A Theory of Markovian Design Machines

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.

[1]  Morris Asimow,et al.  Introduction to design , 1962 .

[2]  D. H. Freeman.  Statistical Decomposition Analysis , 1974 .

[3]  B. Harshbarger.  An Introduction to Probability Theory and its Applications, Volume I , 1958 .

[4]  J. French.  A formal theory of social power. , 1956, Psychology Review.

[5]  John G. Kemeny,et al.  Finite Markov Chains. , 1960 .

[6]  B. A. Farbey,et al.  Structural Models: An Introduction to the Theory of Directed Graphs , 1966 .

[7]  J. F. C. Kingman,et al.  Dynamic Probabilistic Systems. Volume 1: Markov Models. Volume 2: Semi‐Markov and Decision Processes , 1972 .

[8]  L. Keeble.  Principles and Practice of Town and Country Planning , 1969 .

[9]  E. Jantsch.  The design of inquiring systems,: by C. West Churchman New York, Basic Books, 1972. , 1972 .

[10]  J. Christopher Jones,et al.  Design methods: Seeds of human futures , 1970 .

[11]  Ronald A. Howard,et al.  Dynamic Programming , 1966 .

[12]  M L Manheim,et al.  THE USE OF DIAGRAMS IN HIGHWAY ROUTE LOCATION: AN EXPERIMENT , 1962 .

[13]  R. Bellman.  Dynamic programming. , 1957, Science.

[14]  John G. Kemeny,et al.  Finite Markov chains , 1960 .

[15]  Gregory K. Miller,et al.  Elements of Applied Stochastic Processes , 1972 .

[16]  R. Bellman.  A Markovian Decision Process , 1957 .

[17]  G. Dantzig,et al.  Linear Programming in a Markov Chain , 1962 .

[18]  Herbert A. Simon,et al.  The Structure of Ill Structured Problems , 1973, Artif. Intell..

[19]  Michael Batty,et al.  Social Power in Plan-Generation , 1974 .

[20]  Ronald A. Howard,et al.  Dynamic Programming and Markov Processes , 1960 .

[21]  Samuel Karlin,et al.  ELEMENTS OF STOCHASTIC PROCESSES , 1975 .

[22]  Solomon Kullback,et al.  Information Theory and Statistics , 1960 .

[23]  Christopher Alexander,et al.  Notes on the synthesis of form harvard university press , 1968 .

[24]  Christopher Alexander.  Notes on the Synthesis of Form , 1964 .

[25]  Feller William,et al.  An Introduction To Probability Theory And Its Applications , 1950 .

[26]  Frank Harary,et al.  The Dynamics of Brand Loyalty: A Markovian Approach , 1962 .