Establishing optimal project-level strategies for pavement maintenance and rehabilitation – A framework and case study

This article presents a framework and an illustrative example for identifying the optimal pavement maintenance and rehabilitation (M&R) strategy using a mixed-integer nonlinear programming model. The objective function is to maximize the cost-effectiveness expressed as the ratio of the effectiveness to the cost. The constraints for the optimization problem are related to performance, budget, and choice. Two different formulations of effectiveness are derived using treatment-specific performance models for each constituent treatment of the strategy; and cost is expressed in terms of the agency and user costs over the life cycle. The proposed methodology is demonstrated using a case study. Probability distributions are established for the optimization input variables and Monte Carlo simulations are carried out to yield optimal solutions. Using the results of these simulations, M&R strategy contours are developed as a novel tool that can help pavement managers quickly identify the optimal M&R strategy for a given pavement section.     

Reliability-based performance simulation for optimized pavement maintenance

Roadway pavement maintenance is essential for driver safety and highway infrastructure efficiency. However, regular preventive maintenance and rehabilitation (M&R) activities are extremely costly. Unfortunately, the funds available for the M&R of highway pavement are often given lower priority compared to other national development policies, therefore, available funds must be allocated wisely. Maintenance strategies are typically implemented by optimizing only the cost whilst the reliability of facility performance is neglected. This study proposes a novel algorithm using multi-objective particle swarm optimization (MOPSO) technique to evaluate the cost-reliability tradeoff in a flexible maintenance strategy based on non-dominant solutions. Moreover, a probabilistic model for regression parameters is employed to assess reliability-based performance. A numerical example of a highway pavement project is illustrated to demonstrate the efficacy of the proposed MOPSO algorithms. The analytical results show that the proposed approach can help decision makers to optimize roadway maintenance plans.     

A MODIFIED DEMPSTER-SHAFER THEORY FOR MULTICRITERIA OPTIMIZATION

Abstract

A new methodology, based on a modified Dempster-Shafer (DS) theory, is proposed for solving multicriteria design optimization problems. It is well known that considerable amount of computational information is acquired during the iterative process of optimization. Based on the computational information generated in each iteration, an evidence-based approach is presented for solving a multiobjective optimization problem. The method handles the multiple design criteria, which are often conflicting and non-commensurable, by constructing belief structures that can quantitatively evaluate the effectiveness of each design in the range 0 to 1. An overall satisfaction function is then defined for converting the original multicriteria design problem into a single-criterion problem so that standard single-objective programming techniques can be employed for the solution. The design of a mechanism in the presence of seven design criteria and eighteen design variables is considered to illustrate the computational details of the approach. This work represents the first attempt made in the literature at applying DS theory for numerical engineering optimization.     

An uncertain multidisciplinary design optimization method using interval convex models

This article proposes an uncertain multi-objective multidisciplinary design optimization methodology, which employs the interval model to represent the uncertainties of uncertain-but-bounded parameters. The interval number programming method is applied to transform each uncertain objective function into two deterministic objective functions, and a satisfaction degree of intervals is used to convert both the uncertain inequality and equality constraints to deterministic inequality constraints. In doing so, an unconstrained deterministic optimization problem will be constructed in association with the penalty function method. The design will be finally formulated as a nested three-loop optimization, a class of highly challenging problems in the area of engineering design optimization. An advanced hierarchical optimization scheme is developed to solve the proposed optimization problem based on the multidisciplinary feasible strategy, which is a well-studied method able to reduce the dimensions of multidisciplinary design optimization problems by using the design variables as independent optimization variables. In the hierarchical optimization system, the non-dominated sorting genetic algorithm II, sequential quadratic programming method and Gauss–Seidel iterative approach are applied to the outer, middle and inner loops of the optimization problem, respectively. Typical numerical examples are used to demonstrate the effectiveness of the proposed methodology.     

Explicit consideration of multiple objectives in cellular manufacturing

Although many methodologies have been proposed for solving the cell-formation problem, few of them explicitly consider the existence of multiple objectives in the design process. In this article, the development of multi-objective genetic programming single-linkage cluster analysis (GP-SLCA), an evolutionary methodology for the solution of the multi-objective cell-formation problem, is described. The proposed methodology combines an existing algorithm for the solution of single-objective cell-formation problems with NSGA-II, an elitist evolutionary multi-objective optimization technique. Multi-objective GP-SLCA is able to generate automatically a set of non-dominated solutions for a given multi-objective cell-formation problem. The benefits of the proposed approach are illustrated using an example test problem taken from the literature and an industrial case study.     

