Hypotrochoid spiral optimization approach for sizing and layout optimization of truss structures with multiple frequency constraints

Engineering with Computers - The primary aim of this article is to present a new improved version of the spiral optimization algorithm (SPO) for shape and size optimization of truss structures...     

A unified approach to optimization of structural members under general constraints

A unified numerical approach, based on a control parameterization technique, for solving structural crosssectional optimization problems is presented. The key factor to the unified formulation lies in the framing of the objective functional and the constraints into the same unified canonical form. Consequently, the different types of objective functionals, geometrical and performance constraints can be treated in the same way, thus paving the path for the problems to be solved under a single approach using a general purpose software. To demonstrate this versatile approach, several illustrative examples of cross-sectional shape optimization of structural members under a variety of constraints were examined.     

An integrated approach to topology,sizing, and shape optimization

Topology optimization has become very popular in industrial applications, and most FEM codes have implemented certain capabilities of topology optimization. However, most codes do not allow simultaneous treatment of sizing and shape optimization during the topology optimization phase. This poses a limitation on the design space and therefore prevents finding possible better designs since the interaction of sizing and shape variables with topology modification is excluded. In this paper, an integrated approach is developed to provide the user with the freedom of combining sizing, shape, and topology optimization in a single process.     

Mixed-integer linear programming approach for global discrete sizing optimization of frame structures

This paper focuses on discrete sizing optimization of frame structures using commercial profile catalogs. The optimization problem is formulated as a mixed-integer linear programming (MILP) problem by including the equations of structural analysis as constraints. The internal forces of the members are taken as continuous state variables. Binary variables are used for choosing the member profiles from a catalog. Both the displacement and stress constraints are formulated such that for each member limit values can be imposed at predefined locations along the member. A valuable feature of the formulation, lacking in most contemporary approaches, is that global optimality of the solution is guaranteed by solving the MILP using branch-and-bound techniques. The method is applied to three design problems: a portal frame, a two-story frame with three load cases and a multiple-bay multiple-story frame. Performance profiles are determined to compare the MILP reformulation method with a genetic algorithm.     

Damage approach: A new method for topology optimization with local stress constraints

In this paper, we propose a new method for topology optimization with local stress constraints. In this method, material in which a stress constraint is violated is considered as damaged. Since damaged material will contribute less to the overall performance of the structure, the optimizer will promote a design with a minimal amount of damaged material. We tested the method on several benchmark problems, and the results show that the method is a viable alternative for conventional stress-based approaches based on constraint relaxation followed by constraint aggregation.     

A two-stage robust optimization approach for the mobile facility fleet sizing and routing problem under uncertainty

We propose a two-stage robust optimization model for the mobile facility fleet sizing and routing problem with demand uncertainty. A two-level cutting plane based method is developed, which includes an algorithm to generate problem-specific lower bound inequalities in the outer level, and a hybrid algorithm in the inner level that combines heuristic and exact methods to solve the recourse problem. Numerical tests show that the design and operation from the proposed method outperforms other solution approaches. The efficiency of the proposed solution algorithm in identifying the optimal solution is quantified and the robustness of the proposed model is demonstrated for varying degrees of uncertainty in demand.     

Structural optimization on geometrical configuration and element sizing with statical and dynamical constraints

In this paper, a bi-factor -β algorithm based on the Kuhn-Tucker criteria about the minimal weight design of a structure under statical and dynamical constraints, is presented. Among the constraints, that of “frequency-prohibited band” is a new formulation which requires any characteristic frequency of the structure not to fall into a certain frequency region. The desing variables may cover sizes of the elements and/or coordinates of the nodes. The upper and lower bounds of each variable are specified, and the stress constraints based on full-stress criteria may also be taken into account. Satisfactory results have been obtained over varous examples wherein the stiffness and/or mass matrices of the structure may be highly nonlinear about the design variables.     

On an alternative approach to stress constraints relaxation in topology optimization

The paper deals with the imposition of local stress constraints in topology optimization. The aim of the work is to analyze the performances of an alternative methodology to the ε-relaxation introduced in Cheng and Guo (Struct Optim 13:258–266, 1997), which handles the well-known stress singularity problem. The proposed methodology consists in introducing, in the SIMP law used to apply stress constraints, suitable penalty exponents that are different from those that interpolate stiffness parameters. The approach is similar to the classical one because its main effect is to produce a relaxation of the stress constraints, but it is different in terms of convergence features. The technique is compared with the classical one in the context of stress-constrained minimum-weight topology optimization. Firstly, the problem is studied in a modified truss design framework, where the arising of the singularity phenomenon can be easily shown analytically. Afterwards, the analysis is extended to its natural context of topology bidimensional problems.     

