Valuating Different Penalty Functions for Optimization of Highway Vertical Alignment using Accelerated Particle Swarm Optimization (APSO) and Colliding Bodies Optimization (CBO) Algorithms

Design of vertical alignment with minimum earthwork cost can effectively reduce the construction costs of highways. In most past researches, the objective function has been considered as the sum of the absolute value of difference between the vertical alignment and the existing ground and due to the complexity of earthwork calculation, real costs of earthwork have been ignored. Also, to deal with constraints just the static penalty functions are employed. In case of static penalty functions, if one of the constraints is violated, a relatively large coefficient is multiplied by the objective function and as a result, many early populations are removed in the next iteration and the convergence time increases. This paper aims to compare different penalty functions for problem of vertical alignment optimization. To this end, station, elevation and vertical curve length in case of each point of vertical intersection (PVI) were considered as decision variables. The objective function was considered as earthwork cost and constraints were assumed as the maximum and minimum longitudinal slope, minimum elevation of compulsory points, and the minimum length of vertical curves. For solving of this optimization problem, the accelerated particle swarm optimization (APSO) and the colliding bodies optimization (CBO) algorithm were employed. The results illustrate that the selected penalty function greatly affects the convergence speed as well as the optimum solution (earthwork costs). This study also showed that the effective optimization of highway vertical alignment can be achieved using annealing penalty function and CBO algorithm.