Applicability of surrogates to improve efficiency of particle swarm optimization for simulation-based problems

Particle swarm optimization (PSO) is a population-based, heuristic technique based on social behaviour that performs well on a variety of problems including those with non-convex, non-smooth objective functions with multiple minima. However, the method can be computationally expensive in that a large number of function calls is required. This is a drawback when evaluations depend on an off-the-shelf simulation program, which is often the case in engineering applications. An algorithm is proposed which incorporates surrogates as a stand-in for the expensive objective function, within the PSO framework. Numerical results are presented on standard benchmarking problems and a simulation-based hydrology application to show that this hybrid can improve efficiency. A comparison is made between the application of a global PSO and a standard PSO to the same formulations with surrogates. Finally, data profiles, probability of success, and a measure of the signal-to-noise ratio of the the objective function are used to assess the use of a surrogate.     

Data analytics and optimization for smart industry

Industrial intelligence is a core technology in the upgrading of the production processes and management modes of traditional industries. Motivated by the major development strategies and needs of industrial intellectualization in China, this study presents an innovative fusion structure that encompasses the theoretical foundation and technological innovation of data analytics and optimization, as well as their application to smart industrial engineering. First, this study describes a general methodology for the fusion of data analytics and optimization. Then, it identifies some data analytics and system optimization technologies to handle key issues in smart manufacturing. Finally, it provides a four-level framework for smart industry based on the theoretical and technological research on the fusion of data analytics and optimization. The framework uses data analytics to perceive and analyze industrial production and logistics processes. It also demonstrates the intelligent capability of planning, scheduling, operation optimization, and optimal control. Data analytics and system optimization tech-nologies are employed in the four-level framework to overcome some critical issues commonly faced by manufacturing, resources and materials, energy, and logistics systems, such as high energy consumption, high costs, low energy efficiency, low resource utilization, and serious environmental pollution. The fusion of data analytics and optimization allows enterprises to enhance the prediction and control of unknown areas and discover hidden knowledge to improve decision-making efficiency. Therefore, industrial intelligence has great importance in China’s industrial upgrading and transformation into a true industrial power.     

Quality assessment of coarse models and surrogates for space mapping optimization

One of the central issues in space mapping optimization is the quality of the underlying coarse models and surrogates. Whether a coarse model is sufficiently similar to the fine model may be critical to the performance of the space mapping optimization algorithm and a poor coarse model may result in lack of convergence. Although similarity requirements can be expressed with proper analytical conditions, it is difficult to verify such conditions beforehand for real-world engineering optimization problems. In this paper, we provide methods of assessing the quality of coarse/surrogate models. These methods can be used to predict whether a given model might be successfully used in space mapping optimization, to compare the quality of different coarse models, or to choose the proper type of space mapping which would be suitable to a given engineering design problem. Our quality estimation methods are derived from convergence results for space mapping algorithms. We provide illustrations and several practical application examples. This work was supported in part by the Natural Sciences and Engineering Research Council of Canada under Grants RGPIN7239-06 and STPGP336760-06.     

Surrogate modelling and optimization using shape-preserving response prediction: A review

Computer simulation models are ubiquitous in modern engineering design. In many cases, they are the only way to evaluate a given design with sufficient fidelity. Unfortunately, an added computational expense is associated with higher fidelity models. Moreover, the systems being considered are often highly nonlinear and may feature a large number of designable parameters. Therefore, it may be impractical to solve the design problem with conventional optimization algorithms. A promising approach to alleviate these difficulties is surrogate-based optimization (SBO). Among proven SBO techniques, the methods utilizing surrogates constructed from corrected physics-based low-fidelity models are, in many cases, the most efficient. This article reviews a particular technique of this type, namely, shape-preserving response prediction (SPRP), which works on the level of the model responses to correct the underlying low-fidelity models. The formulation and limitations of SPRP are discussed. Applications to several engineering design problems are provided.     