Truss optimization on shape and sizing with frequency constraints based on parallel genetic algorithm

Truss shape and sizing optimization under frequency constraints is extremely useful when improving the dynamic performance of structures. However, coupling of two different types of design variables, nodal coordinates and cross-sectional areas, often lead to slow convergence or even divergence. Because shape and sizing variables coupled increase the number of design variables and the changes of shape and sizing variables are of widely different orders of magnitude. Otherwise, multiple frequency constraints often cause difficult dynamic sensitivity analysis. Thus optimal criteria and mathematical programming methods have considerable limitations on solving the problems because of needing complex dynamic sensitivity analysis and being easily trapped into the local optima. Genetic Algorithms (GAs) show great potentials to solve the truss shape and sizing optimization problems. Since GAs adopt global probabilistic population search techniques and require no gradient information. The improved genetic algorithms can effectively increase the solution quality. However, the serial GA is computationally expensive and is limited on gaining higher quality solutions. To solve the truss shape and sizing optimization problems with frequency constraints more effectively and efficiently, a Niche Hybrid Parallel Genetic Algorithm (NHPGA) is proposed to significantly reduce the computational cost and to further improve solution quality. The NHPGA is to blend the advantages of parallel computing, simplex search and genetic algorithm with niche technique. Several typical truss optimization examples demonstrate that NHPGA can significantly reduce computing time and attain higher quality solutions. It also suggests that the NHPGA provide a potential algorithm architecture, which effectively combines the robust and global search characteristics of genetic algorithm, strong exploitation ability of simplex search and computational speedup property of parallel computing.     

A simplified approach to time-dependent subsoil–structure interaction

The aim of the present paper is to present a very simple and effective model, describing the long-term deformations of both interacting sub domains – the subsoil and upper-structure in a similar manner. The effectiveness of the proposed approach consists in converting the integral constitutive equations for creep in the upper-structure and consolidation of a fully saturated subsoil layer into a set of the first order differential equations. Subsequently, the algebraic incremental solution is obtained by applying Dirichlet–Prony’s series for both the compliance function and degree of consolidation. The incremental method also comprises the building progress by taking into account the increments of individual segments consecutively added.     

Optimal discrete sizing of truss structures subject to buckling constraints

The selective dynamic rounding (SDR) algorithm previously developed by the authors, and based on a dual step rounding approach, is used for the optimal sizing design of truss structures subject to linear buckling constraints. The algorithm begins with a continuous optimum followed by a progressive freezing of individual variables while solving the remaining continuous problems. The allowable member stresses are predicted by the linear regression of the tabular section properties, while the exact allowable compressive stresses are back-substituted for those variables fixed on discrete values in each intermediate mixed-discrete nonlinear problem. It is shown that a continuous design based on the regression analysis of section effectiveness vs. area is effective as a starting point for the dual step discrete optimization phase. A range of examples is used to illustrate that with conservative regression, discrete designs can be achieved which are significantly lighter than those in which the variables have been rounded up.     

An optimization approach for the lot sizing and scheduling problem in the brewery industry

This study considers a production lot sizing and scheduling problem in the brewery industry. The underlying manufacturing process can be basically divided into two main production stages: preparing the liquids including fermentation and maturation inside the fermentation tanks; and bottling the liquids on the filling lines, making products of different liquids and sizes. This problem differs from other problems in beverage industries due to the relatively long lead times required for the fermentation and maturation processes and because the “ready” liquid can remain in the tanks for some time before being bottled. The main planning challenge is to synchronize the two stages (considering the possibility of a “ready” liquid staying in the tank until bottling), as the production bottlenecks may alternate between these stages during the planning horizon. This study presents a novel mixed integer programming model that represents the problem appropriately and integrates both stages. In order to solve real-world problem instances, MIP-based heuristics are developed, which explore the model structure. The results show that the model is able to comprise the problem requirements and the heuristics produce relatively good-quality solutions.     

Isogeometric sizing and shape optimization of thin structures with a solid-shell approach

Structural and Multidisciplinary Optimization - This work explores the use of solid-shell elements in the the framework of isogeometric shape optimization of shells. The main difference of these...     

A review of optimization of structures subjected to transient loads

Various aspects of structural optimization techniques under transient loads are extensively reviewed. The main themes of the paper are treatment of time-dependent constraints, calculation of design sensitivity, and approximation. Each subject is reviewed with corresponding papers that have been published since the 1970s. The treatment of time-dependent constraints in both the direct method and the transformation method is discussed. Two ways of calculating design sensitivity of a structure under transient loads are discussed—direct differentiation method and adjoint variable method. The approximation concept mainly focuses on the response surface method in crashworthiness and local approximation with the intermediate variables. Especially, a method using the equivalent static load is discussed as an approximation method. It takes advantage of the well-established static response optimization. The structural optimization in flexible multibody dynamic systems is reviewed in the viewpoint of the above three themes.     

