Fuzzy Adaptive Tuning of a Particle Swarm Optimization Algorithm for Variable-Strength Combinatorial Test Suite Generation

Combinatorial interaction testing is an important software testing technique that has seen lots of recent interest. It can reduce the number of test cases needed by considering interactions between combinations of input parameters. Empirical evidence shows that it effectively detects faults, in particular, for highly configurable software systems. In real-world software testing, the input variables may vary in how strongly they interact, variable strength combinatorial interaction testing (VS-CIT) can exploit this for higher effectiveness. The generation of variable strength test suites is a non-deterministic polynomial-time (NP) hard computational problem \cite{BestounKamalFuzzy2017}. Research has shown that stochastic population-based algorithms such as particle swarm optimization (PSO) can be efficient compared to alternatives for VS-CIT problems. Nevertheless, they require detailed control for the exploitation and exploration trade-off to avoid premature convergence (i.e. being trapped in local optima) as well as to enhance the solution diversity. Here, we present a new variant of PSO based on Mamdani fuzzy inference system \cite{Camastra2015,TSAKIRIDIS2017257,KHOSRAVANIAN2016280}, to permit adaptive selection of its global and local search operations. We detail the design of this combined algorithm and evaluate it through experiments on multiple synthetic and benchmark problems. We conclude that fuzzy adaptive selection of global and local search operations is, at least, feasible as it performs only second-best to a discrete variant of PSO, called DPSO. Concerning obtaining the best mean test suite size, the fuzzy adaptation even outperforms DPSO occasionally. We discuss the reasons behind this performance and outline relevant areas of future work.Comment: 21 page

Adaptive particle swarm optimization

An adaptive particle swarm optimization (APSO) that features better search efficiency than classical particle swarm optimization (PSO) is presented. More importantly, it can perform a global search over the entire search space with faster convergence speed. The APSO consists of two main steps. First, by evaluating the population distribution and particle fitness, a real-time evolutionary state estimation procedure is performed to identify one of the following four defined evolutionary states, including exploration, exploitation, convergence, and jumping out in each generation. It enables the automatic control of inertia weight, acceleration coefficients, and other algorithmic parameters at run time to improve the search efficiency and convergence speed. Then, an elitist learning strategy is performed when the evolutionary state is classified as convergence state. The strategy will act on the globally best particle to jump out of the likely local optima. The APSO has comprehensively been evaluated on 12 unimodal and multimodal benchmark functions. The effects of parameter adaptation and elitist learning will be studied. Results show that APSO substantially enhances the performance of the PSO paradigm in terms of convergence speed, global optimality, solution accuracy, and algorithm reliability. As APSO introduces two new parameters to the PSO paradigm only, it does not introduce an additional design or implementation complexity