Using Simulation for Performance Analysis and Visualization of Parallel Branch-and-Bound Methods

The Branch-and-Bound (B&B) is a fundamental algorithmic scheme for a large variety of global optimization methods. For many problems B&B requires the amount of computing resources far beyond the power of a single-CPU workstation thus making parallelization almost inevitable. The approach proposed in this paper allows one to evaluate load balancing algorithms for parallel B&B with various numbers of processors, sizes of the search tree, the characteristics of the supercomputer's interconnect. The proposed approach was implemented as a special tool that simulates the process of resolution of the optimization problem by B&B method as a stochastic tree branching process. Data exchanges are modeled using the concept of logical time. The user-friendly graphical interface can render both real traces and ones produced by the simulator. It provides efficient visualization of the CPU's load, data exchanges and progress of the optimization process.