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In this paper, we present an approach for simultaneous identification of the system parameters and the input dynamic force time history. The inverse problem associated with the system identification is formulated as an optimization problem and is solved using a newly developed dynamic hybrid adaptive firefly algorithm (DHAFA). A modified version of Tikhonov regularization is employed while solving the inverse problem associated with the force identification in order to improve the quality of the solution. Numerical simulation studies have been carried out by solving three distinct numerical examples. Studies presented in this paper indicate that the proposed algorithm is effective in identifying the system parameters as well as the input dynamic force simultaneously and can be effectively used for structural health monitoring purposes. Convergence studies presented in this paper on the newly developed dynamic hybrid firefly algorithm indicate that the proposed algorithm has better convergence characteristics and can be effectively employed for solving complex nonlinear optimization problems associated with system identification. [ABSTRACT FROM AUTHOR]

The present paper deals with structural health monitoring of trusses, space frame and plate structure utilizing the Bayesian data fusion approach. The application of the proposed approach has been demonstrated on a 25-member plane truss, a 42-member space frame, a cantilever plate and a 120-member space truss. Different damage indexes of interest have been calculated for the damaged structure utilizing the natural frequency and modeshapes as damage indicators. Damage indexes used are modal strain energy (DIMSE), frequency response function strain energy dissipation ratio (FRFSEDR), flexibility strain energy damage ratio (FSEDR) and residual force-based damage index (RFBDI). Next, the Bayesian data fusion approach has been applied to these four damage indexes to find out the accurate damage location. The proposed approach reduces the number of suspected damaged elements in the structure significantly, thus reducing the computational time of optimization algorithm. Proposed algorithm has also shown encouraging performance in noisy environments. Overall present approach is found to be robust and computationally efficient, and thus can be applied for damage detection involving field evaluation of various structures. [ABSTRACT FROM AUTHOR]

This paper presents the design of a suspension system for a Heavy Goods Vehicle (HGV). Four types of linear and non-linear, passive and semi-active suspension systems are modelled with Quarter Vehicle Model (QVM). A modified control law is proposed for the semi-active suspension system that uses a Proportional, Integral, Derivative (PID) controller. Suspension systems are designed by performing multi-objective optimization with road damage and goods damage as design criteria. In current optimization problems, objective function calculation is costly in terms of computational resources and time. Thus, it is necessary to reach actual optimal values in fewer generations with a small population. A fast-converging optimization algorithm is proposed to save computational cost and is used to design suspension systems. The results of the proposed algorithm are compared with the Non-dominated Sorting Genetic Algorithm II (NSGA-II). The proposed algorithm saves a substantial amount of computational cost by fast convergence with a small population. Our results show that the semi-active suspension system with proposed control law performs better in terms of road-friendliness and goods safety. [ABSTRACT FROM AUTHOR]

This paper presents a new multi-objective optimization algorithm called FC-MOPSO for optimal design of engineering problems with a small number of function evaluations. The proposed algorithm expands the main idea of the single-objective particle swarm optimization (PSO) algorithm to deal with constrained and unconstrained multi-objective problems (MOPs). FC-MOPSO employs an effective procedure in selection of the leader for each particle to ensure both diversity and fast convergence. Fifteen benchmark problems with continuous design variables are used to validate the performance of the proposed algorithm. Finally, a modified version of FC-MOPSO is introduced for handling discrete optimization problems. Its performance is demonstrated by optimizing five space truss structures. It is shown that the FC-MOPSO can effectively find acceptable approximations of Pareto fronts for structural MOPs within very limited number of function evaluations. [ABSTRACT FROM AUTHOR]

In practical engineering, the layout optimization technique driven by the thermal performance is faced with a severe computational burden when directly integrating the numerical analysis tool of temperature simulation into the optimization loop. To alleviate this difficulty, this paper presents a novel deep learning surrogate-assisted heat source layout optimization method. First, two sampling strategies, namely the random sampling strategy and the evolving sampling strategy, are proposed to produce diversified training data. Then, regarding mapping between the layout and the corresponding temperature field as an image-to-image regression task, the feature pyramid network (FPN), a kind of deep neural network, is trained to learn the inherent laws, which plays as a surrogate model to evaluate the thermal performance of the domain with respect to different input layouts accurately and efficiently. Finally, the neighborhood search-based layout optimization (NSLO) algorithm is proposed and combined with the FPN surrogate to solve discrete heat source layout optimization problems. A typical two-dimensional heat conduction optimization problem is investigated to demonstrate the feasibility and effectiveness of the proposed deep learning surrogate-assisted layout optimization framework. [ABSTRACT FROM AUTHOR]

The paper proposes four improved proportional topology optimization (IPTO) algorithms which are called IPTO_A, IPTO_B, IPTO_C, and IPTO_D, respectively. The purposes of this work are to solve the minimum compliance optimization problem, avoid the problems of numerical derivation and sensitivity calculation involved in the process of obtaining sensitivity information, and overcome the deficiencies in the original proportional topology optimization (PTO) algorithm. Inspired by the PTO algorithm and ant colony algorithm, combining the advantages of the filtering techniques, the new algorithms are designed by using the compliance proportion filter and the new density variable increment update scheme and modifying the update way of the density variable in the inner and main loops. To verify the effectiveness of the new algorithms, the minimum compliance optimization problem for the MBB beam is introduced and used here. The results show that the new algorithms (IPTO_A, IPTO_B, IPTO_C, and IPTO_D) have some advantages in terms of certain performance aspects and that IPTO_A is the best among the new algorithms in terms of overall performance. Furthermore, compared with PTO and Top88, IPTO_A has some advantages such as improving the objective value and the convergence speed, obtaining the optimized structure without redundancy, and suppressing gray-scale elements. Besides, IPTO_A also possesses the advantage of strong robustness over PTO. [ABSTRACT FROM AUTHOR]

