Evaluation of Metaheuristic Methods to Optimize Vertical Alignment of Highway Route

In road design, pavement has detailed design and its cost is inevitable. But, in the infrastructure, the costs can be considerably reduced by optimizing the position of vertical alignment. One of the most expensive parts of the infrastructure is earthwork costs, which is highly dependent on the project vertical alignment. Therefore, the aim of this study was to evaluate various meta-heuristic methods for proposing a method for vertical-alignment optimization to have the lowest cost of earthwork operations. In this study, first, the objective function and constraints of the problem were formulated and then the distance, height, and length of the vertical curve in every point of vertical intersection (PVI) were considered as decision variables. Initial vertical alignment and position of the PVIs were defined according to the guidelines and demands. The objective function was defined as the sum of absolute difference of the vertical alignment height and ground surface. Meanwhile, the constraints were defined as minimum and maximum longitudinal slope, minimum height of the bridges, avoiding interference of the curves, and minimum length of the vertical curve. For optimization of the problem, Genetic Algorithm (GA), Accelerated Particle Swarm Algorithm (APSA) and Firefly Algorithm (FA) were used in the MATLAB software. For better evaluation of the developed method, three different topographies (plain, rolling, and mountainous) were designed and the original vertical alignment was optimized by each algorithm. In addition to the difference of vertical alignment and ground surface, comparison of the ratio of volume of fill to volume of cut, and earthwork costs, was carried out. Results showed that the highest optimiztion percentage for the three topographies belonged to FA, APSA and GA, respectively. Therefore, application of FA highly reduced the costs of road infrastructure. In addition, the time and replications needed to solve the problem show that the necessary time for optimization and obtaining the optimum solution is ignorable in comparison to the achieved cost saving.