岩体随机不连续面产状数据划分方法研究

动态聚类算法从本质上讲是单目标组合优化算法,一般需要事先给定目标分类数和初始聚类中心,且初始聚类中心的选择对数据划分结果影响较大。为了解决该问题,提出将产状数据的划分问题转化为多目标优化问题,并采用小生境Pareto遗传算法进行求解。针对聚类问题的特殊性,采用基于链表的编码方案,并建议相应的遗传操作算子;通过引入小生境技术和Pareto支配集理论,仅通过一次求解可由Pareto支配集给出对应于不同目标组数的最优分组结果,而且不用事先给定目标组数以及初始聚类中心。最后,将算法应用于三峡船闸高边坡岩体实测不连续面产状数据的划分,得到较为符合实际的优势结构面分组。     

Pareto-Optimal Conceptual Design of the Structural Layout of Buildings Using a Multicriteria Genetic Algorithm

This article presents a computational procedure for multicriteria optimal conceptual design of the structural layout of buildings subject to given specifications and requirements. Two objective criteria are considered for evaluating alternative designs. The first objective concerns minimizing the building project cost through minimization of a function defining the combined costs of the building structural system and the land for the building site. The second objective concerns optimizing the flexibility of floor space usage, which is a qualitative criterion that is given a quantitative form through minimization of an exponential function that relates tributary load area to the spacing of columns. A multicriteria genetic algorithm (MGA) is applied to solve the biobjective conceptual building layout design problem using Pareto optimization theory . The MGA process is shown to be similar to that of the simple genetic algorithm, except that the fitness evaluation of candidate designs is based on a distance metric related to the Pareto-optimal set. A variable‐mutation technique is introduced to maintain genetic diversity and to accelerate the stochastic search for the global optimum. An example conceptual building layout design is presented using the MGA, and the applicability and efficiency of the developed computational conceptual design procedure are discussed.     

Multi-criterion stochastic optimal selection of a double glazing system

In this paper, the authors present the multi-criterion stochastic optimal selection of a double glazing system for a given office building. Four elements are required for a multi-criterion stochastic optimal design: an accurate and fast simulation model, an optimization solver, correct handling of the multi-criterion decision problem, and consideration of the stochastic performance quantification. Since stochastic optimal design is a double-exponential problem, the Gaussian Process (GP) emulator, as a surrogate to EnergyPlus, was used to achieve computational efficiency. The GP emulator was derived based on the training set generated from EnergyPlus simulation runs. A genetic algorithm and Pareto optimality were then applied to deal with the multi-criterion optimization. Stochastic performance quantification was performed using a stochastic objective function and Latin Hypercube Samplings (LHS). Using the aforementioned four elements, the authors realized the multi-criterion stochastic optimal design of a double glazing system. The differences in the mean values of energy consumption and PMV between EnergyPlus and both GP emulators are 0.27 (kWh/m²) and 0.16 (kWh/m²), respectively, and 0.01 and 0.00, respectively. In addition, 13 non-dominated Pareto optimal solutions were successfully obtained. The approach presented in this paper improves computation efficiency for a multi-criterion stochastic optimal design problem and contributes to higher-fidelity simulation-based decision making.     

Road side unit location optimization for optimum link flow determination

This study addresses the problem of road side unit (RSU) location optimization for optimum link flow determination. The error of link flow determination using RSU information comes from two sources: measurement error and inference error. The inference error is caused by the propagation and accumulation of measurement error during the link flow inference process. The direct problem formulation aiming to minimize the total error is impossible because the minimization of inference error has to be indirectly formulated as the minimization of the cumulative number of unobserved links. Further, for a given number of RSU, the decrease in the cumulative number of unobserved links results in the increase of the number of observed links, and thus results in the increase of measurement error due to data packet queueing delay. Therefore, for a given RSU installation budget, the balance between the two types of error needs to be optimized in order to achieve the optimum link flow determination accuracy. To fulfill this goal, the RSU location optimization problem is formulated as a bi‐objective nonlinear binary integer programming. This programming is constrained by complete link flow determination requirements. In order to accelerate computation, an efficient ε‐constraint method is designed to generate Pareto optimal frontier. The subproblem solved at each iteration is linearized using piecewise linear approximation and solved using a constraint generation method. The proposed model and the solution algorithm are evaluated through numerical examples. The results reveal that the Pareto optimal solutions achieved by the proposed model are at least not inferior to a non‐Pareto solution obtained in the baseline scenario. Further, both the measurement error and inference error associated with some of the Pareto optimal points are lower than those associated with the non‐Pareto optimal solution.     