This paper proposes formulations and algorithms for design optimization under both aleatory (i.e., natural or physical variability) and epistemic uncertainty (i.e., imprecise probabilistic information), from the perspective of system robustness. The proposed formulations deal with epistemic uncertainty arising from both sparse and interval data without any assumption about the probability distributions of the random variables. A decoupled approach is proposed in this paper to un-nest the robustness-based design from the analysis of non-design epistemic variables to achieve computational efficiency. The proposed methods are illustrated for the upper stage design problem of a two-stage-to-orbit (TSTO) vehicle, where the information on the random design inputs are only available as sparse point data and/or interval data. As collecting more data reduces uncertainty but increases cost, the effect of sample size on the optimality and robustness of the solution is also studied. A method is developed to determine the optimal sample size for sparse point data that leads to the solutions of the design problem that are least sensitive to variations in the input random variables. [ABSTRACT FROM AUTHOR]

This paper introduces a set of skeleton operators for characterizing topologies evolving in a bit-array represented structural topology optimization problem. It is shown that the design generally converges to a stable skeleton fairly early in the optimization process. It is observed that further optimization is more about finding optimal gross shape for the various branches of the converged skeleton and the bit-array representation is not appropriate. A two-phase approach to topology optimization is proposed in which the first phase, where bit-array is used to represent the topology, ends with the detection of stabilization of skeleton, and the second phase proceeds further with the geometry based representation that directly addresses gross variation in shape of the branches of the converged skeleton. Genetic Algorithm has been used for optimization in both the phases. The efficiency and effectiveness of the use of skeleton operators and geometric variables for identification of convergence in the first phase and optimization in the second phase respectively is demonstrated. [ABSTRACT FROM AUTHOR]

Among population-based optimization algorithms guided by meta-heuristics, Particle Swarm Optimization (PSO) has gained significant popularity in the past two decades, particularly due to its ease of implementation and fast convergence capabilities. This paper seeks to translate the beneficial features of PSO from solving typical continuous single-objective problems to solving multi-objective mixed-discrete problems, which is relatively a new ground for PSO application. The original Mixed-Discrete PSO (MDPSO) algorithm, which included an exclusive diversity preservation technique to significantly mitigate premature particle clustering, has been shown to be a powerful single-objective solver for highly constrained MINLP problems. This papers makes fundamental advancements to MDPSO, enabling it to solve complex multi-objective problems with mixed-discrete design variables. Specifically, in the velocity update equation for any particle, the explorative term is modified to point towards a stochastically selected non-dominated solution at that iteration − thereby adopting the concept of multi-leader swarms. The fractional domain in the diversity preservation technique, which was previously defined in terms of the best global particle, is now formulated as a function of the extreme members in the set of intermediate Pareto optimal solutions. With this advancement, diversity preservation not only mitigates premature particle stagnation, but also promotes more uniform coverage of the Pareto frontier. The multi-objective MDPSO algorithm is tested using a set of benchmark problems and a wind farm layout optimization problem. To illustrate the competitive benefits of the new MO-MDPSO algorithm, the results are compared with those given by other popular multi-objective solvers such as NSGA-II and SPEA. [ABSTRACT FROM AUTHOR]

In this paper, a new multi-objective uniform-diversity differential evolution (MUDE) algorithm is proposed and used for Pareto optimum design of mechanisms. The proposed algorithm uses a diversity preserving mechanism called the ε-elimination algorithm to improve the population diversity among the obtained Pareto front. The proposed algorithm is firstly tested on some constrained and unconstrained benchmarks proposed for the special session and competition on multi-objective optimizers held under IEEE CEC 2009. The inverted generational distance (IGD) measure is used to assess the performance of the algorithm. Secondly, the proposed algorithm has been used for multi-objective optimization of two different combinatorial case studies. The first case contains a two-degree of freedom leg mechanism with springs. Three conflicting objective functions that have been considered for Pareto optimization are namely, leg size, vertical actuating force, and the peak crank torque. The second case is a two-finger robot gripper mechanism with two conflicting objectives which are the difference between the maximum and minimum gripping force and the transmission ratio of actuated and experienced gripper forces. Comparisons of obtained Pareto fronts using the method of this work with those obtained in other references show significant improvements. [ABSTRACT FROM AUTHOR]

In this paper, multi-objective particle swarm optimization with preference information (MOPSO-PI) has been proposed. In the proposed algorithm, the information entropy is employed for measuring the probability distribution of particles; the user's preference information is represented as the ranking of each particle through the possible matrix. The optimal procedure is guided by the preference information since the global best performance of particle is randomly chosen among non-dominated solutions with higher ranking value in each iteration. Finally, the MOPSO-PI is applied to optimize the steelmaking process; the power supply curve obtained reduces the electric energy consumption, shortens the smelting time and prolongs the lifespan of the furnace lining. The application results show the effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

The paper concerns worst-case compliance optimization by finding the structural topology with minimum compliance for the loading due to the worst possible acceleration of the structure and attached non-structural masses. A main novelty of the paper is that it is shown how this min-max problem can be formulated as a non-linear semi-definite programming (SDP) problem involving a small-size constraint matrix and how this problem is solved numerically. Our SDP formulation is an extension of an eigenvalue problem seen previously in the literature; however, multiple eigenvalues naturally arise which makes the eigenvalue problem non-smooth, whereas the SDP problem presented in this paper provides a computationally tractable problem. Optimized designs, where the uncertain loading is due to acceleration of applied masses and the weight of the structure itself, are shown in two and three dimensions and we show that these designs satisfy optimality conditions that are also presented. [ABSTRACT FROM AUTHOR]

