A Novel TRUST-TECH Guided Branch-and-Bound Method for Nonlinear Integer Programming

Nonlinear integer programming has not reached the same level of maturity as linear programming, and is still difficult to solve, especially for large-scale systems. Branch-and-bound ( B&B) and its variants are widely used methods for integer programming, and numerical solutions obtained by them still can be far away from the global optimum. In this paper, we propose a novel approach to guide the deterministic/heuristic methods and the commercial solvers for nonlinear integer programming, and aim at improving the solution quality by taking advantage of transformation under stability-retraining equilibrium characterization (TRUST-TECH) method. Moreover, we examine the effectiveness by developing and simulating TRUST-TECH guided B&B and TRUST-TECH guided commercial solver(s), and compare their performance with that of the original methods/solvers (e.g., GAMS (General Algebraic Modeling System)/ BARON, GAMS/SCIP, and LINDO (Linear, INteractive, Discrete Optimizer)/MINLP) and also with that of recently-reported evolutionary-algorithm (EA)-based methods. Simulation results provide evidence that, the solution quality is substantially improved, and the global-optimal solutions are usually obtained after the application of TRUST-TECH. The proposed approach can be immediately utilized to guide other EA-based methods and commercial solvers which incorporate intelligent searching components.