Hybrid Numerical Optimization for Combinatorial Network Problems

We discuss a general approach to hybridize traditional construction heuristics for combinatorial optimization problems with numerical based evolutionary algorithms. Therefore, we show how to augment a construction heuristic with real-valued parameters, called

control values

. An evolutionary algorithm for numerical optimization uses this enhanced heuristic to find assignments for these control values, which in turn enable the latter to find high quality solutions for the original combinatorial problem. Additionally to the actual optimization task, we thereby experimentally analyze the heuristic’s substeps.

Furthermore, after finding a good assignment for a specific instance set, we can use it for similar yet different problem instances, without the need of an additional time-consuming run of the evolutionary algorithm. This concept is of particular interest in the context of computing efficient bounds within Branch-and-Cut algorithms. We apply our approach to a real-world problem in network optimization, and present a study on its effectiveness.