This paper presents network load path optimisation for the weight minimisation of compression-only thrust networks, allowing for the design of material efficient surface structures. A hybrid evolutionary and function-gradient optimisation process finds the optimal internal force state of the network, by manipulating the force densities of a selected number of edges based on the network indeterminacy. These selected edges are the independent sets, and are found through the Reduced Row Echelon form of the network's equilibrium matrix. It was found that networks can have certain independent sets that have a significant influence on both the stability of the optimisation algorithm, and in the final load path/volume of the structure. Finding the most effective independent sets was handled by data-driven methods, applied to many thousands of independent set trials. This provided insight into the behaviour of the underlying network and dramatically increased the rate of finding successful independent sets. The importance and weights of the network edges highlighted key areas of the network that allowed structural judgement and improvements to be made. [ABSTRACT FROM AUTHOR]

Length scale control in topology optimization is an important area of research with direct implications on numerical stability and solution manufacturability. Projection-based algorithms for continuum topology optimization have received considerable attention in recent years due to their ability to control minimum length scale in a flexible and computationally efficient manner. In this paper, we propose a new projection-based algorithm that embeds minimum length scale control on two material phases (e.g., solid and void) as well as optional maximum length scale on one material phase (e.g., solid or void) into the projection methodology used for material distribution approaches to topology optimization. The proposed algorithms are demonstrated on benchmark problems and are shown to satisfy the length scale constraints imposed. [ABSTRACT FROM AUTHOR]

A new local search algorithm for multiobjective optimization problems is proposed to find the global optima accurately and diversely. This paper models the cooperatively local search as a potential field, which is called neighborhood field model (NFM). Using NFM, a new Multiobjective Neighborhood Field Optimization (MONFO) algorithm is proposed. In MONFO, the neighborhood field can drive each individual moving towards the superior neighbor and away from the inferior neighbor. MONFO is compared with other popular multiobjective algorithms under twelve test functions. Intensive simulations show that MONFO is able to deliver promising results in the respects of accuracy and diversity, especially for multimodal problems. [ABSTRACT FROM AUTHOR]

In level set based structural optimization, semi-Lagrange method has an advantage to allow for a large time step without the limitation of Courant-Friedrichs-Lewy (CFL) condition for numerical stability. In this paper, a line search algorithm and a sensitivity modulation scheme are introduced for the semi-Lagrange method. The line search attempts to adaptively determine an appropriate time step in each iteration of optimization. With consideration of some practical characteristics of the topology optimization process, incorporating the line search into semi-Lagrange optimization method can yield fewer design iterations and thus improve the overall computational efficiency. The sensitivity modulation is inspired from the conjugate gradient method in finite-dimensions, and provides an alternative to the standard steepest descent search in level set based optimization. Two benchmark examples are presented to compare the sensitivity modulation and the steepest descent techniques with and without the line search respectively. [ABSTRACT FROM AUTHOR]

This paper presents a methodology for constrained efficient global optimization (EGO) using support vector machines (SVMs). While the objective function is approximated using Kriging, as in the original EGO formulation, the boundary of the feasible domain is approximated explicitly as a function of the design variables using an SVM. Because SVM is a classification approach and does not involve response approximations, this approach alleviates issues due to discontinuous or binary responses. More importantly, several constraints, even correlated, can be represented using one unique SVM, thus considerably simplifying constrained problems. In order to account for constraints, this paper introduces an SVM-based 'probability of feasibility' using a new Probabilistic SVM model. The proposed optimization scheme is constituted of two levels. In a first stage, a global search for the optimal solution is performed based on the 'expected improvement' of the objective function and the probability of feasibility. In a second stage, the SVM boundary is locally refined using an adaptive sampling scheme. An unconstrained and a constrained formulation of the optimization problem are presented and compared. Several analytical examples are used to test the formulations. In particular, a problem with 99 constraints and an aeroelasticity problem with binary output are presented. Overall, the results indicate that the constrained formulation is more robust and efficient. [ABSTRACT FROM AUTHOR]

The paper presents an approach for simultaneous optimization of structural mass and reliability in discrete truss structures. In addition to member sizing, the selection of an optimal topology from a pre-specified ground structure is a feature of the proposed methodology. To allow for a global search, optimization is performed using a multiobjective evolutionary algorithm. System reliability is based on a recently developed computational approach that is efficient and could be integrated within the framework of an evolutionary optimization process. The presence of multiple allowable topologies in the optimization process was handled through co-evolution in competing subpopulations. A unique feature of the algorithm is an automatic reunification of these populations using hypervolume measure-based indicator as reunification criterion to attain greater search efficiency. Numerical experiments demonstrate the computational advantages of the proposed method. These advantages become more pronounced for large-scale optimization problems, where the standard evolutionary approach fails to produce the desired results. [ABSTRACT FROM AUTHOR]