Optimal design of hysteretic dampers connecting adjacent structures using multi-objective genetic algorithm and stochastic linearization method

An optimal design method is proposed for nonlinear hysteretic dampers that enhance the seismic performance of two adjacent structures. The proposed method employs nonlinear random vibration analyses by use of a stochastic linearization method in order to efficiently estimate the stochastic responses of coupled buildings without performing numerous nonlinear time-history analyses. The main objectives of the optimal design are not only to reduce the seismic responses but also to minimize the total cost of the damper system. To deal with such conflicting objectives, a multi-objective genetic algorithm is adopted. This approach systematically obtains a set of Pareto optimal solutions that are non-inferior or non-superior to each other. The process for choosing a reasonable design from the optimal surface of Pareto solutions is also discussed. As an example of a nonlinear hysteretic damping device, this study considers passive-type magneto-rheological dampers with fixed input voltages. The optimal voltages and numbers of installed dampers are simultaneously determined. The robustness of the optimal design against uncertain characteristics of ground motions is examined through extensive nonlinear random vibration analyses.     

Genetic Algorithms in Optimal Detailed Design of Reinforced Concrete Members

Genetic algorithms emulate biologic evolutionary concepts to solve search and optimization problems. In this work, they are employed to perform the optimal detailed design of reinforced concrete members of multistory buildings. The objective is to convert the required reinforcement in square centimeters, given at a number of cross sections, into a set of reinforcing bars of specific diameter and length located at specific places along the member taking into account different criteria and rules of design practice. The anchorage lengths are taken into account, and the bars are cut at appropriate locations. For such problems, enumeration methods lead to expensive solutions, whereas genetic algorithms tend to provide near-optimal solutions in reasonable computing time. The genetic algorithms used in this work are based on a roulette wheel reproduction scheme; single, multiple-point, and uniform crossover; and constant or variable mutation schemes. A constant or variable elitist strategy is also used that passes the best designs of a generation to the next generation. The method decides the detailed design on the basis of a multicriterion objective that represents a compromise between a minimum weight design, a maximum uniformity, and the minimum number of bars for a group of members. By varying the weighting factors, designs with different characteristics result. Various parameters of the genetic algorithm are considered, and the corresponding results are presented.     

Decentralized decision-making and capacitated facility location

Given a set of candidate sites, the capacitated location problem consists of finding a most economical subset of facilities to be located. This paper works with aweak formulation of the problem, having in mind the application in an economic sector with partially decentralized decision-making. The model considers the activities of production, transportation and export, looking for facility locations and distribution alternatives that satisfy the domestic demands, while minimizing the total cost. We have shown improved criteria to locate facilities, assured their optimality and given computational results. We introduce clear economic interpretation of such criteria for the decentralized behavior of the production and distribution agents, based on a pricing system associated with dual variables. Some insight is also given on the possibility of analyzing a location algorithm as a competitive and adaptive process of searching for maximal profit. Within such context, an attempt is made to define the role of government in handling the indivisibility of the production resources, in order to assure stability at an optimal solution.     

索穹顶结构预应力多目标优化的小生境遗传算法

根据索穹顶结构的柔性结构特点和力学特性,探索以质量最小、刚度最大和支座反力最小为目标函数,以预应力整体可行性准则、荷载态应力控制和位移限值为约束条件的多目标优化模型。结合自适应技术、预选择机制和共享函数小生境技术对传统遗传算法进行改进,利用加权系数法将多目标优化问题转换为单目标Pareto最优解问题。利用向量式有限元对不同预应力水平的结构进行静力分析。最后通过两个不同类型索穹顶算例,采用自编程序的计算结果证明所提出的方法是有效的,为索穹顶结构预应力优化分析提供了新的计算方法。     

Optimal Hybrid Control for Structures

A new method for integrated design of passive and active elements is presented. Rather than the existing qualitative selection of parameters for passive elements, a quantitative approach is proposed that finds optimal active and passive parameters with respect to an H₂/H_∞ performance requirement. This new approach automatically yields passive designs when the given performance limits are high enough and active (hybrid) designs when the given performance constraints are stringent. Furthermore, our algorithm finds the special performance requirement (the peak of the frequency response) that cannot be satisfied by any passive design. Hence this article shows how to determine when control is required rather than assuming a priori that it is or is not required. A simple design method given herein yields either passive, active, or hybrid designs depending only on the level of the performance constraints that are specified in the statement of the problem.     

