lin 的局部搜索方法进一步优化获得的解。还提出了连续 Kernighan Lin 驱动的对数屏障方法（Successive KD-LBA）来解决 CPU/FPGA 异构系统中的调度问题。它通过将其转换为 MMAP 来解决 CPU/FPGA 调度问题。