Prescreening and Repairing in a Genetic Algorithm for Highway Alignment Optimization

Abstract:   The method of handling infeasible solutions in an evolutionary search algorithm [e.g., genetic algorithms (GAs)] is crucial to the effectiveness of the solution search process. This problem arises because solution search steps, techniques, and operators used in GAs (such as reproduction, mutation, and recombination) are normally  " blind " to the constraints, and thus GAs can generate solutions that do not satisfy the requirements of the problems. In GA-based highway alignment optimization (HAO), many infeasible solutions, which violate model constraints, are also possibly generated, and evaluation of such solutions is wasteful. This study focuses on ways to avoid wasting computation time on evaluating infeasible solutions generated from the GA-based HAO, and develops a prescreening and repairing (P&R) method for an efficient search of highway alignments. The key idea of the P&R method is to repair (before the very detailed alignment evaluation) any candidate alignments whose violations of design constraints can be fixed with reasonable modifications. However, infeasible alignments whose violations of constraints are too severe to repair are discarded (prescreened) before any detailed evaluation procedure is applied. The proposed P&R method is simple, but significantly improves computation time and solution quality in the GA-based HAO process. Such improvements are demonstrated with a test example for a real road project. Through the example study, it is shown that the model incorporating the P&R method can find a good solution much faster (by approximately 23%) than the model with the conventional penalty method. In addition, the P&R method allows the model to evaluate about 70% more solutions than that it can evaluate with the penalty method for the same number of generations.     

Optimal placement of steel plate shear walls for steel frames by bat algorithm

Layout optimization of steel frames with steel plate walls (SPWs) using a meta‐heuristic search algorithm is the main aim of the present study. SPWs are lateral load‐resisting systems, especially against earthquake excitation. These systems offer significant advantages in terms of cost, performance and ease of design compared with other systems. In this study, orthotropic membrane model is used to model the behaviour of steel plate shear walls. The newly developed bat algorithm, which is based on the echolocation behaviour of bats, is employed as the present study optimizer. Design variables of the optimization problem consist of the cross sections of beams and columns of the frame, the web plate thicknesses of SPWs and the placement of SPW in the frame. The bat algorithm performs suitable selection of sections from the AISC wide‐flange (W) shapes list. Strength constraints of the American Institute of Steel Construction Load and Resistance Factor Design and displacement constraints are checked during the optimization process. The results reveal the effectiveness of the proposed method for optimization of steel frames with SPWs. Copyright © 2014 John Wiley & Sons, Ltd.     

A three‐dimensional distance transform for optimizing constrained mountain railway alignments

Railway alignment optimization is considered one of the most complicated and time‐consuming problems in railway planning and design. It requires searching among the infinite potential alternatives in huge three‐dimensional (3D) search spaces for a near‐optimal alignment, while considering complex constraints and a nonlinear objective function. In mountainous regions, the complex terrain and constructions require additional and more complex constraints than in topographically simpler regions. In this paper, the authors solve this problem with an algorithm based on a 3D distance transform (3D‐DT). Compared with previous two‐dimensional distance transform (2D‐DT) methods developed in this field, the feasible search spaces of 3D‐DT are greatly increased. Consequently, this new method can find more alternatives with higher qualities. In this approach, an erythrocyte‐shaped 3D neighboring mask is developed to narrow local search spaces and speed up the search process. Besides, a stepwise‐backstepping strategy is designed to dynamically determine feasible 3D search spaces and efficiently search the study area. During the 3D‐DT search process, multiple constraints, including geometric, construction, and location constraints, are effectively handled. After the 3D‐DT search, a genetic algorithm is employed to optimize the 3D‐DT paths into final alignments. Finally, this novel approach is applied to an actual case in a complex mountainous region. The comprehensive cost of the best solution generated by 3D‐DT is 16% below a manual solution produced by very experienced human designers. Furthermore, the total number of feasible alternatives found by 3D‐DT is 4.3 times greater than by 2D‐DT. The comprehensive cost of the best 3D‐DT solution is 10% below the best one generated by 2D‐DT.     