Simultaneous topology and build orientation optimization for minimization of additive manufacturing cost and time

The ever-present demand for increased performance in mechanical systems, and reduced cost and manufacturing time, has led to the adoption of computational design tools and innovative manufacturing methods. One such tool is topology optimization (TO), which often produces designs that are impracticable to manufacture. However, recent developments in additive manufacturing (AM) have made production of such complex designs feasible. Therefore, integration of these technologies has the potential to innovate the design and manufacture of mechanical components. This work presents a novel mathematical methodology for multiobjective minimization of structural compliance and AM cost and time, in simultaneous build orientation and density-based TO. Component surface area and support volume were implemented in this method as the physical factors influencing AM cost and time. A new methodology was produced to approximate support volume throughout TO with variable build orientation, enabling direct minimization of support volume in the proposed optimization. The methodology allows derivation of sensitivity expressions, thereby permitting the use of efficient gradient-based optimization solvers. Three numerical examples demonstrated that the proposed methodology can efficiently produce optimum build orientations and topologies, which significantly reduce structural compliance and AM cost and time.     

Combinatorial thin film materials science: From alloy discovery and optimization to alloy design

This paper provides an overview of modern alloy development, from discovery and optimization towards alloy design, based on combinatorial thin film materials science. The combinatorial approach, combining combinatorial materials synthesis of thin film composition-spreads with high-throughput property characterization has proven to be a powerful tool to delineate composition-structure-property relationships, and hence to efficiently identify composition windows with enhanced properties. Furthermore, and most importantly for alloy design, theoretical models and hypotheses can be critically appraised. Examples for alloy discovery, optimization, and alloy design of functional as well as structural materials are presented.Using Fe-Mn based alloys as an example, we show that the combination of modern electronic-structure calculations with the highly efficient combinatorial thin film composition-spread method constitutes an effective tool for knowledge-based alloy design.     

A multi-objective approach for multi-material topology and shape optimization

An automated multi-material approach that integrates multi-objective Topology Optimization (TO) and multi-objective shape optimization is presented. A new ant colony optimization algorithm is presented and applied to solving the TO problem, estimating a trade-off set of initial topologies or distributions of material. The solutions found usually present irregular boundaries, which are not desirable in applications. Thus, shape parameterization of the internal boundaries of the design region, and subsequent shape optimization, is performed to improve the quality of the estimated Pareto-optimal solutions. The selection of solutions for shape optimization is done by using the PROMETHEE II decision-making method. The parameterization process involves identifying the boundaries of different materials and describing these boundaries by non-uniform rational B-spline curves. The proposed approach is applied to the optimization of a C-core magnetic actuator, with two objectives: the maximization of the attractive force on the armature and the minimization of the volume of permanent magnet material.     

Hybrid approximation algorithm with Kriging and quadratic polynomial‐based approach for approximate optimization

This paper describes a new hybrid algorithm that uses a Kriging and quadratic polynomial‐based approach for approximate optimization. The Kriging method is used for generating a global approximation model, and the polynomial‐based approximation method is used for generating a local approximation model. The Kriging system is only used to construct a polynomial‐based locally approximate model by estimating some function values and Hessian components of an estimated surface. The number of Kriging estimations can be reduced in comparison with direct Kriging‐based optimization, and a local optimum solution on an approximated surface can be clearly estimated without use of an optimization procedure based on a local appropriate quadratic polynomial model. Numerical examples of engineering optimization using the proposed method illustrate validity and effectiveness of the proposed method. Copyright © 2006 John Wiley & Sons, Ltd.     

Using support vector machine and dynamic parameter encoding to enhance global optimization

This study presents an approach which combines support vector machine (SVM) and dynamic parameter encoding (DPE) to enhance the run-time performance of global optimization with time-consuming fitness function evaluations. SVMs are used as surrogate models to partly substitute for fitness evaluations. To reduce the computation time and guarantee correct convergence, this work proposes a novel strategy to adaptively adjust the number of fitness evaluations needed according to the approximate error of the surrogate model. Meanwhile, DPE is employed to compress the solution space, so that it not only accelerates the convergence but also decreases the approximate error. Numerical results of optimizing a few benchmark functions and an antenna in a practical application are presented, which verify the feasibility, efficiency and robustness of the proposed approach.     

Combined particle swarm optimization and heuristic fuzzy inference systems for a smart home one-step-ahead load forecasting

This article presents a hybrid approach that combines particle swarm optimization (PSO) and heuristic fuzzy inference system (HFIS) for smart home one-step-ahead load forecasting. Smart home load forecasting is an important issue in the development of smart grids. Generally, the electricity consumption of a household is inherently nonlinear and dynamic and heavily dependent on the habitual nature of power demand, activities of daily living and on holidays or weekends, so it is often difficult to construct an adequate forecasting model for this type of load. To address this problem, a hybrid model, consisting of two phases, is proposed in this article. In the first phase, the popular PSO algorithm is used to determine the locations of fuzzy membership functions. Then, the proposed HFIS technique is used to develop the one-step-ahead load forecasting model in the second phase. Because of the robust nature of the proposed HFIS technique, which does not need to retrain or re-estimate model parameters, it is very suitable for smart home load forecasting. The proposed method was verified using two different households’ load data. Simulation results indicate that the proposed method produces better forecasting accuracy than existing methods.     

