A bi-objective optimization framework for three-dimensional road alignment design

Abstract

Optimization of three-dimensional road alignments is a nonlinear non-convex optimization problem. The development of models that fully optimize a three-dimensional road alignment problem is challenging due to numerous factors involved and complexities in the geometric specification of the alignment. In this study, we developed a novel bi-objective optimization approach to solve a three dimensional road alignment problem where the horizontal and vertical alignments are optimized simultaneously. Two conflicting cost objective functions, earthwork cost and the utility cost, are cast in a bi-objective optimization problem. We numerically compare several multiobjective optimization solvers, and find that it is possible to determine the Pareto front in a reasonable time.good road alignments and approximate construction costs have been developed [23]. The automation of the road design problem reduces the tedious and error-prone manual tasks, most notably drafting [27]. In addition, this procedure allows the use of optimization techniques in search of a good alignment [38]. Optimization techniques save design time and provide the decision maker with powerful tools that search for an alignment with minimum cost from a large number of alternative alignments. In fact, optimization of road alignment can yield considerable savings in construction costs when compared with unoptimized design procedures [38].The road design problem can be broken down into three interconnected stages: the horizontal alignment, the vertical alignment, and the earthwork [18]. The horizontal alignment is a bird's eye view of a road trajectory. A typical horizontal alignment is composed of a sequence of tangents, circular curves, and transition curves. Transition curves have the property that the radius of curvature changes progressively along them. The main considerations in horizontal alignment design are that it should avoid lands which are restricted or expensive to purchase, obstacles which present engineering difficulties, and ground which may involve large amount of earthwork. The cost of road construction for the horizontal alignment problem depends on the cost of acquiring land and on the output of the vertical alignment stage [18]. Optimization of the horizontal alignment seeks a low cost route while adhering to the design standards and reducing environmental impacts [1]. However, optimization of horizontal alignment should also seek a highly utile route. These two goals may often be in conflict with each other. In the literature, the following models have been developed for optimizing horizontal alignments: calculus of variation [37], network optimization [40], dynamic programming [38], and genetic algorithms [24]. Detailed discussion on the advantages and disadvantage of these methods can be found in [22].The vertical alignment is the view of the centreline of the road when seen along the longitudinal cross-section of the road. A typical vertical alignment is composed of straight sections known as vertical tangents and parabolic curves, n...

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