Interactive design optimization of architectural layouts

Many areas of design involve both quantifiable and subjective goals, preferences, and constraints. Aesthetic and other subjective aspects of design are typically ignored in optimization models because they are difficult to model with mathematics; however, they are extremely important in areas such as product design and architectural design. This article presents an interactive method for integrating mathematical optimization with human decision-making during conceptual design of architectural floorplan layouts. The optimization models and algorithms were presented in a previous article. Here, an object-oriented representation allows the designer to interact with physically relevant building objects during optimization. The designer's interaction causes the program to dynamically change the optimization representation on-the-fly by adding, deleting, and modifying objectives, constraints, and structural units. This work presents mathematical optimization as a tool to assist the designer in refining ill-defined design problems during the early conceptual design phase. The designer can quickly explore design alternatives visually and computationally by taking advantage of computational algorithms to maintain feasibility and compute efficient solutions.     

Bilevel formulation of a policy design problem considering multiple objectives and incomplete preferences

A bilevel optimization formulation of policy design problems considering multiple objectives and incomplete preferences of the stakeholders is presented. The formulation is presented for Feed-in-Tariff (FIT) policy design for decentralized energy infrastructure. The upper-level problem is the policy designer's problem and the lower-level problem is a Nash equilibrium problem resulting from market interactions. The policy designer has two objectives: maximizing the quantity of energy generated and minimizing policy cost. The stakeholders decide on quantities while maximizing net present value and minimizing capital investment. The Nash equilibrium problem in the presence of incomplete preferences is formulated as a stochastic linear complementarity problem and solved using expected value formulation, expected residual minimization formulation, and the Monte Carlo technique. The primary contributions in this article are the mathematical formulation of the FIT policy, the extension of computational policy design problems to multiple objectives, and the consideration of incomplete preferences of stakeholders for policy design problems.     

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.     

Multidisciplinary design and optimization of an air launched satellite launch vehicle using a hybrid heuristic search algorithm

A multidisciplinary design and optimization strategy for a multistage air launched satellite launch vehicle comprising of a solid propulsion system to low earth orbit with the implementation of a hybrid heuristic search algorithm is proposed in this article. The proposed approach integrated the search properties of a genetic algorithm and simulated annealing, thus achieving an optimal solution while satisfying the design objectives and performance constraints. The genetic algorithm identified the feasible region of solutions and simulated annealing exploited the identified feasible region in search of optimality. The proposed methodology coupled with design space reduction allows the designer to explore promising regions of optimality. Modules for mass properties, propulsion characteristics, aerodynamics, and flight dynamics are integrated to produce a high-fidelity model of the vehicle. The objective of this article is to develop a design strategy that more efficiently and effectively facilitates multidisciplinary design analysis and optimization for an air launched satellite launch vehicle.     

Optimal design of dynamically loaded continuous structures

A computational algorithm is developed and applied for optimization of beam and plate structures, subject to constraints on transient dynamic response. A continuous design formulation is retained, with dynamic response governed by partial differential operator equations. Adjoint equations are employed for sensitivity analysis and a function space gradient projection optimization approach is presented. Finite element analysis methods are applied for solution of the system dynamic and adjoint differential equations. Displacement constrained beam and plate minimum weight examples are solved, with a variety of boundary conditions.     

基于映射的拓扑优化最大尺寸控制方法

拓扑优化方法经过几十年的发展,已成功应用于机械工程、航空航天、电磁等领域的构型设计中。然而,由于制造工艺的限制,拓扑优化结果通常无法直接应用,需根据工艺要求进行修改,因此在拓扑优化模型中考虑制造约束成为重要的研究方向。其中,尺寸控制广泛存在于大部分制造工艺中,主要包括最小尺寸控制与最大尺寸控制。该文提出了一种基于映射的拓扑优化最大尺寸控制方法,构造了一种新的映射模型,对结构中不满足最大尺寸约束的中心单元密度进行惩罚,在不引入任何约束条件的情况下实现了对结构最大尺寸的控制。此外,该文将该方法中的惩罚转变为一个全局约束条件后与具有最小尺寸控制功能的拓扑优化鲁棒列式相结合,实现了对构件的最大最小尺寸协同控制。数值算例表明了该方法的有效性。     

Variation-aware clock network buffer sizing using robust multi-objective optimization

