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The morphological matrix is an important element of the engineering design methodology and is present in many textbooks. This method originally aimed at generating an exhaustive set of solutions for a given problem, by decomposing it into subproblems, finding solutions to each subproblem, and combining them. One issue associated with the morphological matrix has been the necessity to deal with the combinatorial explosions of solutions, especially at the conceptual design phase, when the still fuzzy nature of the design problem precludes the use of automated search for an optimal solution by means of specific algorithms (the "manual engineering design" context), apart from a few exceptions. Several heuristics based on the reduction of the number of combinations are investigated, and their efficiency is assessed. It is showed that the often-recommended compatibility matrix heuristic is the least efficient and can result in overlooking potentially interesting combinations. In fact all heuristics, even combined, generally fail to decrease the number of combinations to a level that can be handled by the designers, unless the original number of combinations is low. However, if one abandons the principle of an exhaustive investigation of the combinations in order to find the "best" solution, it can be showed statistically that the probability of ending up with a "good" concept among a very large number of combinations can be attained. Moreover, it is showed that the number of combinations one is willing to investigate also can contribute to increase this probability. Moreover the experience gained from the first round of investigation can serve as a guide to choose and assess other combinations. Based on those results, some recommendations for using the morphological matrix with all the different heuristics are given. Moreover, this paper discusses and relativizes the importance of the combinatorial explosion issue of morphological matrix compared with some other advantages and shortcomings of the method

Dealing With the Combinatorial Explosion of the Morphological Matrix in a “Manual Engineering Design” Context