Metamorphic relationship generation based on Faure Sequence Initialized Slime Mould Algorithm

Metamorphic relationship is an extremely important software testing method in the field of software engineering, and after years of research by scholars, a relatively complete system has been formed. However, the objective function of the metamorphic relationship generation algorithm is essentially a non-differentiable L1 norm, which means that the algorithm can finally be transformed into a non-smooth optimization problem. If traditional gradient dependent methods like gradient descent (GD) or stochastic gradient descent (SGD) are used, the objective function cannot be solved. The coordinate descent (CD) or sub-gradient descent (SubGD) methods usually used to solve the objective function are prone to falling into the trap of local minima, making it difficult to find the global optimal solution. Therefore, it is necessary to find a derivative-free optimization method to solve the objective function of metamorphic relationship generation algorithm. In this paper, a novel slime mold algorithm (SMA), which is called the Faure sequence initialized SMA (FSSMA) has been proposed for global optimization of the objective function. FSSMA can effectively overcome the shortcomings of CD and SubGD methods. Through numerical experiments, the effectiveness and computational efficiency of FSSMA have been demonstrated.