This paper presents a single-loop algorithm for system reliability-based topology optimization (SRBTO) that can account for statistical dependence between multiple limit-states, and its applications to computationally demanding topology optimization (TO) problems. A single-loop reliability-based design optimization (RBDO) algorithm replaces the inner-loop iterations to evaluate probabilistic constraints by a non-iterative approximation. The proposed single-loop SRBTO algorithm accounts for the statistical dependence between the limit-states by using the matrix-based system reliability (MSR) method to compute the system failure probability and its parameter sensitivities. The SRBTO/MSR approach is applicable to general system events including series, parallel, cut-set and link-set systems and provides the gradients of the system failure probability to facilitate gradient-based optimization. In most RBTO applications, probabilistic constraints are evaluated by use of the first-order reliability method for efficiency. In order to improve the accuracy of the reliability calculations for RBDO or RBTO problems with high nonlinearity, we introduce a new single-loop RBDO scheme utilizing the second-order reliability method and implement it to the proposed SRBTO algorithm. Moreover, in order to overcome challenges in applying the proposed algorithm to computationally demanding topology optimization problems, we utilize the multiresolution topology optimization (MTOP) method, which achieves computational efficiency in topology optimization by assigning different levels of resolutions to three meshes representing finite element analysis, design variables and material density distribution respectively. The paper provides numerical examples of two- and three-dimensional topology optimization problems to demonstrate the proposed SRBTO algorithm and its applications. The optimal topologies from deterministic, component and system RBTOs are compared with one another to investigate the impact of optimization schemes on final topologies. Monte Carlo simulations are also performed to verify the accuracy of the failure probabilities computed by the proposed approach. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to propose a size-dependent topology optimization formulation of periodic cellular material microstructures, based on the effective couple-stress continuum model. The present formulation consists of finding the optimal layout of material that minimizes the mean compliance of the macrostructure subject to the constraint of permitted material volume fraction. We determine the effective macroscopic couple-stress constitutive constants by analyzing a unit cell with specified boundary conditions with the representative volume element (RVE) method, based on equivalence of strain energy. The computational model is established by the finite element (FE) method, and the design density and FE stiffness of the RVE are related by the solid isotropic material with penalization power (SIMP) law. The required sensitivity formulation for gradient-based optimization algorithm is also derived. Numerical examples demonstrate that this present formulation can express the size effect during the optimization procedure and provide precise topologies without increase in computational cost. [ABSTRACT FROM AUTHOR]

Evolutionary Structural Optimization (ESO) andits later version bi-directional ESO (BESO) have gainedwidespread popularity among researchers in structural optimizationand practitioners in engineering and architecture.However, there have also been many critical comments onvarious aspects of ESO/BESO. To address those criticisms,we have carried out extensive work to improve the originalESO/BESO algorithms in recent years. This paper summarizeslatest developments in BESO for stiffness optimizationproblems and compares BESO with other well-establishedoptimization methods. Through a series of numerical examples,this paper provides answers to those critical commentsand shows the validity and effectiveness of the evolutionarystructural optimization method. [ABSTRACT FROM AUTHOR]

Abstract  This paper shows a promising method for acoustic barrier design using a new acoustic material called Sonic Crystals (SCs). The configuration of these SCs is set as a multiobjective optimization problem which is very difficult to solve with conventional optimization techniques. The paper presents a new parallel implementation of a Multiobjective Evolutionary Algorithm called ev-MOGA (also known as ) and its application in a complex design problem. ev-MOGA algorithm has been designed to converge towards a reduced, but well distributed, representation of the Pareto Front (solution of the multiobjective optimization problem). The algorithm is presented in detail and its most important properties are discussed. To reduce the ev-MOGA computational cost when objective functions are substantial, a basic parallelization has been implemented on a distributed platform. [ABSTRACT FROM AUTHOR]

Abstract  Instead of the past mathematical analyses, an intuitive geometric analysis of the collaborative optimization (CO) algorithm is presented in this paper, which reveals some geometric properties of CO and gives a direct geometric interpretation of the reason for the reported computational difficulties in CO. The analysis shows that if the system-level optimum point at one iteration is outside the feasible region of the original optimization problem, at the next iteration, the system-level optimization problem may be infeasible due to the system-level consistency equality constraints. One way to solve the problem of the infeasibility is to relax the system-level consistency equality constraints using inequality constraints. However it is a delicate job to determine a rational relaxed tolerance because feasibility and consistency have conflicting requirements for the tolerance, that is, the more relaxed the better for feasibility while the stricter the better for consistency. Based on the geometric analysis, a method of variable relaxed tolerance is put forward to solve this problem. In this method, an adaptive adjustment of the tolerance is made at each iteration according to the quantified inconsistency between two subsystems. In the last section, the capabilities and limitations of the proposed method are illustrated by three examples. [ABSTRACT FROM AUTHOR]

Truss optimization based on the ground structure approach often leads to designs that are too complex for practical purposes. In this paper we present an approach for design complexity control in truss optimization. The approach is based on design complexity measures related to the number of bars (similar to Asadpoure et al. Struct Multidisc Optim 51(2):385-396 2015) and a novel complexity measure related to the number of nodes of the structure. Both complexity measures are continuously differentiable and thus can be used together with gradient based optimization algorithms. The numerical examples show that the proposed approach is able to reduce design complexity, leading to solutions that are more fit for engineering practice. Besides, the examples also indicate that in some cases it is possible to significantly reduce design complexity with little impact on structural performance. Since the complexity measures are non convex, a global gradient based optimization algorithm is employed. Finally, a detailed comparison to a classical approach is presented. [ABSTRACT FROM AUTHOR]

The present paper studies the integrated size and topology optimization of skeletal structures under natural frequency constraints. It is found that, unlike the conventional compliance-oriented topology optimization problems, the considered problem may be strongly singular in the sense that the corresponding feasible domain may be disconnected and the global optimal solutions are often located at the tips of some separated low dimensional sub-domains when the cross-sectional areas of the structural components are used as design variables. As in the case of stress-constrained topology optimization, this unpleasant behavior may prevent the gradient-based numerical optimization algorithms from finding the true optimal topologies. To overcome the difficulties posed by the strongly singular optima, some particular forms of area/moment of inertia-density interpolation schemes, which can restore the connectedness of the feasible domain, are proposed. Based on the proposed optimization model, the probability of finding the strongly singular optimum with gradient-based algorithms can be increased. Numerical examples demonstrate the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

