Abstract: Highlights•The Fit-IAMB algorithm is combined the advantages of Inter-IAMB and Fast-IAMB, and three-aspect strategies areused to improve the performance.•Fit-IAMB not only adds more variables into the MB at each iteration, but also interleaves the growth and shrink phasesto remove the false positive variables into the candidate MB at an early time.•Fit-IAMB adopts heuristic search strategy to find the variables in the MB.•Fit-IAMB does not add the non-parent-child node variables in the growth phase to consider again, and checks thefalsely removed spouse node in the third phase. This algorithm is sound under broad conditions, scale-up to thousands of variables.