Particle swarm optimization: an alternative in marine propeller optimization?

This article deals with improving and evaluating the performance of two evolutionary algorithm approaches for automated engineering design optimization. Here a marine propeller design with constraints on cavitation nuisance is the intended application. For this purpose, the particle swarm optimization (PSO) algorithm is adapted for multi-objective optimization and constraint handling for use in propeller design. Three PSO algorithms are developed and tested for the optimization of four commercial propeller designs for different ship types. The results are evaluated by interrogating the generation medians and the Pareto front development. The same propellers are also optimized utilizing the well established NSGA-II genetic algorithm to provide benchmark results. The authors' PSO algorithms deliver comparable results to NSGA-II, but converge earlier and enhance the solution in terms of constraints violation.     

Teaching–learning-based optimization algorithm for unconstrained and constrained real-parameter optimization problems

An efficient optimization algorithm called teaching–learning-based optimization (TLBO) is proposed in this article to solve continuous unconstrained and constrained optimization problems. The proposed method is based on the effect of the influence of a teacher on the output of learners in a class. The basic philosophy of the method is explained in detail. The algorithm is tested on 25 different unconstrained benchmark functions and 35 constrained benchmark functions with different characteristics. For the constrained benchmark functions, TLBO is tested with different constraint handling techniques such as superiority of feasible solutions, self-adaptive penalty, ?-constraint, stochastic ranking and ensemble of constraints. The performance of the TLBO algorithm is compared with that of other optimization algorithms and the results show the better performance of the proposed algorithm.     

Developing a fuzzy proportional–derivative controller optimization engine for engineering design optimization problems

In real world engineering design problems, decisions for design modifications are often based on engineering heuristics and knowledge. However, when solving an engineering design optimization problem using a numerical optimization algorithm, the engineering problem is basically viewed as purely mathematical. Design modifications in the iterative optimization process rely on numerical information. Engineering heuristics and knowledge are not utilized at all. In this article, the optimization process is analogous to a closed-loop control system, and a fuzzy proportional–derivative (PD) controller optimization engine is developed for engineering design optimization problems with monotonicity and implicit constraints. Monotonicity between design variables and the objective and constraint functions prevails in engineering design optimization problems. In this research, monotonicity of the design variables and activities of the constraints determined by the theory of monotonicity analysis are modelled in the fuzzy PD controller optimization engine using generic fuzzy rules. The designer only needs to define the initial values and move limits of the design variables to determine the parameters in the fuzzy PD controller optimization engine. In the optimization process using the fuzzy PD controller optimization engine, the function value of each constraint is evaluated once in each iteration. No sensitivity information is required. The fuzzy PD controller optimization engine appears to be robust in the various design examples tested.     

AESOP—a numerical platform for aerodynamic shape optimization

Aerodynamic shape optimization based on Computational Fluid Dynamics can automatically improve the design of aircraft components. In order to obtain the best computational efficiency, the adjoint method is applied on the complete mapping, from the parameters of design to the evaluation of the cost function or constraints. The mapping considered here includes the parameterization, the mesh deformation, the primal-to-dual mesh transformation and the flow equations solved by the unstructured flow solver Edge distributed by FOI. The numerical platform AESOP integrates the flow and adjoint flow solver, mesh deformation schemes, algorithms of shape parameterization and algorithms for gradient-based optimization. The result is a portable and efficient implementation for large scale aerodynamic shape optimization and future applications in multidisciplinary shape optimization. The structure of the program is outlined and examples of applications are presented. The method of shape parameterization using Radial Basis Functions is discussed in more details because it is expected to play a major role in the development of multidisciplinary optimization.     

A parameter optimization heuristic for a temperature estimation model

We present a heuristic technique for solving a parameter estimation problem that arises in modeling the thermal behavior of electronic chip packages. Compact Thermal Models (CTMs) are network models of steady state thermal behavior, which show promise in augmenting the use of more detailed and computationally expensive models. The CTM parameter optimization problem that we examine is a nonconvex optimization problem in which we seek a set of CTM parameters that best predicts, under general conditions, the thermal response of a particular chip package geometry that has been tested under a small number of conditions. We begin by developing a nonlinear programming formulation for this parameter optimization problem, and then develop an algorithm that uses special characteristics of the optimization problem to quickly generate heuristic solutions. Our algorithm descends along a series of solutions to one-dimensional nonconvex optimization problems, obtaining a locally optimal set of model parameters at modest computational cost. Finally, we provide some experimental results and recommendations for extending this research. The authors are indebted to four anonymous referees for their help in improving the contribution and presentation of this paper.     