Set-based design is a design approach where feasible regions for the design variables are determined from different disciplines, with the goal of locating and working with the areas of feasible overlap. During the process the constraints are adjusted in order to accommodate conflicting requirements between disciplines. The main objective of set-based design is to narrow the design space, while delaying the pursuit of a single point design as much as possible. This process avoids finalizing decisions early and allows for flexibility in dealing with requirement creep. This paper presents the development and application of a new multidisciplinary design optimization (MDO) algorithm inspired by the principles of set-based design. The new MDO algorithm was developed with the core concept of describing the design using sets to incorporate features of set-based design and achieve greater flexibility than with a single-point optimization. The MDO algorithm was applied to a ship design problem and the ship design application demonstrated the value of utilizing set-based design as a space-reducing technique before approaching the problem with a point-based optimization. Furthermore, incorporating flexibility in the constraints allowed the optimization to handle a problem with very strict constraints in a rational manner and minimize the necessary constraint violation. [ABSTRACT FROM AUTHOR]

In this paper, a new robust optimization technique with the ability of solving multi-objective constrained design optimization problems in aerodynamics is presented. This new technique is Multi-objective Territorial Particle Swarm Optimization (MOTPSO) algorithm in which diversity is actively preserved by avoiding overcrowded clusters of particles and encouraging broader exploration. Adaptively varying 'territories' are formed around promising individuals to prevent many of the lesser individuals from premature clustering and encouraged them to explore new neighborhoods based on a hybrid self-social metric. Also, a new social interaction scheme is introduced which guided particles towards the weighted average of their 'elite' neighbors' best found positions instead of their own personal bests which in turn helps the particles to exploit the candidate local optima more effectively. The MOTPSO algorithm takes into account multiple objective functions using a Pareto-Based approach. The non-dominated solutions found by swarm are stored in an external archive and nearest neighbor density estimator method is used to select a leader for the individual particles in the swarm. Efficiency and robustness of the proposed algorithm is demonstrated using multiple traditional and newly-composed optimization benchmark functions and aerodynamic design problems. In final airfoil designs obtained from the Multi Objective Territorial Particle Swarm Optimization algorithm, separation point is delayed to make the airfoil less susceptible to stall in critical operating conditions and it also reveal an evident improvement over the test case airfoil across all objective functions presented. [ABSTRACT FROM AUTHOR]

The objective of this study is to obtain the optimum design for reinforced concrete continuous beams in terms of cross section dimensions and reinforcement details using a fine tuned Artificial Bee Colony (ABC) Algorithm while still satisfying the constraints of the ACI Code (). The ABC algorithm used in this paper has been slightly modified to include a Variable Changing Percentage (VCP) that further improves its performance when dealing with members consisted of multiple variables. The objective function is the total cost of the continuous beam which includes the cost of concrete, formwork and reinforcing steel bars. The design variables used are beam width, beam height, number and diameter of: bottom continuous reinforcing bars, bottom cutoff reinforcing bars, top continuous reinforcing bars and top cutoff reinforcing bars as well as the diameter of stirrups. Four RC beams of varying complexity are presented and optimized. The first three beams are used to fine tune the control parameters of the ABC algorithm, whereas the fourth beam was previously optimized by Arafa et al. (J Artif Intell 76-88, 2011) and is presented here to prove the superiority of this relatively new optimization algorithm. [ABSTRACT FROM AUTHOR]

This article is a continuation of the paper Kočvara and Stingl (Struct Multidisc Optim 33(4-5):323-335, ). The aim is to describe numerical techniques for the solution of topology and material optimization problems with local stress constraints. In particular, we consider the topology optimization (variable thickness sheet or 'free sizing') and the free material optimization problems. We will present an efficient algorithm for solving large scale instances of these problems. Examples will demonstrate the efficiency of the algorithm and the importance of the local stress constraints. In particular, we will argue that in certain topology optimization problems, the addition of stress constraints must necessarily lead not only to the change of optimal topology but also optimal geometry. Contrary to that, in material optimization problems the stress singularity is treated by the change in the optimal material properties. [ABSTRACT FROM AUTHOR]

Many solutions in geotechnical problems are the result of optimization analysis. There are many practical engineering problems where the objective function is non-convex, discontinuous with the presence of multiple strong local minima, and the classical optimization methods may sometime be trapped by the local minimum during the analysis. In this paper, a coupled optimization method is proposed for such difficult cases. The mixed optimization algorithm can takes the advantage of different algorithms, and the proposed algorithm is demonstrated to be effective and efficient in solving a very complicated hydropower problem with a high level of confidence. The proposed method can further be applied to different kinds of difficult engineering problems. [ABSTRACT FROM AUTHOR]

In this paper, three direct search algorithms, i.e. a modified simplex, random direction search and enhanced Powell's methods together with a new localised response surface method are presented and applied to solve die shape optimisation problems for achieving net-shape accuracy in metal forming processes. The main motivation is to develop efficient and easy to implement optimisation algorithms in metal forming simulations which often involve complex tool and workpiece interaction and coupled thermal and mechanical analysis. Three case studies are presented including a simple upsetting, a 2D blade forging and a forward extrusion problem. In all cases, the objective was to achieve net-shape accuracy of the formed parts, one important criterion for precision forming. C+ + programs were developed to implement these algorithms and to automatically integrate optimisation computation and forging simulation. The optimisation results from the three case problems show that direct search based methods especially the modified simplex and the localised response surface methods are computationally efficient and robust for net-shape forging and extrusion optimisation problems. It is also suggested that these methods can be used in more complex forging problems where die shape design and optimisation are essential for achieving net-shape accuracy. [ABSTRACT FROM AUTHOR]

