Keywords: layout optimisation, traffic, transportation, town-planning, VMT.

This paper presents a novel way of reducing the total volume of traffic in a town by optimising the town layout. The variables, cost function and the constraints of the problem are identified and optimisation problem formulation is presented. The problem is formulated as a layout optimisation problem of unequal area rectangular modules representing various blocks of a town. Each module may represent one of the entities or blocks that exist in a town. For example Module 1 may be a residential area, module 2 may be a school, and module 3 may be shopping center, and so on. The traffic is assumed to be generated by vehicles travelling from one module to another. The cost function to be minimised is the 24-hour VMT (Vehicle Miles Travelled).

Layout optimisation of arbitrary size rectangular modules is considered one of the most difficult optimisation problems. Quite a large number of solution algorithms have been published [1,6]. The use of any published algorithm was however not possible for the town layout problem because the published algorithms can handle only small problems and most cannot deal with the real-world constraints like a given boundary of non-rectangular shape, bounds on the maximum allowable distances, hard modules with fixed aspect ratios, anchored modules which are fixed in position, padding of empty space around a module for flow of traffic, etc. Therefore, a readily available software package called VIP-PLANOPT [7] recommended in the famous textbook on facilities planning [1] was used. It was found to be the only available software package suitable for this extremely hard layout optimisation problem.

The presented technique is applied to a simple academic example and a real-world type problem. The data and the results are presented. To evaluate the quality of the layout and to get a sense of its optimality, each module in the optimised layouts was perturbed from its position and cost functions were re-calculated for the layouts. It was found that all perturbed layouts had larger cost function value than the optimal layouts produced by VIP-PLANOPT. This ensured that the optimal layouts represent local optima. An optimal layout represents local optima if movement of any one of the modules to another position raises the cost function value. Another experiment was to randomly generate layouts of different configurations. This was a difficult exercise because random generation of layouts with no overlaps is not easy. However, no layouts were found with cost function value lower than the optimal.

The paper provides all the details for applying the technique to any real-world problem. It is shown that the approach is readily applicable to any real-world problem. It is found that the optimal layouts may reduce the VMT drastically saving millions of miles of driving per year. The advantages of this approach are obvious. The total traffic volume reduces. This in turn reduces the traffic jams, accidents, pollution, energy consumption and the road maintenance cost. In addition, all the other techniques of traffic calming become more.

It was found that the VMT is quite sensitive to the layout of a town. From the problems presented in this paper, it can be easily concluded that a bad layout may cost the public a substantial and significant increase in unnecessary mileage. For the real world like problem presented in the paper, the estimated increase in 24-hour VMT due to non-optimal layout was shown to be greater than 38,000 kilometres. This represents annual waste of more than 13 million kilometres of unnecessary driving just because of non-optimal layout. Even a small perturbation to the optimal layout that was done to smooth out the layout costs 1955 kilometres per day that calculates to about 0.7 million kilometres of vehicle travel per year. The presented approach can be extremely effective if a proposed town layout or an urban expansion plan is optimised at the town-planning stage.

1

Tompkin et al, "Facilities Planning", John Wiley, New York, USA, 2000

2

Mir, M. and Imam, M.H., "A hybrid optimization approach for layout design of unequal-area facilities", J. Computers and Industrial Engineering, 39, 49-63, 2001. doi:10.1016/S0360-8352(00)00065-6

3

Imam, M.H. and Mir, M., "Cluster boundary search algorithm for building-block layout optimization", Advances in Engineering Software, 29(2), 165-173, 1998. doi:10.1016/S0965-9978(98)00056-8

4

Imam, M.H., Mir, M., "Nonlinear programming approach to automated topology optimization", J. Computer-Aided Design, 21(2), 107-115, 1989. doi:10.1016/0010-4485(89)90146-2

5

Welgama, P.S., Gibson, P.R., "Computer-aided facility layout - a status report", International Journal of Advanced Manufacturing Technology, 10(1), 66-77, 1995. doi:10.1007/BF01184280

6

Gloria, A.D., Faraboschi, P., Olivieri, M., "Block placement with a boltzmann machine", IEEE Trans. On CAD, 13(6), 694-701, 1994. doi:10.1109/43.285242

7

Engineering Optimization Software, "VIP-PLANOPT software package", http://www.planopt.com, Georgia, USA, 2004.

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