Optimal heat exchanger network synthesis using particle swarm optimization

Heat exchanger network (HEN) synthesis has been a well-studied subject over the past decades. Many studies and methodologies were proposed to make possible the energy recovery, minimizing the utilities consumption and the number of heat transfer equipment.     

Development of a multidisciplinary–multiresponse robust design optimization model

Robust design is an efficient process improvement methodology that combines experimentation with optimization to create systems that are tolerant to uncontrollable variation. Most traditional robust design models, however, consider only a single quality characteristic, yet customers judge products simultaneously on a variety of scales. Additionally, it is often the case that these quality characteristics are not of the same type. To addresses these issues, a new robust design optimization model is proposed to solve design problems involving multiple responses of several different types. In this new approach, noise factors are incorporated into the robust design model using a combined array design, and the results of the experiment are optimized using a new approach that is formulated as a nonlinear goal programming problem. The results obtained from the proposed methodology are compared with those of other robust design methods in order to examine the trade-offs between meeting the objectives associated with different optimization approaches.     

Canonical duality for solving nonconvex and nonsmooth optimization problem

This paper presents an application of the canonical duality theory for solving a class of nonconvex and nonsmooth optimization problems. It is shown that by use of the canonical dual transformation, these difficult optimization problems in R ⁿ can be converted into a one-dimensional canonical dual problems, which can be solved to obtain all extremal points. Both global and local extremality conditions can be identified by the triality theory. Applications are illustrated.     

Note on “A fuzzy approach to transport optimization problem”

In the article (Sudhagar and Ganesan in Optim Eng  10.1007/s11081-012-9202-6) Sudhagar and Ganesan presented an algorithm to solve a fuzzy transportation problem without converting it into a crisp transportation problem based upon score method of ranking fuzzy numbers. Using an example we show that their method will not always lead to a fuzzy optimal solution. Specially, we give a non negative fuzzy solution for the numerical example solved by them which has less total fuzzy transportation cost.     

Nonlinear response topology optimization using equivalent static loads—case studies

Nonlinear structural optimization is fairly expensive and difficult, because a large number of nonlinear analyses is required due to the large number of design variables involved in topology optimization. In element density based topology optimization, the low density elements create mesh distortion and the updating of finite element material with low density elements has a severe effect on the optimization results in the next cycles. In order to overcome these difficulties, the equivalent static loads method for nonlinear response structural optimization (ESLSO) primarily used for size and shape optimization has been applied to topology optimization. The nonlinear analysis is performed with the given loading conditions to calculate equivalent static loads (ESLs) and these ESLs are used to perform linear response optimization. In this paper, the authors have presented the results of five case studies with material, geometric and contact nonlinearities showing good agreement and providing justification of the proposed method.     

Metamodel-assisted distributed genetic algorithms applied to structural shape optimization problems †

This article is concerned with the development of a general optimization tool based on distributed real genetic algorithms (DRGAs) assisted by metamodel evaluation and applied to structural shape optimization problems of general boundary-element models (BEMs). The evaluation fitness function is performed by a surrogate function based on multidimensional Gaussian random field models (MGRFMs) in order to minimize the computational cost of the evolutionary algorithms. The model boundary of a structural system or a mechanical tool is discretized using the BEM, and selected parts of the boundary are modelled using β-spline curves or surfaces in order to facilitate re-meshing and adaptation of the boundary to the external actions. Then a hypercube topology of populations of these models follows a genetic evolution process to determine the optimum shape of the system. The optimum models have minimum weight and satisfy all imposed constraints. A numerical example is presented and discussed in order to show the efficiency and robustness of the developed computational tool. The number of function evaluations is substantially reduced compared with previous versions of the optimization algorithm without the metamodel evaluation technique.     

