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Frank Schweitzer, Werner Ebeling, Helge Rose, Olaf Weiss:

Optimization of Road Networks Using Evolutionary Strategies
 in:
 Evolutionary Computation 5/4 (1998) 419438
 Abstract:

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, (ii) the costs for road construction and maintainance, which are
assumed proportional to the total length of the roads, should be low.
The optimal solution is a compromise between these contradicting
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, evolutionary strategies, such as
the Boltzmann and Darwin strategy, are applied to find different
optimized solutions (graphs of varying density) for the road network in
dependence 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, which defines a range of
possible compromises.
Further, 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, where more effort in optimization certainly yields better
solutions. An analytical approximation for the relation between effort
and improvement is derived.
 Keywords:

network, evolutionary strategy, frustrated
problem, compromise
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