Topology optimization for thermal insulation: an application to building engineering

This article deals with a numerical implementation for topology optimization that is based on the heat conduction equation and addresses problems such as the optimal design of thermal insulation in building engineering. The formulation handles heat diffusivity under the steady-state assumption for a domain with assigned convective-like boundary conditions. The optimization framework is implemented within a general-purpose finite-elements code that is set to solve the thermal problem iteratively, thus allowing for a straightforward handling of two-dimensional and three-dimensional problems. A few numerical results are firstly presented to compare classical formulations for maximum heat conduction and the addressed scheme for optimal thermal insulation. The proposed methodology is therefore exploited to cope with issues peculiar to the optimal design of building envelopes, such as the mitigation of the effects of thermal bridges and the design for minimum thermal transmittance of the components of a modular curtain wall.     

Non-dominated archiving multi-colony ant algorithm for multi-objective optimization: Application to multi-purpose reservoir operation

Multi-objective optimization using heuristic methods has been established as a subdiscipline that combines the fields of heuristic computation and classical multiple criteria decision making. This article presents the Non-dominated Archiving Ant Colony Optimization (NA-ACO), which benefits from the concept of a multi-colony ant algorithm and incorporates a new information-exchange policy. In the proposed information-exchange policy, after a given number of iterations, different colonies exchange information on the assigned objective, resulting in a set of non-dominated solutions. The non-dominated solutions are moved into an offline archive for further pheromone updating. Performance of the NA-ACO is tested employing two well-known mathematical multi-objective benchmark problems. The results are promising and compare well with those of well-known NSGA-II algorithms used in real-world multi-objective-optimization problems. In addition, the optimization of reservoir operating policy with multiple objectives (i.e. flood control, hydropower generation and irrigation water supply) is considered and the associated Pareto front generated.     

Practical solutions for multi-objective optimization: An application to system reliability design problems

For multiple-objective optimization problems, a common solution methodology is to determine a Pareto optimal set. Unfortunately, these sets are often large and can become difficult to comprehend and consider. Two methods are presented as practical approaches to reduce the size of the Pareto optimal set for multiple-objective system reliability design problems. The first method is a pseudo-ranking scheme that helps the decision maker select solutions that reflect his/her objective function priorities. In the second approach, we used data mining clustering techniques to group the data by using the k-means algorithm to find clusters of similar solutions. This provides the decision maker with just k general solutions to choose from. With this second method, from the clustered Pareto optimal set, we attempted to find solutions which are likely to be more relevant to the decision maker. These are solutions where a small improvement in one objective would lead to a large deterioration in at least one other objective. To demonstrate how these methods work, the well-known redundancy allocation problem was solved as a multiple objective problem by using the NSGA genetic algorithm to initially find the Pareto optimal solutions, and then, the two proposed methods are applied to prune the Pareto set.     

The MINLP optimization approach to structural synthesis. Part I: A general view on simultaneous topology and parameter optimization

This paper presents the Mixed-Integer Non-linear Programming (MINLP) optimization approach to structural synthesis. Non-linear continuous/discrete non-convex problems of structural synthesis are proposed to be solved by means of simultaneous topology, parameter and standard dimension optimization. Part I of this three-part series of papers contains a general view of the MINLP approach to simultaneous topology and continuous parameter optimization. The MINLP optimization approach is performed through three steps. The first one includes the generation of a mechanical superstructure of different topology alternatives, the second one involves the development of an MINLP model formulation and the last one consists of a solution for the formulated MINLP problem. Some MINLP methods are also presented. A Modified OA/ER algorithm is applied to solve the MINLP problem and a simple example of a multiple cantilever beam is given to demonstrate the steps of the proposed MINLP optimization approach. As simultaneous optimization, extended to include also standard dimensions, requires additional effort, the development of suitable strategies to carry out the optimization is further discussed in Part II. The modelling of MINLP superstructures and the topology and parameter optimization of roller and sliding hydraulic steel gate structures are shown in Part III of the paper. An example of the synthesis of an already erected roller gate, i.e. the Intake Gate of Aswan II in Egypt, is presented as a comparative design research work. © 1998 John Wiley & Sons, Ltd.     

