Parallel–Series Multiobjective Genetic Algorithm for Optimal Tests Selection With Multiple Constraints

It is known that optimal tests selection is an important issue in design for testability field. The selection is subjected to constraints of testability metrics. At the same time, test time and economic costs need to be minimized. The tests selection is a combinatorial multiobjective optimization problem. According to the schema theory, the more the amount of testability constraints, the more the constraints are violated. Therefore, the canonical genetic algorithm (GA) evolves slowly, and the Pareto-optimal solutions are less likely to be found. Based on these considerations, a parallel-series multiobjective GA (PSMOGA) is proposed. First, each test procedure is handled by a submultiobjective GA (MOGA) independently. The chromosome length of the <inline-formula> <tex-math notation="LaTeX">$i$ </tex-math></inline-formula>th sub-MOGA is equal to the available tests number of the <inline-formula> <tex-math notation="LaTeX">$i$ </tex-math></inline-formula>th test procedure. The sub-MOGAs are executed in parallel. The Pareto-optimal solutions to every procedure are saved for further process. Second, the MOGA is used to handle the optimal test selection problem for the whole product. The length of the chromosome is equal to the amount of the test procedures. The <inline-formula> <tex-math notation="LaTeX">$i$ </tex-math></inline-formula>th gene can vary between one and <inline-formula> <tex-math notation="LaTeX">$k_{i}$ </tex-math></inline-formula>, where <inline-formula> <tex-math notation="LaTeX">$k_{i}$ </tex-math></inline-formula> is the solution amount of the <inline-formula> <tex-math notation="LaTeX">$i$ </tex-math></inline-formula>th procedure. The genetic material from the subproblem will not be changed. Hence, the subconstraints will never be violated in the MOGA. The effectiveness and efficiency of the proposed method are verified by statistical experiments.