Many engineering optimization problems include unavoidable uncertainties in parameters or variables. Ignoring such uncertainties when solving the optimization problems may lead to inferior solutions that may even violate problem constraints. Another challenge in most engineering optimization problems is having different conflicting objectives that cannot be minimized simultaneously. Finding a balanced trade-off between these objectives is a complex and time-consuming task. In this paper, an optimization framework is proposed to address both of these challenges. First, we exploit a self-calibrating multi-objective framework to achieve a balanced trade-off between the conflicting objectives. Then, we develop the robust counterpart of the uncertainty-aware self-calibrating multi-objective optimization framework. The significance of this framework is that it does not need any manual tuning by the designer. We also develop a mathematical demonstration of the objective scale invariance property of the proposed framework. The engineering problem considered in this paper to illustrate the effectiveness of the proposed framework is a popular sizing problem in digital integrated circuit design. However, the proposed framework can be applied to any uncertain multi-objective optimization problem that can be formulated in the geometric programming format. We propose to consider variations in the sizes of circuit elements during the optimization process by employing ellipsoidal uncertainty model. For validation, several industrial clock networks are sized by the proposed framework. The results show a significant reduction in one objective (power, on average 38 %) as well as significant increase in the robustness of solutions to the variations. This is achieved with no significant degradation in the other objective (timing metrics of the circuit) or reduction in its standard deviation which demonstrates a more robust solution.     

A transformation system for interactive reformulation of design optimization strategies

Automatic design optimization is highly sensitive to problem formulation. The choice of objective function, constraints and design parameters can dramatically impact on the computational cost of optimization and the quality of the resulting design. The best formulation varies from one application to another. A design engineer will usually not know the best formulation in advance. To address this problem, we have developed a system that supports interactive formulation, testing and reformulation of design optimization strategies. Our system includes an executable, data-flow language for representing optimization strategies. The language allows an engineer to define multiple stages of optimization, each using different approximations of the objective and constraints or different abstractions of the design space. We have also developed a set of transformations that reformulate strategies represented in our language. The transformations can approximate objective and constraint functions, abstract or reparameterize search spaces, or divide an optimization process into multiple stages. The system is applicable in principle to any design problem that can be expressed in terms of constrained optimization; however, we expect the system to be most useful when the design artifact is governed by algebraic and ordinary differential equations. We have tested the system on problems of racing yacht design and jet engine nozzle design. We report experimental results demonstrating that our reformulation techniques can significantly improve the performance of automatic design optimization. Our research demonstrates the viability of a reformulation methodology that combines symbolic program transformation with numerical experimentation. It is an important first step in a research program aimed at automating the entire strategy formulation process.     

Heuristic guidelines to support conceptual design

The creativity or unforeseeable nature of the design process, especially during the conceptual phase, makes it difficult to apply current design methodologies to aid designers and help them to reach a conceptual solution in an effective manner. In this paper we present some guidelines, based on experimental data about the evolution of the design process, with which to improve the effectiveness of the conceptual phase, above all as regards finding solutions. Here, effectiveness is taken as meaning quickly reaching a design solution that satisfies the requirements of the problem. Some of the guidelines obtained allow the effectiveness of a designer or a group of designers to be enhanced and are oriented towards controlling the divergence and convergence of the design space. Some guidelines for the development of interactive computer systems to aid designers are also put forward.     

Multi-objective analysis of a component-based representation within an interactive evolutionary design system

This article describes research relating to a user-centered evolutionary design system that evaluates both engineering and aesthetic aspects of design solutions during early-stage conceptual design. The experimental system comprises several components relating to user interaction, problem representation, evolutionary search and exploration and online learning. The main focus of the article is the evolutionary aspect of the system when using a single quantitative objective function plus subjective judgment of the user. Additionally, the manner in which the user-interaction aspect affects system output is assessed by comparing Pareto frontiers generated with and without user interaction via a multi-objective evolutionary algorithm (MOEA). A solution clustering component is also introduced and it is shown how this can improve the level of support to the designer when dealing with a complex design problem involving multiple objectives. Supporting results are from the application of the system to the design of urban furniture which, in this case, largely relates to seating design.     

An inductive approach to learning and reusing design strategies

We describe a computer system called LearnIT II, which can observe an iterative solution to a parametric design problem and learn the design strategy employed. The program uses identification tree learning to determine which attributes of the design best indicate which design modifications the designer will make. The program re-represents the identification trees as design rules which it can then use to create new designs automatically. Because the rules are learned from the designer, the new designs reflect the designer's engineering judgment, knowledge of implicit constraints, and overall familiarity with the problem. The program has a number of intended uses. As a design automation tool, it provides a convenient means for exploring a design space. As a design documentation tool, it implicitly captures the original designer's insights about a problem and brings them to bear when it is necessary to modify the design. As a tool for preserving institutional memory, it captures design strategies and preserves them for future use.     