In the 'first-order reliability method' (FORM), the HL-RF iterative algorithm is a recommended and widely used one to locate the design point and calculate the reliability index. However it may fail to converge if the limit state surface at the design point is highly nonlinear. In this paper, an easy iterative algorithm, which introduces a 'new' step length to control the convergence of the sequence and can be named as finite-step-length iterative algorithm, is present. It is proved that the HL-RF method is a special case of this proposed algorithm when the step length tends to infinity and the reason why the HL-RF diverges is illustrated. This proposed algorithm is much easier than other optimization schemes, especially than the modified HL-RF algorithm, because the process of line search for obtaining the step length is not needed. Numerical results indicate that the proposed algorithm is effective and as simple as the HL-RF but more robust. [ABSTRACT FROM AUTHOR]

In this paper the application of bees algorithm (BA) in the finite element (FE) model updating of structures is investigated. BA is an optimization algorithm inspired by the natural foraging behavior of honeybees to find food sources. The weighted sum of the squared error between the measured and computed modal parameters is used as the objective function. To demonstrate the effectiveness of the proposed method, BA is applied on a piping system to update several physical parameters of its FE model. To this end, the modal parameters of the numerical model are compared with the experimental ones obtained through modal testing. Moreover, to verify the performance of BA, it is compared with the genetic algorithm, the particle swarm optimization and the inverse eigensensitivity method. Comparison of the results indicates that BA is a simple and robust approach that could be effectively applied to the FE model updating problems. [ABSTRACT FROM AUTHOR]

This paper presents a modified Ant Colony Algorithm(ACA) called multi-city-layer ant colony algorithm(MCLACA). The research attention is focused on improvingthe computational efficiency in the stacking sequenceoptimisation of a laminated composite plate for maximumbuckling load. A new operator, the so-called two point interchange,is introduced and proved to be effective for reducingthe convergence time and enhancing the robustness in theMCLACA performance. The laminate optimisation is subjectto balanced and symmetric layup with ply contiguousand strength constraints. In order to assess the MCLACAperformance, a simply supported rectangular laminate plate,which was taken as numerical example in previous researchusing traditional ACA and genetic algorithm (GA) is chosenas a benchmark case study. Comparing with the ACAand GA results, it is shown that the presented MCLACAhas better performance in terms of computational efficiencyand robustness. To demonstrate the applicability of theMCLACA to a general case, an additional example of laminateoptimisation has been taken with more design variablesand five different boundary conditions by finite elementanalysis. [ABSTRACT FROM AUTHOR]

This paper discusses the problem of structuraloptimization of product families subjected to multiple loadcases, evaluated by computationally costly finite elementanalysis. Product families generally have a complex compositionof shared components that makes individual productoptimization difficult as the relation between the sharedvariables is not always intuitive. More optimal is to treat theproblem as a product family optimization problem. Though,for product families subjected to multiple and computationallycostly crash loads, the optimization problem takestoo long time to solve with traditional methods. Therefore,a new optimization algorithm is presented that decomposesthe family problem into sub-problems and iterativelyreduces the number of sub-problems, decouple and solvethem. The algorithm is applicable for module based productfamilies with predefined composition of generalizedcommonality, subjected to multiple load cases that can beanalyzed separately. The problem reduction is performed byonly considering the constraints that are critical in the optimalsolution. Therefore the optimization algorithm is calledthe Critical Constraint Method, CCM. Finally the CCMalgorithm is evaluated by two product family optimizationproblems. [ABSTRACT FROM AUTHOR]

In predator–prey algorithm, a relatively small number of predators (“lions”) and a much larger number of prey (“antelopes”) are randomly placed on a two dimensional lattice with connected ends representing an unfolded surface of a torus. The predators are partially or completely biased towards one or more objectives, based on which each predator kills the weakest prey in its neighborhood. A stronger prey created through evolution replaces this prey. In case of constrained problems, the sum of constraint violations serves as an additional objective. Modifications of the basic predator–prey algorithm have been implemented in this paper regarding the selection procedure, apparent movement of the predators, and mutation strategy. Further modifications have been made making the algorithm capable of handling multiple equality and inequality constraints. The final modified algorithm was tested on standard linear/nonlinear and constrained/unconstrained single-objective optimization problems. [ABSTRACT FROM AUTHOR]

Abstract  The hybrid cellular automaton (HCA) algorithm was inspired by the structural adaptation of bones to their ever changing mechanical environment. This methodology has been shown to be an effective topology synthesis tool. In previous work, it has been observed that the convergence of the HCA methodology is affected by parameters of the algorithm. As a result, questions have been raised regarding the conditions by which HCA converges to an optimal design. The objective of this investigation is to examine the conditions that guarantee convergence to a Karush-Kuhn-Tucker (KKT) point. In this paper, it is shown that the HCA algorithm is a fixed point iterative scheme and the previously reported KKT optimality conditions are corrected. To demonstrate the convergence properties of the HCA algorithm, a simple cantilevered beam example is utilized. Plots of the spectral radius for projections of the design space are used to show regions of guaranteed convergence. [ABSTRACT FROM AUTHOR]