A modified motion planning algorithm for horizontal highway alignment development

A horizontal alignment can be represented by three key factors: number of horizontal points of intersection (HPIs), their locations, and corresponding horizontal curve radii. Deciding all the three factors simultaneously requires extensive effort, which is not practically feasible in the manual alignment development process. Most available computer‐aided methods prioritize some or all the three factors in the automated alignment development processes. However, approximation in HPI location or pre‐selection of HPI number and curve radius are the few limitations of these methods. This study presents a modified motion‐planning based algorithm for developing new horizontal alignments with optimized costs and impacts. It simultaneously uses a low‐discrepancy sampling technique to develop increasingly dense potential HPIs, rapidly exploring random trees to find a suitable number of intermediate HPIs at appropriate locations and sequential quadratic algorithm to select optimally fitted curve radii. The proposed algorithm is integrated with the GIS database for realistic location‐dependent cost and environmental impact assessment. Two real‐world study areas were selected to compare the results with the one reported in the literature and to evaluate backtracking capability. Results indicated the proficiency of the proposed algorithm in developing new alignments. The sensitivity analyses revealed the effect of design speed and right‐of‐way width on the alignment generation. The proposed algorithm can automate the new horizontal highway alignment development process and support highway engineers in planning and development.     

Mountain railway alignment optimization integrating layouts of large-scale auxiliary construction projects

Mountain railway alignment design is an important but complex civil engineering problem. To overcome the drastically undulating terrain, long tunnels and high bridges are major structures used along a mountain railway, which poses great challenges for railway design and construction. Unfortunately, despite being studied for many years, the crucial construction factors of complex structures have received slight attention in alignment optimization. In this paper, for the first time, the layout of large-scale auxiliary construction projects (LACPs), including tunnel shafts and access roads, is incorporated into the alignment design process in order to consider construction practicability and economy. Primarily, an alignment–LACPs concurrent optimization model is built. After defining the comprehensive design variables, the alignment–LACPs total construction cost is formulated as the objective function. Besides, the separate constraints for designing the alignment and LACPs are considered. Also, a construction duration computation is proposed for constraining the alignment–LACPs integration. To solve the model, a four-step hybrid solution method is developed. Specifically, the alignment is first generated with a particle swarm optimization (PSO). Afterward, a new divide and conquer approach is devised to search for shaft alternatives along the alignment. Then, a customized Dijkstra algorithm is developed to search for complex access roads. Finally, a novel polynomial mechanism for time-varying acceleration coefficients (TVAC) is designed for PSO to evolve the alignment–LACPs solutions. The above model and methods have been applied to two complex actual mountain railway examples. Their effectiveness is demonstrated through detailed analysis of resulting railway solutions and control experiments with contemporary TVAC-based methods.     

Intersection Modeling for Highway Alignment Optimization

Abstract:   When optimizing a highway alignment, it is desirable to consider new and modified intersections along it. This article develops methods for locally optimizing intersections within highway alignment optimization processes. Design and operational characteristics for intersections are reviewed from the literature. The formulation considers the major costs that are sensitive to intersection characteristics. Genetic algorithms are used for optimal search. The proposed methods are implemented on an artificial study area and on a real one through the use of geographic information systems. The results show how the methods work for local optimization of intersections as well as for optimizing entire alignments. These methods can be used for improving search flexibility, thus allowing more effective intersections. They also provide a basis for extending the alignment optimization from single highways to networks .     

