A quadratic complementarity problem related to the optimal design of a pipeline freely resting on a rough sea bottom

A submarine pipeline resting on a rigid, frictionless seabed assumes an equilibrium configuration which can be determined by solving a unilateral contact problem, i.e. a quadratic program or a variational inequality.When the sea bed is irregular, its profile along the sealine can be modified, in present offshore technology, by means of costly trench excavations or artificial supports, in order to avoid excessive bending moments in the pipe. Thus, the problem arises of determining the minimum cost of the profile changes provided that a specified curvature is nowhere exceeded.This optimal design problem is solved by assuming a quadratic cost function and reducing it to a sequence of convex quadratic programming problems leading to the optimal design situation. Upper and lower bounds on the absolute minimum cost and optimality conditions are established. A suitable algorithm for solving the problem in a finite number of steps is developed. Its generalization to allow for ‘fixed charges’ due to the equipment mobilization cost is presented. Two numerical examples illustrate the optimum (minimum cost) proposed design method.     

Optimal excavation profile for a pipeline freely resting on the sea floor

A submarine pipeline resting on a rigid, frictionless sea bed assumes an equilibrium configuration which can be determined by solving a unilateral contact problem, i.e. a quadratic program or a variational inequality.Since the sea bed profile is usually irregularly hilly, its regularization is often carried out, in present offshore technology, by costly trench excavations, both in order to avoid excessive bending moments in the pipe and to bury it for protection. Thus, the problem arises of determining profile changes of minimum cost under the condition that an assigned curvature be nowhere exceeded.This optimal design problem is tackled in the paper with reference to a discrete model of the mechanical system, as the minimization of a linear cost function under linear constraints and a single, nonlinear and non-convex, complementarity constraint.A theory is developed which reduces this nonlinear programming problem to a sequence of linear programs, the optimal solutions of which are shown to converge to the original NLP solution. Upper and lower bounds on the absolute minimum cost and optimality conditions are established, on the basis of duality theory in linear programming. An algorithm suitable for solving the problem in a finite number of steps is proposed. Generalizations obtained by relaxing some of the simplifying hypotheses are considered.     

Optimal placement of metallic dampers for seismic upgrading of multistory buildings based on a cost‐effectiveness criterion using genetic algorithm

In this paper, an optimal placement methodology for metallic dampers is proposed to upgrade the seismic performance of multistory buildings. Most previous studies on optimal damper placement (ODP) problems have been focused on minimizing the seismic responses, whereas the present study aims to utilize the minimum total cost of dampers to achieve a prescribed level of seismic response. To this end, the optimization objective is constructed based on a cost‐effectiveness criterion, and the optimization constraint is defined based on a desired level of seismic response. An improved integer‐coded genetic algorithm is presented for solving the ODP problem. A 16‐story shear building is illustrated to verify the proposed optimal placement methodology. It is shown that the proposed methodology can be used to achieve the predetermined performance level while minimizing the retrofitting cost. Moreover, different algorithms, objective functions, and levels of accuracy on the optimization are also compared. Finally, a two‐step optimization approach is proposed for achieving better placement schemes with less computational efforts.     

Optimization of tower crane and material supply locations in a high-rise building site by mixed-integer linear programming

Facility layout design and planning within construction sites are a common construction management problem and regarded as a complex combinatorial problem. To transport heavy materials, tower cranes are needed and should be well located to reduce operating costs and improve overall efficiency. Quadratic assignment problem (QAP), non-linear in nature, has been developed to simulate the material transportation procedure. Applying linear constraint sets, the quadratic problem can be linearized and the problem could be formulated into a mixed-integer-linear programming (MILP) problem solvable by a standard branch-and-bound technique for true optimal results. Numerical findings show that MILP results outperform those optimized by Genetic Algorithms with almost 7% on improving the objective function values in which facilities and locations can be modeled using integer variables. To demonstrate the design flexibility of using MILP formulation, the problem is also extended to non-homogeneous storages where different materials can be stored at a single supply point.     

