This article presents and validates a new branch-and-bound algorithm for effectively solving the generalized polynomial problem (GPP). In this algorithm, a new affine relaxed technique is derived for establishing the relaxed linear programs problem of the GPP. In addition, some box reducing manipulations are employed to improve the speed of branch-and-bound search of the algorithm. Combining the relaxed linear programs problem with the box reducing manipulations, a new branch-and-bound algorithm is constructed. Some numerical examples are solved to verify the potential practical and computing advantages of the algorithm. At last, several engineering design problems are solved to validate the usefulness of the algorithm.

本文介绍并验证了一种新的分支定界算法，可有效解决广义多项式问题 (GPP)。在该算法中，导出了一种新的仿射松弛技术来建立 GPP 的松弛线性规划问题。此外，为了提高算法的分支定界搜索速度，还采用了一些减少框的操作。将松弛线性规划问题与减框操作相结合，构造了一种新的分支定界算法。解决了一些数值示例，以验证该算法的潜在实用和计算优势。最后，解决了几个工程设计问题，验证了算法的有效性。