Multimodal Multi-Objective Test Data Generation Method based on Particle Swarm Optimization

Cyber-Physical Systems (CPS) confront significant challenges in the assessment of state after experiencing disturbances or attacks, attributed to their inherent complexity. This situation demands comprehensive and expensive experiments for evaluation. Employing black-box optimization methods to optimize test data generation proves efficacious. Nevertheless, prevailing black-box optimization techniques often prioritize trade-offs among objectives, neglecting the search space's multimodality. To bridge this divide, we draw inspiration from multi-objective multimodal optimization problems (MMOPs) to address black-box optimization problems, proposing a multimodal multi-objective test data generation method (MMOTDG) for testing the state of CPS under disturbances and attacks. The clustering-based particle swarm optimization leveraging adaptive resonance theory, termed CARTPSO, is employed to solve MMOPs in the test data generation process. Experiment results demonstrate that CARTPSO shows significantly superior performance to five leading multimodal multi-objective algorithms across 11 benchmark functions. A novelty co-simulation testing environment is built for testing the state of aircraft encountering wind disturbance in a black-box manner. The proposed MMO-TDG is applied in this environment to generate test data against random search and NSGAII-based test data generation method. Results show that test data generated by MMO-TDG not only exhibit diversity but also effectively fulfill the testing objectives.