Exploring and exploiting ant colony optimization algorithm for vertical highway alignment development

Abstract

The vertical alignment optimization is about developing a minimum cost curvilinear vertical profile of constrained grade sections and appropriate non‐overlapping vertical curves passing through fixed control points with elevation constraints. Variations in ground profile and discreteness in unit cutting and filling costs make it a non‐convex, noisy, constrained optimization problem with many local minima. Further, the gradient related constraints and vertical curvature are non‐linear. This paper presents an innovative exploring and exploiting ant colony optimization (E&E‐ACO) algorithm with an appropriate point sampling, vertical curve fitting strategies, and an intuitive feasible region identification approach for solving the vertical alignment optimization problem. The E&E‐ACO algorithm extensively explores the feasible search space to generate a set of potential solutions and effectively exploit the space around the potential solutions for developing the optimized vertical alignment. The efficacy of the proposed method is demonstrated using two case studies. In one case study, the optimized solution by the proposed method had a marginally better objective function value and about three times lesser computational time than the solution by the mesh adaptive direct search method. The optimized alignment satisfied the elevation constraints of fixed control points and imitated the manually designed real‐world vertical alignment. The linearly varying exploration and exploitation parameters had better convergence rate than the other tested variations. Further, the proposed method at the end of 1000 iterations yielded about six times better result than the traditional ACO algorithm.

Modeling side slopes in vertical alignment resource road construction using convex optimization

“…Another extension would be to consider depthdependent cutting and filling costs as used in Fwa et al (2002) and Sushma et al (2022). The QCQP model could accommodate such costs by adding a linear or even convex quadratic function of 𝑢 𝑖 into the objective function; such modification would not change the structure of the model, and we expect that it would not change numerical results significantly.…”

A sequential exploration algorithm for the design optimization of horizontal road alignment

“…In addition to the HAS algorithm that inspired this paper, other nature‐inspired computing and optimization algorithms proposed in recent years, such as the neural dynamic model (Park & Adeli, 1997), PSO (Imran et al., 2019; T. Song, Pu, Schonfeld, Zhang, et al., 2022), ACO (Sushma et al., 2022), harmony search algorithm (Siddique & Adeli, 2015), simulated annealing (Siddique & Adeli, 2016b), water drop algorithms (Siddique & Adeli, 2014b), gravitational search algorithm (Siddique & Adeli, 2016a), bacteria foraging algorithm (Wang et al., 2018), spider monkey optimization (Akhand et al., 2020), and spiral dynamics algorithm (Siddique & Adeli, 2014a), have been enhanced and improved to varying degrees in terms of spatial optimizations and ideas for solving optimization problems, all of which have promising prospects for improvement and application to the field of road or railway design. Some of these algorithms, such as the PSO and the ACO, have already been employed in road or railway design as shown in Table 1.…”

Vertical alignment optimization of mountain railways with terrain‐driven greedy algorithm improved by Monte Carlo tree search

“…Besides the vertical alignment, analytical methods were also applied to optimize horizontal alignments (Casal et al., 2017) as well as 3D alignments (Vázquez‐Méndez et al., 2018) and achieved satisfactory results. Despite the good performance, most of these methods oversimplify the vertical alignment optimization problem by formulating it as a continuous and differentiable function with various assumptions, which limits their applicability in real‐world scenarios (Sushma et al., 2022).…”

“…Sushma et al. (2022) proposed an exploring and exploiting ACO algorithm to optimize the vertical alignment of highways.…”