Dynamic Programming for QFD Optimization

Quality function deployment (QFD) is a useful method in product design and development and its aim is to improve the quality and to better meet customers' needs. Due to cost and other resource constraints, trade‐offs are always needed. Many optimization methods have been introduced into the QFD process to maximize customer satisfaction under certain constraints. However, current optimization methods sometimes cannot give practical optimal results and the data needed are hard or costly to get. To overcome these problems, this paper proposes a dynamic programming approach for the optimization problem. We first use an extended House of Quality to gather more information. Next, limited resources are allocated to the technical attributes using dynamic programming. The value of each technical attribute can be determined according to the resources allocated to them. Compared with other optimization methods, the dynamic programming method requires less information and the optimal results are more relevant. Copyright © 2005 John Wiley & Sons, Ltd.     

An optimum selection strategy of reflective cracking mitigation methods for an asphalt concrete overlay over flexible pavements

Reflective Cracking (RC) has been a daunting challenge in pavement maintenance and rehabilitation (M&R), yet, still, after several decades of research, no exclusive solution prevails. Moreover, RC mitigation methods have shown significant variation in in situ performance. Therefore, a technique tailored to select an effective RC mitigation method is essential for the success of pavement M&R. In this study, a life cycle cost (LCC) and multi-criteria decision-making (MCDM) analyses were conducted to evaluate the effectiveness of currently available RC mitigation methods and to select the optimal method for an asphalt concrete overlay above flexible pavements. The MCDM includes three components: LCC, performance, and materials (recyclability). These criteria determine the selection ranking of each RC mitigation method. In addition, the effects of the priority level including cost, performance, and recyclability on the final decision were evaluated by conducting a series of sensitivity analysis under multiple scenarios; therefore, weight combination of the three criteria were recorded to define the measurements affecting the final decision.     

Optimization of structures under material parameter uncertainty using evidence theory

An evidence-based approach is developed for optimization of structural components under material parameter uncertainty. The approach is applied to evidence-based design optimization (EBDO) of externally stiffened circular tubes under axial impact load using an isotropic–elastic–plastic plasticity model to simulate dynamic material behaviour. Uncertainty modelling considers the changes in material parameters that are caused by variability in material properties as well as incertitude and errors in experimental data and procedure to determine the material parameters. Spatial variation of material parameters across the structural component is modelled using a field joint belief structure and propagated for the calculation of evidence-based objective function and design constraints. Surrogate models are used in both uncertainty propagation and solution of the optimization problem. The methodology and the solution to the EBDO example problem are presented and discussed.     

Optimization of the Active Composition of the Wind Farm Using Genetic Algorithms

The article presents the results of research on the possibilities of using genetic algorithms for solving the multicriteria optimization problem of determining the active components of a wind farm. Optimization is carried out on two parameters: efficiency factor of wind farm use (integrated parameter calculated on the basis of 6 parameters of each of the wind farm), average power deviation level (average difference between the load power and energy generation capabilities of the active wind farm). That was done an analysis of publications on the use of genetic algorithms to solve multicriteria optimization problems. Computer simulations were performed, which allowed us to analyze the obtained statistical data and determine the main optimization indicators. That was carried out a comparative analysis of the obtained results with other methods, such as the dynamic programming method; the dynamic programming method with the general increase of the set loading; the modified dynamic programming method, neural networks. It is established that the average power deviation for the genetic algorithm and for the modified dynamic programming method is located at the same level, 33.7 and 28.8 kW, respectively. The average value of the efficiency coefficient of wind turbine used for the genetic algorithm is 2.4% less than for the modified dynamic programming method. However, the time of finding the solution by the genetic algorithm is 3.6 times less than for the modified dynamic programming method. The obtained results provide an opportunity to implement an effective decision support system in energy flow management.     

An effective simultaneous approach with variable time nodes for dynamic optimization problems

An effective simultaneous approach with variable time nodes is proposed to solve the dynamic optimization problems with multiple control components, where the variable time nodes for each control component are considered as parameters directly and the interval between the neighbouring variable nodes is further refined uniformly to ensure accuracy. Consequently, the method does not treat all the nodes as parameters to ensure efficiency. The gradient formulae and the sensitivities of the states with respect to the controls and the variable time nodes are further derived to solve the nonlinear programming problem transformed from the original dynamic optimization problem. The complete framework and detailed steps of the proposed method are also given. Two classic constrained dynamic optimization problems have been tested as an illustration, and detailed comparisons of the reported literature methods are carried out. The research results show the characteristics and the effectiveness of the proposed approach.     

