A Theory of Markovian Design Machines

Abstract

A theory of the design process, based on an analogy with the well-known Markov process in probability theory, is developed and applied in this paper. Design is considered as a process of averaging a set of conflicting factors, and the sequential averaging characteristic of the Markov process is presented algebraically with an emphasis upon the weight of each factor in the final solution. A classification of Markov chains and an interpretation using linear graph theory serves to delimit the set of relevant design problems, and a particular group of such problems based on symmetric structures is specifically described. A second analogy between the choice of design method and the theory of Markov decision processes exists, and the problem of selecting an optimal method using this decision theory is solved using a dynamic programming algorithm due to Howard (1960). The theory is then applied to the classic highway location problem first discussed by Alexander and Manheim (1962), and some comparisons between the different results are attempted. Finally the place of the theory in the wider context of design is briefly alluded to.

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