Use of the Constrained Optimization Algorithms in Some Problems of Fracture Mechanics

In this paper we consider an algorithm of constrained optimization which arises from boundary variational principles of elastodynamics for bodies with cracks and unilateral constraints on the cracks edges. Variational formulation of unilateral contact problems with friction was considered, boundary variational functionals used with boundary integral equations were obtained and algorithm for solution of the unilateral contact problem with friction was developed. Some numerical results for 3-D elastodynamic unilateral contact problem for bodies with cracks are presented.     

Rigorous mathematical optimization of synthetic hepatic vascular trees

In this paper, we introduce a new framework for generating synthetic vascular trees, based on rigorous model-based mathematical optimization. Our main contribution is the reformulation of finding the optimal global tree geometry into a nonlinear optimization problem (NLP). This rigorous mathematical formulation accommodates efficient solution algorithms such as the interior point method and allows us to easily change boundary conditions and constraints applied to the tree. Moreover, it creates trifurcations in addition to bifurcations. A second contribution is the addition of an optimization stage for the tree topology. Here, we combine constrained constructive optimization (CCO) with a heuristic approach to search among possible tree topologies. We combine the NLP formulation and the topology optimization into a single algorithmic approach. Finally, we attempt the validation of our new model-based optimization framework using a detailed corrosion cast of a human liver, which allows a quantitative comparison of the synthetic tree structure with the tree structure determined experimentally down to the fifth generation. The results show that our new framework is capable of generating asymmetric synthetic trees that match the available physiological corrosion cast data better than trees generated by the standard CCO approach.     

Application of manufacturing constraints to structural optimization of thin-walled structures

Topology optimization can be a very useful tool for creating conceptual designs for vehicles. Structures suggested by topology optimization often turn out to be difficult to implement in manufacturing processes. Presently, rail vehicle structures are made by welding sheet metal parts. This leads to many complications and increased weight of the vehicle. This article presents a new design concept for modern rail vehicle structures made of standardized, thin-walled, closed, steel profiles that fulfil the stress and manufacturing requirements. For this purpose, standard software for topology optimization was used with a new way of preprocessing the design space. The design methodology is illustrated by an example of the topology optimization of a freight railcar. It is shown that the methodology turns out to be a useful tool for obtaining optimal structure design that fulfils the assumed manufacturing constraints.     

Multiobjective stacking sequence optimization for laminated composite structures

A Pareto-based multiobjective evolutionary algorithm is presented for stacking sequence optimization of composite structural parts. Special attention has been paid to engineering design guidelines for stacking sequence design. These guidelines are included into the formulation of the optimization problem as constraints or additional objectives. A new initialization strategy is proposed following mechanical considerations. The method is applied to the optimal design of a composite plate for weight minimization and maximization of the buckling margins under three hundred load cases that make also the originality of this work. It is shown that the introduction of new ply orientations compared to the classical 0°, ±45° and 90° plies can lead to significantly improved optimal designs.     

Design optimization using multiple dominance relations

A challenge in engineering design is to choose suitable objectives and constraints from many quantities of interest, while ensuring an optimization is both meaningful and computationally tractable. We propose an optimization formulation that can take account of more quantities of interest than existing formulations, without reducing the tractability of the problem. This formulation searches for designs that are optimal with respect to a binary relation within the set of designs that are optimal with respect to another binary relation. We then propose a method of finding such designs in a single optimization by defining an overall ranking function to use in optimizers, reducing the cost required to solve this formulation. In a design under uncertainty problem, our method obtains the most robust design that is not stochastically dominated faster than a multiobjective optimization. In a car suspension design problem, our method obtains superior designs according to a k-optimality condition than previously suggested multiobjective approaches to this problem. In an airfoil design problem, our method obtains designs closer to the true lift/drag Pareto front using the same computational budget as a multiobjective optimization.     

