Combinatorial testing (CT) is an effective testing method that can detect failures caused by the interaction of parameters of the software under test (SUT). With the increasing complexity of SUT and the parameters involved, the variable strength test suite supporting high strength interaction is challenging in a practical testing scenario. This paper presents a multi-learning-based quantum particle swarm optimization (IQIPSO) for high and variable strength covering array generation (VSCAG). Specifically, a specially designed data structure and several combination location methods are proposed to support and speed up the high-strength VSCAG. Besides, multi-learning strategies, including Lamarckian and Baldwinian learning, are applied to IQIPSO to address the premature convergence leading to a large test suite size. Studies for parameter settings of IQIPSO are presented systematically. The IQIPSO method successfully builds test suites where strength is up to 15 and totally reports 13 new best test suite size records. Extensive experiments demonstrate that IQIPSO tends to outperform most other existing methods.