No abstract

In this paper we introduce , a global optimization solver specifically designed for (continuous) polynomial programming problems with box-constrained variables. Written entirely in , is based on the Reformulation-Linearization (Sherali and Tuncbilek in J Glob Optim 103:225–249, 1992). We present a description of the main characteristics of along with a thorough analysis of the impact on its performance of various enhancements discussed in the literature, such as bound tightening and SDP cuts. We also present a comparative study with three of the main state-of-the-art global optimization solvers: , and .

The use of machine learning techniques to improve the performance of branch-and-bound optimization algorithms is a very active area in the context of mixed integer linear problems, but little has been done for nonlinear optimization. To bridge this gap, we develop a learning framework for spatial branching and show its efficacy in the context of the Reformulation-Linearization Technique for polynomial optimization problems. The proposed learning is performed offline, based on instance-specific features and with no computational overhead when solving new instances. Novel graph-based features are introduced, which turn out to play an important role for the learning. Experiments on different benchmark instances from the literature show that the learning-based branching rule significantly outperforms the standard rules. History: Accepted by Andrea Lodi, Area Editor/Design & Analysis of Algorithms – Discrete. Funding: This work was supported by Ivey Business School (David G. Burgoyne Faculty Fellowship); FEDER [MTM2014-60191-JIN]; Spanish Ministry of Education [FPU Grant 17/02643, FPU Grant 20/01555]; Conselleria de Cultura, Educacion e Universidade [ED431C 2021/24]; Natural Sciences and Engineering Research Council of Canada [Discovery Grant 2017-04185]; Spanish Ministry of Science and Technology [MTM2017-87197-C3] and Spanish Ministry of Science and Innovation [PID2021-124030NB-C32].

The use of machine learning techniques to improve the performance of branch-and-bound optimization algorithms is a very active area in the context of mixed integer linear problems, but little has been done for non-linear optimization. To bridge this gap, we develop a learning framework for spatial branching and show its efficacy in the context of the Reformulation-Linearization Technique for polynomial optimization problems. The proposed learning is performed offline, based on instance-specific features and with no computational overhead when solving new instances. Novel graph-based features are introduced, which turn out to play an important role for the learning. Experiments on different benchmark instances from the literature show that the learning-based branching rule significantly outperforms the standard rules.