Multiple Black Hole Inspired Meta-Heuristic Searching Optimization for Combinatorial Testing

Combinatorial searching-based software testing (CSST) is a challenging optimization procedure. The achievement of optimal solutions involves a careful formulation of the optimization problem and the selection of an appropriate approach. Meta-heuristic searching procedures have proven to be effective for solving CSST issues. Black hole (BH) optimization is among the more recently developed meta-heuristic searching algorithms. While this approach has been observed to be an effective alternative to particle swarm optimization, its operation is based on only one swarm. To date, no efforts have been made to modify this approach to accommodate multiple swarms. This study proposes a new variant of BH that involves a combination of multiple swarms. The BH optimizer is modified from continuous searching to binary searching and subsequently applied for solving CSST. The evaluation is based on a modified-benchmarking mathematical function and well-known CSST problems. This modified BH method is superior to the original BH and the established particle swarm optimization (PSO) approach. In terms of CSST problems, binary multiple black hole (BMBH) optimizations generate reduction rates between 50% and more than 60% for t = 4 according to the problem.