A Convexification-based Outer-Approximation Method for Convex and Nonconvex MINLP

TL;DR

This paper introduces a refined convexification-based outer-approximation and branch-and-bound methods for convex and nonconvex MINLP, improving solver performance through enhanced domain reduction techniques validated by comprehensive benchmarks.

Contribution

It presents a novel convexification-based outer-approximation method and a branch-and-bound approach integrated into an open-source toolbox for solving MINLP problems.

Findings

Enhanced solution efficiency demonstrated in benchmark tests

Improved reliability of algorithms with convexification techniques

Effective domain reduction leading to faster convergence

Abstract

The advancement of domain reduction techniques has significantly enhanced the performance of solvers in mathematical programming. This paper delves into the impact of integrating convexification and domain reduction techniques within the Outer- Approximation method. We propose a refined convexification-based Outer-Approximation method alongside a Branch-and-Bound method for both convex and nonconvex Mixed-Integer Nonlinear Programming problems. These methods have been developed and incorporated into the open-source Mixed-Integer Nonlinear Decomposition Toolbox for Pyomo-MindtPy. Comprehensive benchmark tests were conducted, validating the effectiveness and reliability of our proposed algorithms. These tests highlight the improvements achieved by incorporating convexification and domain reduction techniques into the Outer-Approximation and Branch-and-Bound methods.