A two-stage approach for multi-objective decision making with applications to system reliability optimization

This paper proposes a two-stage approach for solving multi-objective system reliability optimization problems. In this approach, a Pareto optimal solution set is initially identified at the first stage by applying a multiple objective evolutionary algorithm (MOEA). Quite often there are a large number of Pareto optimal solutions, and it is difficult, if not impossible, to effectively choose the representative solutions for the overall problem. To overcome this challenge, an integrated multiple objective selection optimization (MOSO) method is utilized at the second stage. Specifically, a self-organizing map (SOM), with the capability of preserving the topology of the data, is applied first to classify those Pareto optimal solutions into several clusters with similar properties. Then, within each cluster, the data envelopment analysis (DEA) is performed, by comparing the relative efficiency of those solutions, to determine the final representative solutions for the overall problem. Through this sequential solution identification and pruning process, the final recommended solutions to the multi-objective system reliability optimization problem can be easily determined in a more systematic and meaningful way.     

Convex optimization and limit analysis: Application to Gurson and porous Drucker-Prager materials

First, we summarize our convex optimization method to solve the static approach of limit analysis. Then, we present the main features of a quadratic extension of a recently proposed mixed finite element method of the kinematic approach. Both methods are applied to obtain precise solutions to a forming problem with Gurson and Drucker-Prager materials. Finally, in order to analyze the criterion of “Porous Drucker-Prager” materials, the Gurson micro-macro model involving a Drucker-Prager matrix containing cylindrical cavities is investigated. Comparing previous results shows, among other things, a similarity in the compression case not always observed for the “Porous von Mises” material between cylindrical and spherical cases.     

Decomposition of multidisciplinary optimization problems: formulations and application to a simplified wing design

Several formulations for solving multidisciplinary design optimization (MDO) problems are presented and applied to a test case. Two bi-level hierarchical decomposition approaches are compared with two classical single-level approaches without decomposition of the optimization problem. A methodology to decompose MDO problems and a new formulation based on this decomposition are proposed. The problem considered here for validation of the different formulations involves the shape and structural optimization of a conceptual wing model. The efficiency of the design strategies are compared on the basis of optimization results.     

An efficient and practical approach to obtain a better optimum solution for structural optimization

For many structural optimization problems, it is hard or even impossible to find the global optimum solution owing to unaffordable computational cost. An alternative and practical way of thinking is thus proposed in this research to obtain an optimum design which may not be global but is better than most local optimum solutions that can be found by gradient-based search methods. The way to reach this goal is to find a smaller search space for gradient-based search methods. It is found in this research that data mining can accomplish this goal easily. The activities of classification, association and clustering in data mining are employed to reduce the original design space. For unconstrained optimization problems, the data mining activities are used to find a smaller search region which contains the global or better local solutions. For constrained optimization problems, it is used to find the feasible region or the feasible region with better objective values. Numerical examples show that the optimum solutions found in the reduced design space by sequential quadratic programming (SQP) are indeed much better than those found by SQP in the original design space. The optimum solutions found in a reduced space by SQP sometimes are even better than the solution found using a hybrid global search method with approximate structural analyses.     

A combined global and local search method to deal with constrained optimization for continuous tabu search

Heuristic methods, such as tabu search, are efficient for global optimizations. Most studies, however, have focused on constraint‐free optimizations. Penalty functions are commonly used to deal with constraints for global optimization algorithms in dealing with constraints. This is sometimes inefficient, especially for equality constraints, as it is difficult to keep the global search within the feasible region by purely adding a penalty to the objective function. A combined global and local search method is proposed in this paper to deal with constrained optimizations. It is demonstrated by combining continuous tabu search (CTS) and sequential quadratic programming (SQP) methods. First, a nested inner‐ and outer‐loop method is presented to lead the search within the feasible region. SQP, a typical local search method, is used to quickly solve a non‐linear programming purely for constraints in the inner loop and provides feasible neighbors for the outer loop. CTS, in the outer loop, is used to seek for the global optimal. Finally, another local search using SQP is conducted with the results of CTS as initials to refine the global search results. Efficiency is demonstrated by a number of benchmark problems. Copyright © 2008 John Wiley & Sons, Ltd.