A deep reinforcement learning approach to mountain railway alignment optimization

The design and planning of railway alignments is the dominant task in railway construction. However, it is difficult to achieve self-learning and learning from human experience with manual as well as automated design methods. Also, many existing approaches require predefined numbers of horizontal points of intersection or vertical points of intersection as input. To address these issues, this study employs deep reinforcement learning (DRL) to optimize mountainous railway alignments with the goal of minimizing construction costs. First, in the DRL model, the state of the railway alignment optimization environment is determined, and the action and reward function of the optimization agent are defined along with the corresponding alignment constraints. Second, we integrate a recent DRL algorithm called the deep deterministic policy gradient with optional human experience to obtain the final optimized railway alignment, and the influence of human experience is demonstrated through a sensitivity analysis. Finally, this methodology is applied to a real-world case study in a mountainous region, and the results verify that the DRL approach used here can automatically explore and optimize the railway alignment, decreasing the construction cost by 17.65% and 7.98%, compared with the manual alignment and with the results of a method based on the distance transform, respectively, while satisfying various alignment constraints.     

Preliminary Highway Design with Genetic Algorithms and Geographic Information Systems

A method that integrates geographic information systems (GIS) with genetic algorithms (GAs) for optimizing horizontal highway alignments between two given end points is presented in this article. The proposed approach can be used to optimize alignments in highly irregular geographic spaces. The resulting alignments are smooth and satisfy minimum-radius constraints, as required by highway design standards. The objective function in the proposed model considers land-acquisition cost, environmental impacts such as wetlands and flood plains, length-dependent costs (which are proportional to the alignment length), and user costs. A numerical example based on a real map is employed to demonstrate application of the proposed model to the preliminary design of horizontal alignments.     

Optimal Routing with Multiple Objectives: Efficient Algorithm and Application to the Hazardous Materials Transportation Problem

Abstract: This article presents an efficient parametric optimization method for the biobjective optimal routing problem. The core process is a bounded greedy single‐objective shortest path approximation algorithm. This method avoids the computationally intensive dominance check with labeling methods and overcomes the deficiency with existing parametric methods that can only find extreme nondominated paths. Moreover, we propose a decomposition scheme to convert a multiobjective routing problem into a number of biobjective problems. We then compare its computational performance against the classic label‐correcting method over a set of synthetically generated random networks and illustrate its algorithmic advances and solution behaviors by an example application of routing hazardous materials in a U.S. northeastern highway network.     

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

Vertical alignment design is an important process for railway construction which fundamentally affects the infrastructure investment cost. Determining an optimized vertical alignment is a challenging task since the objective function is non-linear, non-differentiable, and quite unsmooth. Great efforts have been invested in solving the vertical alignment optimization problem and many methods have been proposed. However, for vertical alignment designs in complex mountainous regions, the terrain conditions impose great difficulties and, hence, many bridges and tunnels are generally required. Thus, reasonably locating bridges and tunnels along the entire alignment (EA) is a major concern that deserves further investigations. To solve this problem, this study develops a terrain-driven greedy algorithm improved by Monte Carlo tree search (T-GRA-MCTS). A terrain-driven method is proposed to determine the number and longitudinal distribution of vertical points of intersection (VPIs). In order to trade off the local section of an alignment versus the EA when optimizing each VPI along the alignment to locate bridges and tunnels reasonably, an MCTS is employed and integrated with a GRA. The basic MCTS is modified for vertical alignment optimization with a novel equation for computing the upper confidence bounds for trees and a customized termination criterion is provided. A real-world railway case is used to demonstrate the effectiveness of the proposed method. The results show that the T-GRA-MCTS performs better than a greedy search method without MCTS or a widely used nature-inspired algorithm (i.e., a particle swarm optimization). Moreover, it can find a less expensive solution than the one designed by experienced human engineers.     

A Heuristic Approach for Selecting Highway Investment Alternatives

Abstract: A heuristic approach is developed for systemwide highway project selection. It can assess changes in total project benefits using different project implementation options under budget uncertainty and identify the best option to achieve maximized total benefits. The proposed approach consists of a stochastic model formulated as the zero/one integer doubly constrained multidimensional knapsack problem and an efficient heuristic solution algorithm developed using the Lagrange relaxation technique. A method is also introduced to improve the upper bound for the objective function by simultaneously changing multiple Lagrange multipliers. The approach is applied in a computational study to obtain a comprehensive highway investment plan for a State‐maintained highway system in the United States.     

