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Winter 1997, Vol. 5, No. 4, Pages 419-438
Posted Online December 10, 2007.
© 1997 by the Massachusetts Institute of Technology
Optimization of Road Networks Using Evolutionary Strategies
A road network usually has to fulfill two requirements: (i) it should as far as possible provide direct connections between nodes to avoid large detours; and (ii) the costs for road construction and maintenance, which are assumed proportional to the total length of the roads, should be low. The optimal solution is a compromise between these contradictory demands, which in our model can be weighted by a parameter. The road optimization problem belongs to the class of frustrated optimization problems. In this paper, a special class of evolutionary strategies, such as the Boltzmann and Darwin and mixed strategies, are applied to find differently optimized solutions (graphs of varying density) for the road network, depending on the degree of frustration. We show that the optimization process occurs on two different time scales. In the asymptotic limit, a fixed relation between the mean connection distance (detour) and the total length (costs) of the network exists that defines a range of possible compromises. Furthermore, we investigate the density of states, which describes the number of solutions with a certain fitness value in the stationary regime. We find that the network problem belongs to a class of optimization problems in which more effort in optimization certainly yields better solutions. An analytical approximation for the relation between effort and improvement is derived.
, David Levinson
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, Carlos A. Coello Coello
. (2008) An empirical study about the usefulness of evolution strategies to solve constrained optimization problems. International Journal of General Systems 37
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, Filippo A. Salustri
. (2007) Computational Intelligence in Product Design Engineering: Review and Trends. IEEE Transactions on Systems, Man and Cybernetics, Part C (Applications and Reviews) 37
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, John G. Taylor
, Dieter Suter
. (2007) Evolution of Athletic Records: Statistical Effects versus Real Improvements. Journal of Applied Statistics 34
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, Stefan Hilbert
, Lutz Schimansky-Geier
, Peter Hänggi
. (2004) Stochastic resonance in biological nonlinear evolution models. Physical Review E 69
Online publication date: 1-May-2004.
, Lutz Schimansky-Geier
, Werner Ebeling
. (2004) Exact Solutions for Evolutionary Strategies on Harmonic Landscapes. Evolutionary Computation 12
Online publication date: 1-Mar-2004.Abstract | PDF (399 KB) | PDF Plus (422 KB)
, W. Ebeling
, L. Schimansky-Geier
, P. Hänggi
. (2003) Kramers problem in evolutionary strategies. Physical Review E 67
Online publication date: 1-Jun-2003.
. (2001) Traffic and related self-driven many-particle systems. Reviews of Modern Physics 73
Online publication date: 1-Dec-2001.
, L MOLGEDEY
, A REIMANN
. (2000) Stochastic urn models of innovation and search dynamics. Physica A: Statistical Mechanics and its Applications 287
Online publication date: 1-Dec-2000.