Optimization of Road Networks Using Evolutionary Strategies

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; 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.

Traffic and related self-driven many-particle systems

“…Traffic control and optimization is an old and large field (see, e.g., Cremer, 1978;Cremer and May, 1985;Smulders, 1989;Dougherty, 1995;Kühne, 1993;Kühne et al, 1995Kühne et al, , 1997Taale and Middelham, 1995;Schweitzer et al, 1998a), which can be certainly not discussed in detail, here. Overviews of optimization approaches by physicists can be found in the Proceedings of the Workshops on Traffic and Granular Flow (Wolf et al, 1996;Schreckenberg and Wolf, 1998;Helbing et al, 2000c; see also Claus et al, 1999), while the readers interested in the engineering literature are referred to the books and review articles by Pagageorgiou (1995Pagageorgiou ( , 1999 as well as Lapierre and Steierwald (1987).…”

Short-length routes in low-cost networks via Poisson line patterns

“…An algorithm for minimizing excess for a given length is described in [8], where results for a 39 point configuration are shown. But neither this nor [1] has led to the study of n tending to ∞ asymptotics.…”

Evolution of Athletic Records: Statistical Effects versus Real Improvements

“…The approach should also be useful to obtain estimations for the quality of the best solutions of NP hard problems (employing density-of-states formalisms), like the travelling salesman problem (Beardwood et al, 1958) and the optimization of road networks (Schweitzer et al, 1997). An application to stock-market analysis also appears feasible in principle, either directly or indirectly: we verified that the prerequisite of stationarity is fullfilled at least for some second-line stocks.…”