Unification of robust design and goal programming for multiresponse optimization—a case study

Fixing the levels of input process parameters to meet a required specification of output is a common process quality control problem. Especially when the output has many quality characteristics, and each of these quality characteristics has to satisfy a given specification, difficulties may arise. One such problem was encountered in an injection moulding process. This process was optimized using Taguchi's Robust Design methodology. Details of the process, problems encountered and outcome of optimization are presented in this paper. The optimization study using Taguchi's methodology revealed that the optimum conditions obtained for one response are not completely compatible with those of other responses. So trade-offs were made in selection of levels for factors using engineering judgement. This increases the uncertainty in the decision making process. In this paper, an approach is presented to optimize multiresponses simultaneously using goal programming in conjunction with Taguchi's methodology. Details of modelling, analysis and inferences obtained with relevance to the case are presented. This study revealed that the optimum conditions obtained using goal programming in conjuction with Taguchi's methodology have better goal attainment properties compared to Robust design. To understand goal attainment behaviour of output characteristics for various process conditions, a detailed sensitivity analysis was also conducted. The outcome of this analysis is also discussed in this paper. © 1997 John Wiley & Sons, Ltd.     

A Class of Mathematical Programs with Equilibrium Constraints: A Smooth Algorithm and Applications to Contact Problems

We discuss a special mathematical programming problem with equilibrium constraints (MPEC), that arises in material and shape optimization problems involving the contact of a rod or a plate with a rigid obstacle. This MPEC can be reduced to a nonlinear programming problem with independent variables and some dependent variables implicity defined by the solution of a mixed linear complementarity problem (MLCP). A projected-gradient algorithm including a complementarity method is proposed to solve this optimization problem. Several numerical examples are reported to illustrate the efficiency of this methodology in practice.     

Monotony analysis and sparse-grid integration for nonlinear chance constrained process optimization

The numerical solution of a nonlinear chance constrained optimization problem poses a major challenge. The idea of back-mapping as introduced by M. Wendt, P. Li and G. Wozny in 2002 is a viable approach for transforming chance constraints on output variables (of unknown distribution) into chance constraints on uncertain input variables (of known distribution) based on a monotony relation. Once transformation of chance constraints has been accomplished, the resulting optimization problem can be solved by using a gradient-based algorithm. However, the computation of values and gradients of chance constraints and the objective function involves the evaluation of multi-dimensional integrals, which is computationally very expensive. This study proposes an easy-to-use method for analysing monotonic relations between constrained outputs and uncertain inputs. In addition, sparse-grid integration techniques are used to reduce the computational time decisively. Two examples from process optimization under uncertainty demonstrate the performance of the proposed approach.     

Computer-aided design by optimization in architecture

This paper shows that optimization concepts are particularly useful in design because of their direct assistance in decision making. In this they subsume evaluation or appraisal techniques. One approach based on dynamic programming is presented as being directly applicable in computer-aided architectural design. Multi-attribute objectives in design can be handled using optimization concepts. Finally, multi-objective design, including multi-attribute multi-objective design, can be handled via the use of Pareto optimality approaches. The result of such processes is a solution database which the designer searches. The solution database contains information about the design decisions themselves as well as the performance of each solution in its various objectives. The designer still assumes responsibility for selecting particular solutions since there is no unique solution produced. It is suggested that any problem which can be manipulated quantitatively can be solved using these concepts.     

A dynamic programming-based particle swarm optimization algorithm for an inventory management problem under uncertainty

This article presents a dynamic programming-based particle swarm optimization (DP-based PSO) algorithm for solving an inventory management problem for large-scale construction projects under a fuzzy random environment. By taking into account the purchasing behaviour and strategy under rules of international bidding, a multi-objective fuzzy random dynamic programming model is constructed. To deal with the uncertainties, a hybrid crisp approach is used to transform fuzzy random parameters into fuzzy variables that are subsequently defuzzified by using an expected value operator with optimistic–pessimistic index. The iterative nature of the authors’ model motivates them to develop a DP-based PSO algorithm. More specifically, their approach treats the state variables as hidden parameters. This in turn eliminates many redundant feasibility checks during initialization and particle updates at each iteration. Results and sensitivity analysis are presented to highlight the performance of the authors’ optimization method, which is very effective as compared to the standard PSO algorithm.     