线性约束非线性函数全局优化算法的研究

提出了一种适于处理线性约束条件下非线性规划问题的λ编码稳态遗传算法(λSSGA).首先对线性可行域进行凸分析后将原优化问题I转化为一个仅包含可行域极点信息的等价问题II.问题II具有小边界的约束条件,通过采用特定的凸交叉算子、交换变异算子和倒位算子可以保证算法在遗传操作的过程中不会产生无效的编码,而且能在概率意义上保证λ编码模式在整个可行解空间上充分可达.其次从理论上推导出了得到线性可行区域全部极点的方法,证明了问题I和问题II的等价性.仿真结果表明λSSGA算法在具有较快的收敛速度和精度的同时,还可以有效地维持群体的多样性,得到问题全局的最优解.     

Multimodal processes optimization subject to fuzzy operation time constraints: declarative modeling approach

We present an extension of the resource-constrained multi-product scheduling problem for an automated guided vehicle (AGV) served flow shop, where multiple material handling transport modes provide movement of work pieces between machining centers in the multimodal transportation network (MTN). The multimodal processes behind the multi-product production flow executed in an MTN can be seen as processes realized by using various local periodically functioning processes. The considered network of repetitively acting local transportation modes encompassing MTN’s structure provides a framework for multimodal processes scheduling treated in terms of optimization of the AGVs fleet scheduling problem subject to fuzzy operation time constraints. In the considered case, both production takt and operation execution time are described by imprecise data. The aim of the paper is to present a constraint propagation (CP) driven approach to multi-robot task allocation providing a prompt service to a set of routine queries stated in both direct and reverse way. Illustrative examples taking into account an uncertain specification of robots and workers operation time are provided.     

A quantile-based simulation optimization model for sizing hybrid renewable energy systems

As the public has gradually realized the adverse impacts brought by global warming, hybrid renewable energy system (HRES) has become increasingly popular because it can reduce dependence on fossil fuels, while maintaining the stability of power supply. While the HRES is an attractive option in many aspects, the fundamentally uncertain nature of renewable energy sources makes the determination of the proper sizing of the HRES a very challenging task. Contrasting with the existing models that are largely focused on expectation-based system performance, this paper provides a quantile-based simulation optimization model, followed by the development of an efficient solution methodology, to enable the control of the upside risk and, as a result, to enhance the decision quality regarding the sizing of HRES. One advantage of the proposed model is that they can be based on any existing deterministic model that carries a cost structure regarding the sizing of the HRES. Moreover, the proposed solution methodology, consisting of a Monte Carlo simulation method, quantile estimation techniques, and an efficient stochastic optimizer, allows for not only accurate estimation of the objective function value, but also quick identification of the optimal solution due to a uniquely-defined neighborhood structure. An extensive numerical experiment is conducted to verify the efficacy and efficiency of the proposed solution methodology. Finally, in collaboration with a partner in industry, the proposed model and the solution methodology are integrated into a decision support system to provide visualized results for sizing HRES in practice.     

A multi-level approach to ubiquitous modeling and solving constraints in combinatorial optimization problems in production and distribution

Constraints, although ubiquitous in production and distribution planning, scheduling and control, often lead to inconsistencies in the decision-making process. The constraint-based modeling helps circumvent many organization-impacting issues. To address this, we developed a multi-level approach to the modeling and solving of combinatorial optimization problems. It is versatile and effective owing to the use of multi-level presolving and multiple paradigms, such as constraint programming, logic programming, mathematical programming and fuzzy logic, for their complementary strengths. The capability of this framework and its advantage over mathematical programming alone or over hybrid frameworks is shown in the illustrative example, in which combinatorial optimization is used as a benchmark to prove the effectiveness of the proposed approach. Knowledge of the problem is stored in the form of facts.     

A structured approach to program optimization

Software engineering should provide software engineers with methodologies and tools suitable for use in that small number of applications where efficiency is really important. In order to do that, the optimization process should be a clearly visible phase of the software lifecycle (regardless of the particular software development paradigm adopted), so that it can be regulated, securing the production of good quality and efficient software. With this in mind, the author suggests an approach to program optimization based on a paradigm, a method, some principles and guidelines, and some well-known techniques     

A novel approach to LCD optimization

Abstract— A novel approach to optimization liquid‐crystal displays (LCDs) is presented. The optimization module allows for a prediction with a high accuracy for the best results, which can be obtained for one or the other configuration of the polarizers and phase retarders in various electro‐optical modes, if the LC parameters and the operating voltages are fixed. The module is a part of our program, MOUSE‐LCD, which is efficient software for LCD optimization and modeling.