Abstract  In this paper we study the unconfined potential steady flow through a porous media with semipermeable bottom. We propose a model that leads to a free boundary-value-problem with complementarities conditions on the bottom. The shape of a part of the domain boundary, called free boundary, is one of the unknown of the problem. The pressure of the flow as well as the flow velocity on the another part of the boundary, that is a one way permeable bottom, are also unknowns and satisfy a complementarity condition. We present the numerical implementation of the model based on an optimization approach. Performing a boundary-element discretization we get a nonlinear mathematical programming problem with complementarities conditions. To solve it we use Herskovits’s interior point algorithm. Numerical examples are presented. [ABSTRACT FROM AUTHOR]

Abstract  Solving engineering design and resources optimization via multiobjective evolutionary algorithms (MOEAs) has attracted much attention in the last few years. In this paper, an efficient multiobjective differential evolution algorithm is presented for engineering design. Our proposed approach adopts the orthogonal design method with quantization technique to generate the initial archive and evolutionary population. An archive (or secondary population) is employed to keep the nondominated solutions found and it is updated by a new relaxed form of Pareto dominance, called Pareto-adaptive ϵ-dominance (paϵ-dominance), at each generation. In addition, in order to guarantee to be the best performance produced, we propose a new hybrid selection mechanism to allow the archive solutions to take part in the generating process. To handle the constraints, a new constraint-handling method is employed, which does not need any parameters to be tuned for constraint handling. The proposed approach is tested on seven benchmark constrained problems to illustrate the capabilities of the algorithm in handling mathematically complex problems. Furthermore, four well-studied engineering design optimization problems are solved to illustrate the efficiency and applicability of the algorithm for multiobjective design optimization. Compared with Nondominated Sorting Genetic Algorithm II, one of the best MOEAs available at present, the results demonstrate that our approach is found to be statistically competitive. Moreover, the proposed approach is very efficient and is capable of yielding a wide spread of solutions with good coverage and convergence to true Pareto-optimal fronts. [ABSTRACT FROM AUTHOR]

Particle swarm optimization (PSO) is a relatively new global optimization algorithm. Benefitting from its simple concept, fast convergence speed and strong ability of optimization, it has gained much attention in recent years. However, PSO suffers from premature convergence problem because of the quick loss of diversity in solution search. In order to improve the optimization capability of PSO, design of experiment method, which spreads the initial particles across a design domain, and data mining technique, which is used to identify the promising optimization regions, are studied in this research to initialize the particle swarm. From the test results, the modified PSO algorithm initialized by OLHD (Optimal Latin Hypercube Design) technique successfully enhances the efficiency of the basic version but has no obvious advantage compared with other modified PSO algorithms. An extension algorithm, namely OLCPSO (Optimal Latin hypercube design and Classification and Regression tree techniques for improving basic PSO), is developed by consciously distributing more particles into potential optimal regions. The proposed method is tested and validated by benchmark functions in contrast with the basic PSO algorithm and five PSO variants. It is found from the test studies that the OLCPSO algorithm successfully enhances the efficiency of the basic PSO and possesses competitive optimization ability and algorithm stability in contrast to the existing initialization PSO methods. [ABSTRACT FROM AUTHOR]

This paper addresses single and multiobjective topology optimization of truss-like structures using genetic algorithms (GA's). In order to improve the performance of the GA's (despite the presence of binary topology variables) a novel approach based on kinematic stability repair (KSR) is proposed. The methodology consists of two parts, namely the creation of a number of kinematically stable individuals in the initial population (IP) and a chromosome repair procedure. The proposed method is developed for both 2D and 3D structures and is shown to produce (in the single-objective case) results which are better than, or equal to, those found in the literature, while significantly increasing the rate of convergence of the algorithm. In the multiobjective case, the proposed modifications produce superior results compared to the unmodified GA. Finally the algorithm is successfully applied to a cantilevered 3D structure. [ABSTRACT FROM AUTHOR]

According to the limitation of the interior ballistic charge design with genetic algorithms and some other direct optimization methods, which has complex evolution operators such as crossover and mutation or has poor perferance in solution accuracy and speed, a modified particle swarm optimizer is proposed which is based on a geometrical way and a fuzzy multi-objective optimization. The modified particle swarm optimizer is used to both single-objective and multi-objective optimization problems of interior ballistic charge design for a guided projectile. The solution results show that the modified particle swarm optimizer has a better convergence rate and accuracy than the original particle swarm optimizer and other ever used optimization methods. Combined with deterred propellant technique, the interior ballistic charge design for a guided projectile is optimized by the modified particle swarm optimizer. The optimization results improve the interior ballistic performance and launch safety and provide theoretical direction for the interior ballistic charge design of guided projectile. [ABSTRACT FROM AUTHOR]

Design of composite laminated lay-ups are formulated as discrete multi-material selection problems. The design problem can be modeled as a non-convex mixed-integer optimization problem. Such problems are in general only solvable to global optimality for small to moderate sized problems. To attack larger problem instances we formulate convex and non-convex continuous relaxations which can be solved using gradient based optimization algorithms. The convex relaxation yields a lower bound on the attainable performance. The optimal solution to the convex relaxation is used as a starting guess in a continuation approach where the convex relaxation is changed to a non-convex relaxation by introduction of a quadratic penalty constraint whereby intermediate-valued designs are prevented. The minimum compliance, mass constrained multiple load case problem is formulated and solved for a number of examples which numerically confirm the sought properties of the new scheme in terms of convergence to a discrete solution. [ABSTRACT FROM AUTHOR]

