John F. Brotchie

A model incorporating diversity in urban allocation problems

Abstract A new type of activity allocation model ∗ is presented in which non-homogeneity or diversity is considered within each of the devision options. Urban land use allocation, transport trip distribution, and modal choice are considered in particular. The basis of allocation considered is the maximization of utility. The effect of non-homogeneity in the utility value of each option is to change the nature of the solution from an all or nothing (e.g. zero, one) type to one in which essentially all allocation variables have finite values. The model is related to gravity type-entropy maximizing models for land use and trip distribution,and diasaggregated demand models of modal choice. The model can be prescriptive if the utility of the community including externalities is used, or predictive if only the utility of the decision makers is included. The integration of both types of model in strategic level models of the TOPAZ type is considered on the above basis. The resulting model might be used to (1), select optimal land use-transportation plans, (2), predict response of the community to them, and (3), determine policies to make the two compatible.

A regional planning model and its application to South Eastern Australia

Abstract A mathematical regional planning model is developed primarily for Australian conditions but is sufficiently general for applications elsewhere. The model has an input-output framework with constraints on labour, production, investment, exports and imports, and consumption. The objective function of the model includes production, labour, intermediate demand, consumption, investment, export and import terms (all linear) plus transportation cost terms (quasi-quadratic). The objective and the constraints may be manipulated to reflect various community goals such as maximize exports minus imports, minimize or constrain unemployment, minimize investment, etc.

Evaluation of alternative growth patterns in urban systems

Abstract The paper describes the formulation of the general planning model, TOPAZ (Technique for the Optimum Placement of Activities into Zones) and its application to evaluating and optimizing alternative growth patterns in urban systems. TOPAZ identifies an urban system as a set of interacting activities to be allocated to a set of zones to maximize an objective of overall benefit less cost of interaction between activities together with the benefit less cost of establishment of the activities, over a set of time periods. The model takes the form of a non-linear assignment problem with linear constraints, and is solved using iterative linear programming. The model is illustrated by application at a macro level to the evaluation of alternative corridor growth patterns for the city of Melbourne (population 2.4 million) over three time periods, 1970–80–90–2000. Two activities are involved, residential and employment activity, and the interactions consist of work, residential, industrial and commercial trips. The city is divided into forty zones.

A generalized design approach to solution of the non-convex quadratic programming problem

Abstract This paper outlines a generalized, systematic design approach to solution of the non-convex quadratic programming problem. It is based on a previous formulation of utility of a general system in terms of efficiency and robustness of the system. The approach is to introduce a robustness term of arbitrary magnitude into the design utility function. Mathematically, this makes the problem convex. From a design approach, it yields a more general solution allowing specialization to proceed by decreasing robustness (on an initially convex utility surface in the feasible design space) until the region of the overall optimum is approached. The approach is mathematically related to the Metropolis technique of simulated annealing but a more systematic (less random) solution process is used. It is analogous also to the heuristic technique of Burkard and Bonniger. These two previous techniques are the most effective so far reported for the quadratic programming problem. The robustness approach provides an underpinning for each and opens up further solution options. Applications include layout of buildings and other constructed facilities and information technology layout problems.

Introducing Intelligence and Knowledge into CAD

This paper outlines work in progress in a centre for intelligent knowledge-based systems for computer-aided decision. The centre was recently established in the Division of Building Research CSIRO, Australia. The research is an extension of previous Divisional contributions to the mathematical basis for automated optimal design and planning.

Introduction to Techniques

The purpose of this book is to present a set of techniques which have proved valuable in the solution of planning problems in two major areas (1) urban and regional planning and (2) delivery of urban services including location and planning of facilities. Urban and regional planning has taken on increased importance over the last two decades as populations have increased, as migration from rural to urban areas and from inner to outer urban areas has varied along with changes in lifestyle, and as resource shortages, particularly energy, have begun to bite.

Optimization and robustness of structural engineering systems

This paper outlines several strands in the historical development of structural optimization techniques. The first is indirect via simple optimality conditions such as uniform density of stress or strain for achieving a technical objective like minimum weight, maximum stiffness or minimum strain energy. In the case of prestressed structures, zero net displacement of the concrete in flexure at service loads may be the criterion, and in the case of structural vibration damping, maximum dissipation of energy under dynamic loads. The second is direct via mathematical optimization of a more comprehensive, economic objective such as minimum cost or maximum utility under multiple loading conditions. Further development has led to automated and interactive design and optimization of nonconvex objective functions using improved optimization techniques. A more general, systems theory has been formulated with application to both strongly and weakly interacting systems, including structures, taking uncertainty into account. It relates overall utility of the system to its efficiency, diversity and uncertainty or robustness, and enables an overall optimum to be obtained for a given level of uncertainty and diversity.

Modelling diversity, choice, costs, and benefits in urban activity patterns

Abstract This paper is concerned with patterns of urban development and their evaluation, prediction, and prescription using mathematical models. A utility maximizing model which incorporates diversity of benefits within each allocation option is introduced. This diversity also affects dispersal of activities among zones and is related to cost differences and trip distributions between zones. The degree of diversity is affected by the influence of the different parties in the location decision process, by different levels of planning control, and by different transport and communications futures, and the consequences of these factors on patterns of development and on utility are examined.

A Summary Evaluation

Lack of proper management of resources is one of the major problems facing the world in this decade, and possibly in the distant future. Fossil fuels and other mineral deposits which have taken millions of years to accumulate are facing exhaustion in time periods now under present planning consideration. The impact of these conditions on the planning of facilities must be taken into account if they are not to be rendered obsolete before they even come into existence. Transport systems, urban development, and building complexes all face critical appraisal or reappraisal in this light.

A criterion for optimal damping design

Abstract The design of elements for maximum damping of vibrations in a linear elastic system is described. Single and multiple damping elements of purely viscous, visco-elastic, rigid-plastic, or Coulomb type are treated. A general theorem is developed which equates the optimal impedance (dynamic stiffness) of the damping element to the impedance (elastic plus inertial stiffness) of the linear system at the point at which the element is applied. This theorem provides a criterion which may be used directly to design the elements: Formulae are derived from there to specify the elements and to evaluate their effectiveness and thus indirectly indicate where to locate them. Applications include damping of sway vibrations of tall buildings, and of vibrations in floor systems, vehicles and machines. Noise producing vibrations may be included. In each case, the optimal impedance characteristics of the damping element may be expressed in terms of the impedance characteristics of linear system, e.g. the elastic stiffness of the structure or the mass of the machine, and the frequency of the loading force.