Fuzzy-based MOGA approach to stochastic time–cost trade-off problem

In construction projects, time and cost are manageable objectives with significant interdependencies for which sets of trade-offs may exist. This study presents a new approach for the solution of time–cost trade off problems in an uncertain environment. Fuzzy numbers are used to address the uncertainties in the activities execution times and costs. Fuzzy sets theory is then explicitly embedded into the optimization procedure. A multi-objective genetic algorithm is specially tailored to solve the discontinuous and multi-objective fuzzy time- cost model with relatively large search space. The proposed approach identifies the best set of implementation options defined by the sets of non-dominated solutions Accepted risk level and optimism of the decision maker are addressed using α-cut approach and optimism index (β) respectively. To illustrate the application and performance of the model, two case examples are presented, for which separate Pareto fronts are developed. The fuzzy presentation of the non-dominated solution helps the project manager to apply his own level of risk acceptance and degree of optimism in decision making process. Different risk acceptance level and/or optimism leads to different scheduling and sets of Pareto solutions from which the project manager may select his preferred options.     

Post-Pareto optimality approach to enhance budget allocation process for bridge rehabilitation management

A variety of conflicting criteria in the form of objective functions exist in budget allocation optimisation problem for bridge rehabilitation projects. Budget allocation decision-making for such transportation assets is generally a combinatorial problem. The nature of the problem is a good reason for decision-makers to apply multi-objective optimisation techniques. However, manually choosing an acceptable solution from a set of optimal solutions is a time-consuming task, which would be avoided if the optimisation technique could be followed by a ranking method to obtain unique acceptable solution. To enhance the budget allocation process, this paper develops a posteriori approach to prioritise Pareto-Optimal (PO) solutions generated by genetic algorithm in order to identify a unique package of bridge rehabilitation activities. By identifying the most conventional objective functions for bridge rehabilitation based on technical and managerial criteria, a multi-objective knapsack problem is constructed. PO solutions will then be prioritised applying ‘Technique for Order Preference by Similarity to an Ideal Solution’. The feasibility of the study will be finally demonstrated through an illustrative example. The proposed ranking approach may facilitate the budget allocation optimisation process for bridge rehabilitation where one or a few acceptable solutions are demanded.     

An Approach to Preliminary Design of Precast Pretensioned Concrete Bridge Girders

Abstract: This paper presents an approach to the preliminary design of simple span precast pretensioned highway bridge girders using mathematical optimization methods. This type of bridge system is competitive for short and medium spans but also can accommodate long-span bridges if girder splicing and continuity are introduced. The bridge design problem is formulated as a nonlinear programming problem and is solved by the projected lagrangian algorithm. Several design objectives are investigated either separately or simultaneously with the aim of achieving cost-efficient bridge designs. The approach is used to generate a new set of five optimal girder sections and then to determine the girder spacing and span length capability of each precast girder. The five sections types (A, B, C, D, and E) proposed herein are more cost-effective than the corresponding Canadian standard sections because for similar depths they achieve greater span length and girder spacing while requiring less concrete and prestressing steel. This study also enables identification of the governing design requirements (serviceability and/or ultimate limit states active constraints) that may be adopted as optimality criteria when simplified preliminary designs of this bridge type for different design codes and girder sections are required.     

Optimum Design of Grillage Systems Using Genetic Algorithms

Genetic algorithms have attracted great attention due to their ability to provide a solution to discrete optimum design problems. In this study, a genetic algorithm is presented for the optimum design of grillage systems to decide the cross-sectional properties of members from a standard set of universal beam sections. The deflection limitations and the allowable stress constraints are considered in the formulation of the design problem. Furthermore, in obtaining the response of grillage systems, the effect of warping and shear is also taken into account. The algorithm starts with an initial population of designs and carries out basic genetic operations of selection, mating, crossover, and mutation that yield to a new generation. It continues the generation of populations until the same individual dominates the population. An improvement is also suggested to the general steps of the genetic algorithm to prevent the destruction of good individuals during the generation of new populations. The algorithm is applied to the optimum design of a 40-member grillage system to investigate the effect of warping.     

The optimal cut of sheet metal belts into pieces of given dimensions

The problem of the optimal cut of belts into pieces of given dimensions is resolved using dynamic programming and the genetic algorithm. When using dynamic programming, our basic problem is how to fill the knapsack in the optimal way. We use the solution to this problem to design an algorithm for the optimal cut of the belts into pieces. This problem is also dealt with by applying the genetic algorithm. The dynamic programming and genetic algorithm, the two methods of solving the problem of the optimal cut of belts, are compared and their space and time requirements are determined.     

Integrated scheduling of ready-mixed concrete production and delivery

This study presents an approach for improving the operations of production and delivery in ready-mixed concrete (RMC) plants. A network flow method is applied to formulate the integrated scheduling problem of ready-mixed concrete production and delivery with trucks and pumps, where the demands of construction sites are in certain time windows. A method is developed that applies a genetic algorithm in which the chromosome consists of three sequences (construction sites, delivery order and vehicle IDs); operators work on the sequences of construction sites. The approach is evaluated by simulation of real cases. Comparison with combinations of other priority rules for scheduling production and vehicles demonstrates the effectiveness of the genetic algorithm. Sensitivity analysis reveals the effects of the fleet size of an available vehicle, the cost rates and the time windows of construction sites. The model and algorithm may be helpful for practical integrated operations for operation management at RMC plants.     

