This paper proposes a genetic algorithm, the array histogram-based sampling algorithm (AHBSA), to assemble linear multidimensional forced-choice questionnaires (MFCQs), which are increasingly popular for measuring personality, with forced-choice items including any number of statements (block size).The algorithm also works for traditional multidimensional Likert and cognitive test forms, where items can be seen as having a block size of one.Real and simulated statement pools are used to evaluate AHBSA's performance in terms of test reliability and running speed in assembling Likert forms and MFCQs with two (pair) and three (triplet) statements.Compared to mixed integer programming (MIP) and random assembly, AHBSA achieves as high or higher reliabilities under all conditions: in Likert forms, AHBSA reaches optimal solutions as MIP does, and in the MFCQs, AHBSA gains notable increases in reliabilities over MIP when the forms have no constraint on item direction (i.e., positively versus negatively keyed statements).AHBSA takes more time to converge than MIP.The findings and limitations are discussed, and suggestions for future work are provided.
Fu et al. (Fri,) studied this question.