A Polynomial Parametric Curve (PPC‐CURVE) for the Design of Horizontal Geometry of Highways

Abstract: The use of transition curves in the road design is a solution to make the gradual evolution of curvature and, at the same time, to improve the comfort level of drivers and provide a good visual perception of the curve. Clothoid is the most widely used transition curve in road design so far, because it ensures the continuity of the curvature with the other geometric elements of the alignment. However, several researches allow the use of polynomial functions as an alternative to the clothoid. Such use is permitted in accordance with the verification of allowable vehicle–road dynamics. Polynomial solutions of transition curves can be a valuable alternative for the traditional solutions (first transition curve, circular arc, second transition curve). A fifth‐degree polynomial parametric curve (PPC‐curve) for the design of highway alignment is proposed in this article. An analysis of the theoretical aspects to solve more complex geometrical problems recurring in practical highway geometric design is carried out. With regard to this problem, a shape parameter giving flexibility to the polynomial solution in relation to project needs has also been introduced. To implement the procedure, an original computer program has been developed. Numerical applications have been performed for comparison with the traditional solutions.     

Optimum design of post‐tensioned axially symmetric cylindrical walls using novel hybrid metaheuristic methods

An efficient methodology for various structural design problems is needed to optimize the total cost for structures. Although some methods seem to be efficient for applications, due to using special algorithm parameters, computational cost, and some other reasons, there is still much to be done in order to develop an effective method for general design applications. This paper describes the influence of the selected procedure on the design of cost‐optimized, post‐tensioned axially symmetric cylindrical reinforced concrete walls. In this study, the optimum design of axially symmetric cylindrical walls using several metaheuristic algorithms is investigated. The new generation algorithms used in the study are flower pollination algorithm, teaching–learning‐based optimization, and Jaya algorithm (JA). These algorithms are also compared with one of the previously developed algorithm called harmony search. The numerical examples were done for walls with 4‐ to 10‐m height and for 1, 5, 10, 15, 20, and 25 post‐tensioned load cases, respectively. Several independent runs are conducted, and in some of these runs, JA may trap to a local solution. To overcome this situation, hybrid algorithms such as JA using Lévy flights, JA using Lévy flights with probabilistic student phase (JALS), JA using Lévy Flights with consequent student phase (JALS2), and JA with probabilistic student phase are developed. It is seen that in many respects, the JALS2 and JALS are the most effective within the proposed hybrid approaches.     

A Hybrid Branch‐and‐Bound and Benders Decomposition Algorithm for the Network Design Problem

Given a set of candidate road projects associated with costs, finding the best subset with respect to a limited budget is known as the network design problem (NDP). The NDP is often cast in a bilevel programming problem which is known to be NP‐hard. In this study, we tackle a special case of the NDP where the decision variables are integers. A variety of exact solutions has been proposed for the discrete NDP, but due to the combinatorial complexity, the literature has yet to address the problem for large‐size networks, and accounting for the multimodal and multiclass traffic flows. To this end, the bilevel problem is solved by branch‐and‐bound. At each node of the search tree, a valid lower bound based on system optimal (SO) traffic flow is calculated. The SO traffic flow is formulated as a mixed integer, non‐linear programming (MINLP) problem for which the Benders decomposition method is used. The algorithm is coded on a hybrid and synchronized platform consisting of MATLAB (optimization engine), EMME 3 (transport planning module), MS Access (database), and MS Excel (user interface). The proposed methodology is applied to three examples including Gao's network, the Sioux‐Falls network, and a real size network representing the city of Winnipeg, Canada. Numerical tests on the network of Winnipeg at various budget levels have shown promising results.     

