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TopHighway Alignment Optimization
Highway alignment optimization models, particularly horizontal alignment design, has been developed in the last three decades and it is realized that the design process is more complex and needs substantial amount of data than simple optimization of vertical alignments (OECD, 1973). Inclusion of factors like political, socioeconomic, environmental, and the costs associated with them make the process complicated. The basic approach so far to address the problem can be categorized into calculus of variations, network optimization and dynamic programming.
Calculus of variation is purely a mathematical modeling approach where two spatial points (start and end) are connected by a curve and integration of a cost function is minimized (Wan, 1995). In order to integrate, the cost function should be continuous between the two points of interest, which is very unlikely in real world problems. Based on this principle, Howard et al. (1968) developed the Optimum Curvature Principle (OCP) for horizontal highway alignment design model. This model was applied in finding a maritime route through dynamic ice field (Thomson & Sykes, 1988) and horizontal alignment of an expressway in flat south Florida (Shaw & Howard, 1982). In both applications authors used local cost function to represent the discreteness of cost at different zones. In real world, the right-of-way cost, a component of local cost function, is not continuous within a zone. This makes the process more cumbersome when applied to area with complicated land use patterns.
Network optimization method is based on the concept of optimizing highway alignment as a network problem. The search space is divided into small cells and a network is formed. The nodes represent the location of the cells and the links represent the costs. This methodology was successfully applied and practiced by researchers for horizontal alignment (Turner & Miles, 1971; Turner, 1978; Athanassoulis & Calogero, 1973). Parker (1977) developed a two-stage approach to optimize the vertical alignment along with horizontal alignment. Roise, Shear, and Bianco (2004) used network optimization methodology for sensitivity analysis of corridors in wetland areas. The results obtained by this methodology produces a piecewise linear trajectory which can be well defined as a corridor not as an alignment (Jong, 1998; Jha, Schonfeld, Jong, & Kim, 2006). Apart from this, the methodology should calculate the cost information for each link, which is extensive in nature and needs considerable amount of storage space.