An augmented Lagrange programming optimization neural network for short-term hydroelectric generation scheduling

An approach based on augmented Lagrange programming neural networks is proposed for determining the optimal hourly amounts of generated power for the hydro-units in an electric power system. This methodology is based on the Lagrange multiplier theory in optimization and searches for solutions satisfying the necessary conditions of optimality in the state space. The equilibrium point of the network satisfies the Kuhn–Tucker condition for the problem. The equilibrium point of the network corresponds to the Lagrange solution of the problem. The proposed technique has been applied to a multi-reservoir cascaded hydro-electric system with a non-linear power generation function of water discharge rate and storage volume. The water transportation delay between connected reservoirs is also taken into account. Results obtained from this approach are compared with those obtained from the two phase optimization neural network and the conventional augmented Lagrange multiplier method. It is concluded from the results that the proposed method provides better results with respect to constraint satisfaction and is very effective in yielding optimal hydro-generation schedules.     

Importance measures and genetic algorithms for designing a risk-informed optimally balanced system

This paper deals with the use of importance measures for the risk-informed optimization of system design and management. An optimization approach is presented in which the information provided by the importance measures is incorporated in the formulation of a multi-objective optimization problem to drive the design towards a solution which, besides being optimal from the points of view of economics and safety, is also ‘balanced’ in the sense that all components have similar importance values. The approach allows identifying design systems without bottlenecks or unnecessarily high-performing components and with test/maintenance activities calibrated according to the components’ importance ranking. The approach is tested at first against a multi-state system design optimization problem in which off-the-shelf components have to be properly allocated. Then, the more realistic problem of risk-informed optimization of the technical specifications of a safety system of a nuclear power plant is addressed.     

Lagrangian heuristic-based neighbourhood search for the multiple-choice multi-dimensional knapsack problem

This article addresses a Lagrangian heuristic-based neighbourhood search for the multiple-choice multi-dimensional knapsack problem, an NP-hard combinatorial optimization problem. The problem is solved by using a cooperative approach that uses a local search for exploring a series of neighbourhoods induced from the Lagrangian relaxation. Each neighbourhood is submitted to an optimization process using two alternative strategies: reducing and moving strategies. The reducing strategy serves to reduce the current search space whereas the moving strategy explores the new search space. The performance of the proposed approach is evaluated on benchmark instances taken from the literature. Its obtained results are compared with those reached by some recent methods available in the literature. New solutions have been obtained for almost 80% of the instances tested.     

Optimization of truss topology using tabu search

A design procedure for integrating topological considerations in the framework of structural optimization is presented. The proposed approach is capable of considering multiple load conditions, stress, displacement and local/global buckling constraints, and multiple objective functions in the problem formulation. Further, since the proposed method permits members to be added to or deleted from an existing topology and the topology is not defined by member areas, the difficulty of not being able to reach singular optima is also avoided. These objectives are accomplished using a discrete optimization procedure which uses 0–1 topological variables to optimize alternate designs. Since the topological variables are discrete in nature and the member cross-sections are assumed to be continuous, the topological optimization problem has mixed discrete-continuous variables. This non-linear programming problem is solved using a memory-based combinatorial optimization technique known as tabu search. Numerical results obtained using tabu search for single and multiobjective topological optimization of truss structures are presented. To model the multiple objective functions in the problem formulation, a cooperative game theoretic approach is used. The results indicate that the optimum topologies obtained using tabu search compare favourably, and in some instances, outperform the results obtained using the ground–structure approach. However, this improvement occurs at the expense of a significant increase in computational burden owing to the fact that the proposed approach necessitates that the geometry of each trial topology be optimized.     

Multi-criteria optimization of large composite parts

The objective of the current study is the optimization of the structure and manufacturing processes of large composite plastic parts. The main attention is paid to strengthening of plastic preformed shell by adding variable thickness glass–fiber composite layers and optimizing the material concentrations of the reinforcement layer. The final properties of the part are determined by minimizing the cost and production time simultaneously. The multistage optimization procedure has been applied. According to this approach, the solution of the posed optimization problem has been decomposed into FEA (including free size optimization), meta-modeling and global optimization. Multiple criteria analysis (MCA) is used for evaluating decision options against multiple criteria. Search for global optimum has been performed using of genetic algorithm. The solution has been implemented in MATLAB code. The product family of the composite plastic bathtub, together with the derivate products and their production technologies, is designed using proposed methodology.