Mountain Railway Alignment Optimization with Bidirectional Distance Transform and Genetic Algorithm

Various challenging constraints must be satisfied in railway alignment design for topographically complex mountainous regions. The alignment design for such environments is so challenging that existing methodologies have great difficulties in automatically generating viable railway alignment alternatives. We solve this problem with a hybrid method in which a bidirectional distance transform (DT) algorithm automatically selects control points before a genetic algorithm (GA) refines the alignment. This approach solves the problems of (1) determining the appropriate distribution of control points in the GA and (2) producing alignments that deviate significantly from the DT‐optimized paths. Automatic design of backtracking curves and dynamic generation of vertical points of intersection handling multiple constraints are developed to improve the GA performance. This method has been applied to a real case on the Sichuan–Tibet Railway where excessively severe natural gradients must be overcome. It automatically finds an alignment optimized for the given objectives and complex constraints, as well as various promising alternatives.     

Design optimization of truss structures using cuckoo search algorithm

A new metaheuristic optimization algorithm is developed to solve truss optimization problems. The new algorithm, called cuckoo search (CS), is examined by solving five truss design optimization problems with increasing numbers of design variables and complexity in constraints. The performance of the CS algorithm is further compared with various classical and advanced algorithms, selected from a wide range of the state‐of‐the‐art algorithms in the area. The results identify that the final solutions obtained by the CS are superior compared with the best solutions obtained by the other algorithms. Finally, the unique search features used in the CS and the implications for future researches are discussed in detail. Copyright © 2012 John Wiley & Sons, Ltd.     

Using GIS, Genetic Algorithms, and Visualization in Highway Development

A model for highway development is presented, which uses geographic information systems (GIS), genetic algorithms (GA), and computer visualization (CV). GIS serves as a repository of geographic information and enables spatial manipulations and database management. GAs are used to optimize highway alignments in a complex search space. CV is a technique used to convey the characteristics of alternative solutions, which can be the basis of decisions. The proposed model implements GIS and GA to find an optimized alignment based on the minimization of highway costs. CV is implemented to investigate the effects of intangible parameters, such as unusual land and environmental characteristics not considered in optimization. Constrained optimization using GAs may be performed at subsequent stages if necessary using feedback received from CVs. Implementation of the model in a real highway project from Maryland indicates that integration of GIS, GAs, and CV greatly enhances the highway development process.     

Optimal drift design of tall reinforced concrete buildings with non‐linear cracking effects

This paper presents an efficient, computer‐based technique for the optimum drift design of tall reinforced concrete (RC) buildings including non‐linear cracking effects under service loads. The optimization process consists of two complementary parts: an iterative procedure for the non‐linear analysis of tall RC buildings and a numerical optimality criteria (OC) algorithm. The non‐linear response of tall RC buildings due to the effects of concrete cracking is obtained by a series of linear analyses, the so‐called direct effective stiffness method. In each linear analysis, cracked structural members are first identified and their stiffness modified based on a probability‐based effective stiffness relationship. Stiffness reduction coefficients are introduced as measures of the remaining stiffness for structural elements after cracking. A rigorously derived OC method is developed to solve for the minimum weight/cost design problem subject to multiple drift constraints and member sizing requirements. A shear wall‐frame example is presented to illustrate the application of this optimal design method. The design results of the optimized structure with cracking effects are compared to those of the linear‐elastic structure without concrete cracking. Copyright © 2005 John Wiley & Sons, Ltd.     

Optimization of energy consumption in buildings with hydronic heating systems considering thermal comfort by use of computer-based tools

The paper deals with an optimization of parameters, which influence the energy and investment cost as well as the thermal comfort. The parameters considered in this study are: the insulation thickness of the building envelope, the supply-water temperature and the heat exchange area of the radiators. A combination of the building energy simulation software EnergyPlus ¹ and the generic optimization program GenOpt (see footnote 1) has been used for this purpose. The paper presents the application of a one-objective optimization algorithm solving the problems with two objectives, because the optimization algorithm is one-objective and the problem has two objectives, which are minimal total costs and satisfied thermal comfort. The total costs represent the sum of energy consumption and the investment costs. The thermal comfort is represented by Predicted Percentage of Dissatisfied (PPD) in this study. The optimization is used to determine the values of parameters that give the lowest sum of investment and energy cost, under the condition that the thermal comfort is satisfied. In addition, the optimization processes show the mutual influence of parameters on both the total cost and the thermal comfort.