Thermodynamic analysis and optimisation of an irreversible radiative-type heat engine by using non-dominated sorting genetic algorithm

Finite-time thermodynamics with an ecological principle is used for a heat engine with an irreversible radiative along with losses owing to internal irreversibilities and the heat transfer through finite-temperature differences. In this study, the ecological function is optimised regarding the cycle temperature ratio and the effects of the extreme temperature ratio and the internal irreversibilities are investigated on the optimum cycle performance. Paper presented here used a non-dominated sorting genetic algorithm called NSGA-II to optimise the thermal efficiency, the dimensionless ecological function and the dimensionless power simultaneously. Rather than a sole ultimate optimum outcome resulting in conventional single-objective optimisation, a set of optimum solutions were obtained called the Pareto optimal frontier. Hence, in order to select a final optimal answer, a progression of decision making was utilised. Two decision-making procedures were employed in the objectives’ space to obtain the optimum answers from the Pareto optimum outcomes.     

A Clustering Algorithm for Bi‐Criteria Stop Location Design with Elastic Demand

This article proposes a bi‐criteria formulation to find the optimal location of light rapid transit stations in a network where demand is elastic and budget is constrained. Our model is composed of two competing objective functions seeking to maximize the total ridership and minimize the total budget allocated. In this research, demand is formulated using the random utility maximization method with variables including access time and travel time. The transit station location problem of this study is formulated using mixed integer programming and we propose a heuristic solution algorithm to solve large‐scale instances which is inspired by the problem context. The elastic demand is integrated with the optimization problem in an innovative way which facilitates the solution process. The performance of our model is evaluated on two test problems and we carry out its implementation on a real‐world instance. Due to the special shape of the Pareto front function, significant practical policy implications, in particular budget allocation, are discussed to emphasize the fact that the trade‐off between cost and benefit may result in large investments with little outcomes and vice versa.     

Robust Transportation Network Design Under Demand Uncertainty

Abstract:   This article addresses the problem of a traffic network design problem (NDP) under demand uncertainty. The origin–destination trip matrices are taken as random variables with known probability distributions. Instead of finding optimal network design solutions for a given future scenario, we are concerned with solutions that are in some sense "good" for a variety of demand realizations. We introduce a definition of robustness accounting for the planner's required degree of robustness. We propose a formulation of the robust network design problem (RNDP) and develop a methodology based on genetic algorithm (GA) to solve the RNDP. The proposed model generates globally near-optimal network design solutions, f, based on the planner's input for robustness. The study makes two important contributions to the network design literature. First, robust network design solutions are significantly different from the deterministic NDPs and not accounting for them could potentially underestimate the network-wide impacts. Second, systematic evaluation of the performance of the model and solution algorithm is conducted on different test networks and budget levels to explore the efficacy of this approach. The results highlight the importance of accounting for robustness in transportation planning and the proposed approach is capable of producing high-quality solutions.     

Multiobjective Optimization of Bridge Deck Rehabilitation Using a Genetic Algorithm

The solution methods of multiobjective optimization have undergone constant development over the past three decades. However, the methods available to date are not particularly robust. Because of the complicated relationship between the rehabilitation cost and deterioration degree of infrastructure systems, it is difficult to find a near‐optimal solution using common optimization methods. Since genetic algorithms work with a population of points, they can capture a number of solutions simultaneously and easily incorporate the concept of Pareto optimality. In this paper a simple genetic algorithm with two additional techniques, Pareto optimality ranking and fitness sharing, is implemented for the deck rehabilitation plan of network‐level bridges, aiming to minimize the total rehabilitation cost and deterioration degree. This approach is illustrated by a simple example and then applied to a practical bridge system with a large number of bridges.     

Applying multi-objective genetic algorithms in green building design optimization

Since buildings have considerable impacts on the environment, it has become necessary to pay more attention to environmental performance in building design. However, it is a difficult task to find better design alternatives satisfying several conflicting criteria, especially, economical and environmental performance. This paper presents a multi-objective optimization model that could assist designers in green building design. Variables in the model include those parameters that are usually determined at the conceptual design stage and that have critical influence on building performance. Life cycle analysis methodology is employed to evaluate design alternatives for both economical and environmental criteria. Life cycle environmental impacts are evaluated in terms of expanded cumulative exergy consumption, which is the sum of exergy consumption due to resource inputs and abatement exergy required to recover the negative impacts due to waste emissions. A multi-objective genetic algorithm is employed to find optimal solutions. A case study is presented and the effectiveness of the approach is demonstrated for identifying a number of Pareto optimal solutions for green building design.