既有建筑节能改造保温材料的NSGA-Ⅱ协同设计

保温措施是既有建筑节能改造中最有效的节能措施之一。在墙体节能改造设计中,保温材料种类及其厚度的确定是至关重要的,受到多个目标参数的制约和影响。基于反问题的研究方法,建立数值计算方法与多目标遗传算法NSGA-Ⅱ相结合的优化模型,以单位面积墙体全年总能耗和保温材料成本为目标参数,对成都地区某既有建筑墙体节能改造的保温材料种类与厚度进行了协同设计。结果表明,采用常规的保温厚度,常用的8种保温材料中有6种都不是最优解,但是可以通过改变保温材料的厚度或单价等方法使解向Pareto前沿逼近,以实现单位面积墙体年总能耗最小和改造成本最小之间的平衡。     

Optimal control development for chilled water plants using a quadratic representation

Optimal supervisory control strategy for the set points of controlled variables in the cooling plants has been studied by computer simulation. A quadratic linear regression equation for predicting the total cooling system power in terms of the controlled and uncontrolled variables was developed using simulated data collected under different values of controlled and uncontrolled variables. The optimal set temperatures such as supply air temperature, chilled water temperature, and condenser water temperature, are determined such that energy consumption is minimized as uncontrolled variables, load, ambient wet bulb temperature, and sensible heat ratio are changed. The chilled water loop pump and cooling tower fan speeds are controlled by the PID controller such that the supply air and condenser water set temperatures reach the set points designated by the optimal supervisory controller.The influences of the controlled variables on the total system and component power consumption were determined. The predicted power obtained from the quadratic regression equation was found to be a good fit to the simulated one. Because the Hermitian matrix of the system quadratic cost function was positive, the optimal control variables for the minimum power consumption were able to be obtained. There are relatively high effects of the load and sensible heat ratio on the optimal supply air and chilled water set temperatures, while the effect of ambient wet bulb temperature is less. In contrast to that result, the ambient wet bulb temperature has a much larger effect on the optimal condenser water set temperature, while the load has less, and the sensible heat ratio has no influence on it. The trade-off among the components of power consumption results in that the total system power use in both simulated and predicted systems are minimized at lower supply, higher chilled water, and lower condenser water set temperature conditions.     

预应力钢结构的优化设计

本文将预应力结构的优化设计作为两个问题考虑: 一、给定结构布局、几何尺寸和杆件截面{A},在多种工况和约束(应力、变位和预拉力约束)下求最优的预拉力{T},使结构的承载能力最高。 二、给定结构布局和几何尺寸,在给定的多种工况和约束(应力、变位、尺寸和预拉力约束)下,求最优的截面{A}和最优的预拉力{T},使结构用材最少或价格最低。 “问题一”可以用线性规划来解,“问题二”可以利用类似于满应力准则的办法用一序列“问题一”来逼近,所作的有限的数值实验表明这个方法收敛得相当快。     

Column Generation‐Based Approach for Solving Large‐Scale Ready Mixed Concrete Delivery Dispatching Problems

Ready mix concrete (RMC) dispatching forms a critical component of the construction supply chain. However, optimization approaches within the RMC dispatching continue to evolve due to the specific size, constraints, and objectives required of the application domain. In this article, we develop a column generation algorithm for vehicle routing problems (VRPs) with time window constraints as applied to RMC dispatching problems and examine the performance of the approach for this specific application domain. The objective of the problem is to find the minimum cost routes for a fleet of capacitated vehicles serving concrete to customers with known demand from depots within the allowable time window. The VRP is specified to cover the concrete delivery problem by adding additional constraints that reflect real situations. The introduced model is amenable to the Dantzig–Wolfe reformulation for solving pricing problems using a two‐staged methodology as proposed in this article. Further, under the mild assumption of homogeneity of the vehicles, the pricing sub‐problem can be viewed as a minimum‐cost multi‐commodity flow problem and solved in polynomial time using efficient network simplex method implementations. A large‐scale field collect data set is used for evaluating the model and the proposed solution method, with and without time window constraints. In addition, the method is compared with the exact solution found via enumeration. The results show that on average the proposed methodology attains near optimal solutions for many of the large sized models but is 10 times faster than branch‐and‐cut.     

