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

Abstract

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. INDEX TERMS Black hole optimization, combinatorial searching-based software testing, meta-heuristic searching, multiple black hole optimization, swarm meta-heuristic.

Combinatorial Test Suites Generation Strategy Utilizing the Whale Optimization Algorithm

“…Nevertheless, each of these approaches share a common aspect: when combined with heuristics, these approaches can harness the power of random combinatorial searching to evaluate tstrength covering arrays. Two main aspects must be focused on to formulate the optimization problem: the definition of the objective function; and the selection of the technique, whether utilizing a pure-based approach or a hybrid-based approach [39]. In terms of the objective function, the number of tuples covered for the candidate test case (i.e.…”

“…• Sine Cosine Algorithm (SCA) [17] • Multiple Black Hole (MBH) algorithm [39] Cuckoo Search (CS) [4], which was implemented in t-way combinatorial testing with a small number of control parameters. A variant of CS was also implemented in t-way testing that upgrades the search space with Levi flights [31].…”

“…Multiple Black Hole (MBH) algorithm [39] emerged in 2020 for application in combinatorial testing. The Black Hole algorithm is a modern meta-heuristic method focused on observable evidence of the black hole phenomenon and the behavior of stars when interacting with the black hole.…”

“…MBH is based on the multi-swarm principle, which can be defined as multiple black holes. Additionally, MBH introduced the black hole energy to promote the removal of certain black hole swarms and to produce fresh ones [39]. Another algorithm introduced in 2020 is SCA [17], which is a population-based algorithm that produces numerous initial random test cases and allows the cases to fluctuate outwards or towards the best possible test case using a sine and cosine mathematical model.…”

Dynamic Weighted Heuristic Trust Path Search Algorithm

“…Another important issue in inferring trust values is how to choose the optimal trust path from among the admissible trust paths. Compared with the traditional random search algorithm, the heuristic search algorithm [8] can accelerate the search process. As the most classic path search algorithm, the A * algorithm [9] aimed at combining a mathematical method and a heuristic method to find the optimal solution.…”