Interaction (t-way) testing is a common sampling strategy to minimize combinatorial test data from large configuration space based on the defined interaction strength (t). Here, all t-way strategies generate the t-way test suite with the aim to cover every possible combination produced by the interacting parameters (or also known as tuples). In many systems under test (SUT), there are some known combinations that are impossible to occur based on the requirements set to the system. These combinations (termed constraints) have to be excluded from the final test suite. This paper describes the generation of t-way test suite using the Late Acceptance Hill Climbing based Strategy (LAHC) in the presence of constraints. Our benchmarking results have been promising as LAHC gives competitive results in many constraints configurations considered.