A partitioning algorithm for the mixed integer nonlinear programming problem

An interval partitioning method (IPM) is proposed to solve the (non‐convex) mixed integer nonlinear programming problem (MINLP). The MINLP is encountered in many application areas and solving this problem bears practical importance. This paper proposes an IPM where two tree search strategies (breadth first and mixed breadth/depth first) and three variable subdivision methods are implemented. Two proposed variable subdivision methods are novel and they prioritise variables hierarchically according to several features. The IPM is implemented on a set of non‐convex MINLP instances extracted from the MINLP benchmarks and numerical results show that its performance is quite promising.