We reflect on the convergence and termination of optimization algorithms based on convex and separable approximations using two recently proposed strategies, namely a trust region with filtered acceptance of the iterates, and conservatism. We then propose a new strategy for convergence and termination, denoted filtered conservatism, in which the acceptance or rejection of an iterate is determined using the nonlinear acceptance filter. However, if an iterate is rejected, we increase the conservatism of every unconservative approximation, rather than reducing the trust region. Filtered conservatism aims to combine the salient features of trust region strategies with nonlinear acceptance filters on the one hand, and conservatism on the other. In filtered conservatism, the nonlinear acceptance filter is used to decide if an iterate is accepted or rejected. This allows for the acceptance of infeasible iterates, which would not be accepted in a method based on conservatism. If however an iterate is rejected, the trust region need not be decreased; it may be kept constant. Convergence is than effected by increasing the conservatism of only the unconservative approximations in the (large, constant) trust region, until the iterate becomes acceptable to the filter. Numerical results corroborate the accuracy and robustness of the method. [ABSTRACT FROM AUTHOR]

We propose an effective algorithm to resolve the stress-constrained topology optimization problem. Our procedure combines a density filter for length scale control, the solid isotropic material with penalization (SIMP) to generate black-and-white designs, a SIMP-motivated stress definition to resolve the stress singularity phenomenon, and a global/regional stress measure combined with an adaptive normalization scheme to control the local stress level. [ABSTRACT FROM AUTHOR]

Abstract  A numerical method of structural dynamic shape optimization is presented by using reproducing kernel particle method (RKPM), by which the mesh distortion that exists in shape optimal method based on finite element can be eliminated completely and the optimal model for structural dynamic optimization design is built. The discreteness-based design sensitivity analysis in both natural frequency and dynamic response is proposed by using direct differentiation method and discrete derivatives on the basis of structural dynamic analysis, in which the penalty method is employed into imposing the essential boundary conditions, and the derivatives of shape functions with respect to design variables are derived. The algorithm of dynamic sensitivity analysis is testified by numerical example, and the numerical results obtained are in good agreement with those obtained using semi-analytical method and global finite differences method. Finally, by integrating the algorithm mentioned based on RKPM with parameterized descriptive method of boundary shape, two examples for structural dynamic shape optimization are performed. [ABSTRACT FROM AUTHOR]

We expose an efficient strategy to deal with shape optimization of dynamical systems exhibiting flutter-type instability induced by friction, such as the considered disc-pad system. The stability of such systems can be analyzed through complex eigenvalue analysis, through which we present a squeal noise criterion to be minimized as a computationally expensive black-box function. The computational domain is discretized through isogeometric formulation for its advantages in optimization and superior approximation properties which are well studied in structural dynamics. To be computationally efficient with the expensive black-box function, we defined the optimization based on efficient global optimization scheme in the context of multi-objective optimization, with the integration of Isogeometric design-through-analysis methodology. As gradient information is hard to access for such black-box functions, in addition to the presence of constraints, we relied on meta-heuristic approach as a more generic strategy for realizing optimization of such functions in multi-objective context. As one such scheme with its own advantages was observed to provide lack of resolution to define expected improvement (EI) with a single reference value, we propose a multi-reference acquisition strategy which can be defined through a fast and efficient algorithm with fewer adaptation to the existing scheme. Results show the efficiency of this approach for our applicative example, which can be extended to other such applications as well. [ABSTRACT FROM AUTHOR]

In node-based shape optimization, there are a vast amount of design parameters, and the objectives, as well as the physical constraints, are non-linear in state and design. Robust optimization algorithms are required. The methods of feasible directions are widely used in practical optimization problems and know to be quite robust. A subclass of these methods is the gradient projection method. It is an active-set method, it can be used with equality and non-equality constraints, and it has gained significant popularity for its intuitive implementation. One significant issue around efficiency is that the algorithm may suffer from zigzagging behavior while it follows non-linear design boundaries. In this work, we propose a modification to Rosen's gradient projection algorithm. It includes the efficient techniques to damp the zigzagging behavior of the original algorithm while following the non-linear design boundaries, thus improving the performance of the method. [ABSTRACT FROM AUTHOR]

In this work we present LSEGO, an approach to drive efficient global optimization (EGO), based on LS (least squares) ensemble of metamodels. By means of LS ensemble of metamodels it is possible to estimate the uncertainty of the prediction with any kind of model (not only kriging) and provide an estimate for the expected improvement function. For the problems studied, the proposed LSEGO algorithm has shown to be able to find the global optimum with less number of optimization cycles than required by the classical EGO approach. As more infill points are added per cycle, the faster is the convergence to the global optimum (exploitation) and also the quality improvement of the metamodel in the design space (exploration), specially as the number of variables increases, when the standard single point EGO can be quite slow to reach the optimum. LSEGO has shown to be a feasible option to drive EGO with ensemble of metamodels as well as for constrained problems, and it is not restricted to kriging and to a single infill point per optimization cycle. [ABSTRACT FROM AUTHOR]

Aiming at improving the optimization efficiency, a theoretical optimization method for drawbead is proposed based on plastic flow principles. Essentially different from the existing common optimization methods which are on the basis of mathematics or statistics, this method, which can accurately reflect the relationship between the forming quality and the drawbead restraining force from the perspective of plastic flow theory, is a professional optimization method with higher efficiency. Plastic flow principles are first established to determine the influence degree of the drawbead restraining force to the forming quality. Then an evaluation model of the forming quality near a drawbead segment can be established based on the plastic flow principles to qualify the forming quality near the drawbead segment. Finally, a theoretical optimization method for drawbead is proposed based on the evaluation model, according to which the restraining force of each drawbead segment can be directly adjusted. By using the method, the optimal drawbead scheme in automotive panel forming can be obtained with only 3-5 iterations. The efficiency and accuracy of the optimization method are verified by a numerical example of a fender panel. [ABSTRACT FROM AUTHOR]