Comparison of trust-region-based and evolutionary methods for optimization of flow geometries †

Optimization has become increasingly important in computer-aided engineering, and applications of engineering optimization to design, control, operations, and planning already exist. Since in the context of numerical flow simulation no information on the gradient information of the objective function is available, or is very difficult to obtain, in such optimization cases it is advantageous to use an optimization technique which does not directly depend on the derivative. The aim of this study is to investigate two optimization techniques, the trust-region-based method and the evolutionary algorithm technique, and compare them quantitatively with respect to efficiency, quality, and working strategy. A tool based on free-form deformation (FFD) is employed for the variation of flow geometry. This simulation tool is the parallel multigrid flow solver FASTEST, which uses a fully conservative finite-volume method for solving the incompressible Navier–Stokes equations on a non-staggered cell-centred grid arrangement. The optimization tools are investigated by considering the optimization of the connection of two pipes with respect to the minimization of the pressure drop. This problem can be considered as a representative test case for a practical three-dimensional flow configuration.     

Synthesis of porous–acoustic absorbing systems by an evolutionary optimization method

Topology optimization is frequently used to design structures and acoustic systems in a large range of engineering applications. In this work, a method is proposed for maximizing the absorbing performance of acoustic panels by using a coupled finite element model and evolutionary strategies. The goal is to find the best distribution of porous material for sound absorbing panels. The absorbing performance of the porous material samples in a Kundt tube is simulated using a coupled porous–acoustic finite element model. The equivalent fluid model is used to represent the foam material. The porous material model is coupled to a wave guide using a modal superposition technique. A sensitivity number indicating the optimum locations for porous material to be removed is derived and used in a numerical hard kill scheme. The sensitivity number is used to form an evolutionary porous material optimization algorithm which is verified through examples.     

A note on “A fuzzy approach to transport optimization problem”

Sudhagar and Ganesan (Optim Eng, 2012, doi: 10.1007/s11081-012-9202-6) proposed an approach to find the fuzzy optimal solution of such fuzzy transportation problems in which all the parameters are represented by fuzzy numbers. In this note, it is pointed out that the authors have used some mathematical incorrect assumptions in their proposed method.     

Box–Behnken design directed optimization for sensitivity assessment of anti-platelet drugs

Optimization of electrospray ionization (ESI) parameters is routinely carried out by one factor at a time (OFAT) or auto-tune software (ATS). Design of experiments (DOE) approach has been reported to be an excellent alternative to OFAT or ATS. Box–Behnken Design (BBD) was successfully used to optimize ESI parameters like nebulizing gas flow rate, desolvation line temperature, heat block temperature, and drying gas flow rate for [M?+?H]⁺ intensity of Clopidogrel bisulfate (CLP) and Ticlopidine (TLP). BBD model was found to be significant with p?<?.0001 for both CLP and TLP. The predicted and optimized (OL) ESI parameters were used for chromatographic analysis and were compared against three levels of ESI parameters, i.e. low level (LL), medium level (ML), and high level (HL). The OL ESI parameters were subjected to chromatographic analysis and its mean peak area was significantly higher than mean peak area for LL, ML, and HL ESI in case of CLP and TLP (p?<?.001). However, no significant difference was observed between the mean peak area for ML and OL of TLP. Thus, BBD can be considered with 29 trials to optimize four mass spectrometric parameters. The liquid chromatographic parameters percentage of methanol, percentage of formic acid and flow rate were also optimized using BBD. However, the optimized method did not significantly influence the peak response over the non-optimized method.     

Pareto Tracer: a predictor–corrector method for multi-objective optimization problems

This article proposes a novel predictor–corrector (PC) method for the numerical treatment of multi-objective optimization problems (MOPs). The algorithm, Pareto Tracer (PT), is capable of performing a continuation along the set of (local) solutions of a given MOP with k objectives, and can cope with equality and box constraints. Additionally, the first steps towards a method that manages general inequality constraints are also introduced. The properties of PT are first discussed theoretically and later numerically on several examples.     

Sensitivity analysis and shape optimization based on FE–EFG coupled method

By use of 4-node isoparametric quadrangle interface element between finite element (FE) and meshless regions, a collocation approach is introduced to couple firstly FE and element-free Galerkin (EFG) method in this paper. By taking derivative of discreteness equilibrium equation at interface element with respect to design variable, a numerical method for discreteness-based shape design sensitivity analysis in interface element is obtained. The design sensitivity analysis (DSA) of coupled FE–EFG method is achieved by employing the DSA of nodal displacement at the interface element. The numerical method presented is testified by examples. It can be observed excellent agreement between the numerical results and the analytical solution. Finally the shape optimization of fillet is achieved by using coupled FE–EFG method. The result obtained show that imposing of the essential boundary condition is easy to implement, the computational time is reduced and the distortion of mesh is avoided.