电力网网架结构优化设计的模拟退火算法

电力网的网架结构优化设计是组合最优化问题.笔者用图论方法把电力网线路模型化,并运用图论最优化理论研究线路优化设计问题.在电力网运行在树状结构的前提下,提出了多边形变换的新概念,首次将模拟退火方法应用于电力网线路优化设计中,同时提出网架优化的模拟退火算法,最终得到一个费用最小的电力网的网架结构.     

基于水平集方法的连续体结构拓扑优化

提出了一种用水平集函数作为设计变量求解连续体结构拓扑优化的方法。优化方法以结构的整体柔度最小为目标函数,以实体材料所占的体积为约束条件,综合采用有限元方法和优化准则法对问题进行求解。该方法与密度惩罚法相比,克服了锯齿形边界,得到了光滑的结构边界;与传统水平集方法相比,不用求解复杂的Hamilton-Jacobi方程,提高了计算效率。在对Heaviside函数正则化处理中,考虑了形状导数和拓扑导数信息,加快了收敛速度。用该方法对梁的拓扑优化设计进行了试算,得到了满意的优化结果。     

Mitigation of vortex-induced vibrations in bridges under conflicting objectives

Aerodynamic performance of long-span bridges can be improved by retrofitting cross-sectional shapes or by adding tuned mass dampers. When both the approaches are used simultaneously, the design problem may become too complicated to solve by engineering judgment. The complexity becomes even greater in a real world problem in which both the performance and the cost have to be considered. We propose a multi-objective based approach to obtain optimal solution of the design problem. The approach effectively deals with highly nonlinear design space and the conflicting objectives between the performance and the cost. Due to the conflict of the two objectives, multiple optimal solutions are obtained, which are called Pareto-optimal solutions. The final design is obtained considering the cost and the performance criteria. The proposed method is applied to the mitigation of vortex-induced vibrations, but its general framework is applicable to any other aerodynamic problems.     

区域供冷系统二次管网的优化设计

分析了区域供冷系统二次管网的优化设计方法,建立了管径非连续变化的区域供冷系统二次管网的优化设计模型,并提出了求解方法。在对某区域供冷系统二次管网工程实例进行优化的基础上,进一步分析了传统设计与优化设计方法下二次管网经济性的差异。结果表明,优化设计方法通过权衡二次管网的初投资与二次泵的运行费用,使得二次管网在整个寿命周期内经济性较优;相对于经济流速分别取0.8,1.8,2.5m/s时假设流速法的计算结果,采用优化设计方法可分别节省寿命周期费用14.3%,16.2%,39.9%。     

A comparison of deterministic and probabilistic optimization algorithms for nonsmooth simulation-based optimization

In solving optimization problems for building design and control, the cost function is often evaluated using a detailed building simulation program. These programs contain code features that cause the cost function to be discontinuous. Optimization algorithms that require smoothness can fail on such problems. Evaluating the cost function is often so time-consuming that stochastic optimization algorithms are run using only a few simulations, which decreases the probability of getting close to a minimum. To show how applicable direct search, stochastic, and gradient-based optimization algorithms are for solving such optimization problems, we compare the performance of these algorithms in minimizing cost functions with different smoothness. We also explain what causes the large discontinuities in the cost functions.     

Optimal Layout of Bridge Trusses by Genetic Algorithms

In this paper we present an approach to the layout and shape-optimization problem of bridge truss structures using genetic algorithms. The objective is to find an optimal layout design that will have minimum weight or material volume, subject to performance constraints related to member stresses, joint displacements, and member buckling. An automated two-stage optimization search process, which integrates structural analysis by finite-element method, genetic algorithms, and cognitive topology patterns (domain knowledge), is developed to solve the optimal problem. Two examples concerning bridge truss structure are investigated to demonstrate the effectiveness of the proposed method in solving these layout-optimization problems.     