Topology optimization of buildings subjected to stochastic wind loads

Traditionally, the main structural system of tall buildings is designed iteratively to resist extreme wind loads, which provides safe, but typically suboptimal building systems. Topology optimization provides a general approach to obtain optimal material layout to carry the required load within specified design constraints. The wind loading on a structure is typically modeled as an equivalent static load or as a spatio-temporal stochastic field. While a few models for stochastic wind excitation are available, these approaches are focused on obtaining samples for time history analyses. In this study the stochastic wind excitation is modeled as a filtered vector white noise; the state space representation of the filter is obtained by solving a regularized optimization problem from known stationary wind power spectral densities. An augmented state space representation is formed by combining the equation of motion for the structure with the excitation filter. The stationary covariances of the structural responses of interest are then obtained by solving the associated Lyapunov equation. Dynamic condensation of the equations of motion is employed to increase the efficiency of the proposed approach. Objective functions for the optimization scheme are defined in terms of the stationary covariance of the response; various objectives are considered corresponding to typical design considerations. An equivalent smooth formulation is employed to solve the non-smooth min–max problem. A gradient-based method is used to update the design variables, while the sensitivities are computed from the solution of an adjoint Lyapunov equation. The proposed topology optimization scheme is illustrated for a tall building subjected to along-wind and across-wind loads. The results presented herein demonstrate the efficacy of the proposed approach for efficient topology optimization of buildings subjected to stochastic wind excitation.     

Shape optimization using time evolution equations

In this study, we deal with a numerical solution based on time evolution equations to solve the optimization problem for finding the shape that minimizes the objective function under given constraints. The design variables of the shape optimization problem are defined on a given original domain on which the boundary value problems of partial differential equations are defined. The variations of the domain are obtained by the time integration of the solution to derive the time evolution equations defined in the original domain. The shape gradient with respect to the domain variations are given as the Neumann boundary condition defined on the original domain boundary. When the constraints are satisfied, the decreasing property of the objective function is guaranteed by the proposed method. Furthermore, the proposed method is used to minimize the heat resistance under a total volume constraint and to solve the minimization problem of mean compliance under a total volume constraint.     

Pareto Frontier Based Concept Selection Under Uncertainty,with Visualization

In a recent publication, we presented a new multiobjective decision-making tool for use in conceptual engineering design. In the present paper, we provide important developments that support the next phase in the evolution of the tool. These developments, together with those of our previous work, provide a concept selection approach that capitalizes on the benefits of computational optimization. Specifically, the new approach uses the efficiency and effectiveness of optimization to rapidly compare numerous designs, and characterize the tradeoff properties within the multiobjective design space. As such, the new approach differs significantly from traditional (non-optimization based) concept selection approaches where, comparatively speaking, significant time is often spent evaluating only a few points in the design space. Under the new approach, design concepts are evaluated using a so-calleds-Pareto frontier; this frontier originates from the Pareto frontiers of various concepts, and is the Pareto frontier for thesetof design concepts. An important characteristic of the s-Pareto frontier is that it provides a foundation for analyzing tradeoffs between design objectives and the tradeoffs between design concepts. The new developments presented in this paper include; (i) the notion ofminimally representingthe s-Pareto frontier, (ii) the quantification of concept goodness using s-Pareto frontiers, (iii) the development of an interactive design space exploration approach that can be used to visualizen-dimensional s-Pareto frontiers, and (iv) s-Pareto frontier-based approaches for considering uncertainty in concept selection. Simple structural examples are presented that illustrate representative applications of the proposed method.     

A cross-disciplinary technology transfer for search-based evolutionary computing: from engineering design to software engineering design

Although object-oriented conceptual software design is difficult to learn and perform, computational tool support for the conceptual software designer is limited. In conceptual engineering design, however, computational tools exploiting interactive evolutionary computation (EC) have shown significant utility. This article investigates the cross-disciplinary technology transfer of search-based EC from engineering design to software engineering design in an attempt to provide support for the conceptual software designer. Firstly, genetic operators inspired by genetic algorithms (GAs) and evolutionary programming are evaluated for their effectiveness against a conceptual software design representation using structural cohesion as an objective fitness function. Building on this evaluation, a multi-objective GA inspired by a non-dominated Pareto sorting approach is investigated for an industrial-scale conceptual design problem. Results obtained reveal a mass of interesting and useful conceptual software design solution variants of equivalent optimality—a typical characteristic of successful multi-objective evolutionary search techniques employed in conceptual engineering design. The mass of software design solution variants produced suggests that transferring search-based technology across disciplines has significant potential to provide computationally intelligent tool support for the conceptual software designer.