An optimization method for selecting project risk response strategies

There is wide agreement that the risk response strategy selection is an important issue in project risk management (PRM). Some academic researchers have paid attention to this issue. This paper proposes a novel method for solving the risk response strategy selection problem in PRM. In the method, an optimization model is developed, which integrates three critical elements that are the project cost, project schedule and project quality. By solving the model, the optimal solution could be obtained so that the most desirable risk response strategies to cope with the risk events can be determined. If the optimal solution is not found or project managers are not satisfied with the solution, another pathway can be used to support the managers to get the desirable strategies. The pathway is based on an iterative process which involves making trade-offs between the project budget, time and quality according to objective requirements and managers' judgments. The iterative process comes to an end if the objectives predefined by the managers are reached. A simple example project is also provided to illustrate the practicality and usefulness of the proposed method.     

多管式高效空气过滤器的设计优化

在实验研究确立的多管式高效空气过滤器阻力的理论公式的基础上,以寿命期总费用为目标函数建立了该型过滤器的最优设计数学模型。采用序列二次规划法求解此约束优化模型,得到了该种过滤器在寿命期总费用最小时的最优化结构设计参数。并与按阻力最小化得到的结果进行了比较分析,指出基于寿命期总费用的最优设计更合理。     

Minimum cost route for a highway in heterogeneous terrain

This paper shows that the minimum cost route should satisfy the Snell's law of light refraction and this can be done by successive iteration, in either a forward or backward direction. The number of iterations required for full convergence depends on the geometry of the problem and the cost ratio between each of the two neighbouring cost regions.     

Fuzzy-multi-objective particle swarm optimization for time–cost–quality tradeoff in construction

The time–cost–quality tradeoff (TCQT) problem is to decide an optimal combination of construction methods with the objective of minimizing cost and time while maximizing quality. Searching for such an optimal combination of construction methods needs to evaluate the total cost, time and quality of the project. These performances, especially the quality, may be collected and recorded in terms of imprecise or vague data rather than precise numbers. This paper presents a fuzzy-multi-objective particle swarm optimization to solve the fuzzy TCQT problem. The time, cost and quality are described by fuzzy numbers and a fuzzy multi-attribute utility methodology incorporated with constrained fuzzy arithmetic operations is adopted to evaluate the selected construction methods. The particle swarm optimization is applied to search for the TCQT solutions by incorporating the fuzzy multi-attribute utility methodology. The proposed methodology is implemented and justified through computational analyses. The study is expected to provide an alternative methodology for solving the time–cost–quality tradeoff problem.     

Total Optimal Synthesis Method for Truss Structures Subject to Static and Frequency Constraints

Abstract: In a previous study, we presented an efficient optimal structural synthesis method for truss structures in which the design variables are coordinates of the panel points, cross-sectional areas, and discrete material kinds subjected to stress and displacement constraints. In this paper, the synthesis method is extended to solve design problems subject to stress, displacement, and fundamental natural-frequency constraints. The design problem is formulated in terms of discrete material kinds and continuous shape and sizing variables and which are approximated by a convex and separable subproblem. The approximate subproblem is expressed in direct and/or reciprocal design variables and shape, material, and sizing sensitivities. Each subproblem is solved by a two-stage minimization process. In the first stage, the continuous shape and sizing variables are optimized by a dual method. Second, the discrete material and continuous sizing variables are improved by a discrete sensitivity analysis. Using the proposed two-stage minimization procedure, both the discrete material kinds and the continuous shape and sizing variables can be systematically improved to obtain an optimal solution. The rigorousness, reliability, and efficiency of the method are illustrated by applying it to the minimum cost design of truss structures subject to stress, displacement, and fundamental natural-frequency constraints.     

城市交通网络设计问题中的双层规划模型

城市交通网络设计问题的主要内容就是通过规划的思想建立数学模型,通过优化计算方法寻找最优的用于道路网络新建或改善的交通建设投资决策方案,即研究如何能用最少的资金投入达到使整个交通网络中某种指标最优的目的。这些具体的系统性能指标可以是使整个网络中的系统总阻抗最小、交通拥挤程度最低、能源消耗最少等,从而为交通规划部门和决策人员提供科学、系统、合理、有效的决策方案和决策数据,使政府有限的资金投入能取得最佳的投资效益。本文首先简单介绍了城市交通网络设计问题研究的主要内容,然后给出了城市交通网络设计中一般形式的双层规划模型及其推广形式。