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The purpose of this paper is to propose variants of an adaptive penalty scheme for steady-state genetic algorithms applied to constrained engineering optimization problems.

For each constraint a penalty parameter is adaptively computed along the evolution according to information extracted from the current population such as the existence of feasible individuals and the level of violation of each constraint. The adaptive penalty method (APM), as originally proposed, computes the constraint violations of the initial population, and updates the penalty coefficient of each constraint after a given number of new individuals are inserted in the population. A second variant, called sporadic APM with constraint violation accumulation, works by accumulating the constraint violations during a given insertion of new offspring into the population, updating the penalty coefficients, and fixing the penalty coefficients for the next generations. The APM with monotonic penalty coefficients is the third variation, where the penalty coefficients are calculated as in the original method, but no penalty coefficient is allowed to have its value reduced along the evolutionary process. Finally, the penalty coefficients are defined by using a weighted average between the current value of a coefficient and the new value predicted by the method. This variant is called the APM with damping.

The paper checks new variants of an APM for evolutionary algorithms; variants of an APM, for a steady-state genetic algorithm based on an APM for a generational genetic algorithm, largely used in the literature previously proposed by two co-authors of this manuscript; good performance of the proposed APM in comparison with other techniques found in the literature; innovative and general strategies to handle constraints in the field of evolutionary computation.

The proposed algorithm has no limitations and can be applied in a large number of evolutionary algorithms used to solve constrained optimization problems.

The proposed algorithm can be used to solve real world problems in engineering as can be viewed in the references, presented in this manuscript, that use the original (APM) strategy. The performance of these variants is examined using benchmark problems of mechanical and structural engineering frequently discussed in the literature.

It is the first extended analysis of the variants of the APM submitted for possible publication in the literature, applied to real world engineering optimization problems.

Conceiving reliable systems is a strategic issue for any industrial society for its economical and technical development. This paper aims to focus on solving highly constrained redundancy optimization problems in complex systems.

Genetic algorithms (GAs), one of the metaheuristic techniques, have been used and a dynamic adaptive penalty strategy is proposed, which makes use of feedback obtained during the search along with a dynamic distance metric and helps the algorithm to search efficiently for final, optimal or near optimal solution.

The effectiveness of the adaptive penalty function is studied and shown graphically on the solution quality as well as the speed of evolution convergence for several highly constrained problems. The investigations show that this approach can be powerful and robust for problems with large search space, even of size 1017, and difficult‐to‐satisfy constraints.

The results obtained in this paper would be applicable on designing highly reliable systems meeting the requirement of today's society. Moreover, an important advantage of applying GA is that it generates several good solutions (mostly optimal or near optimal) providing a lot of flexibility to decision makers. As such, the paper would be of interest and importance to the system designers, reliability practitioners, as well as to the researchers in academia, business and industry. The paper would have wide applications in the fields of electronics design, telecommunications, computer systems, power systems etc.

Genetic algorithms have been recently used in combinatorial optimization approaches to reliable design, mainly for series‐parallel systems. This paper presents a GA for parallel redundancy optimization problem in complex systems.

The purpose of this paper is to propose and analyze the use of local surrogate models to improve differential evolution’s (DE) overall performance in computationally expensive problems.

DE is a popular metaheuristic to solve optimization problems with several variants available in the literature. Here, the offspring are generated by means of different variants, and only the best one, according to the surrogate model, is evaluated by the simulator. The problem of weight minimization of truss structures is used to assess DE’s performance when different metamodels are used. The surrogate-assisted DE techniques proposed here are also compared to common DE variants. Six different structural optimization problems are studied involving continuous as well as discrete sizing design variables.

The use of a local, similarity-based, surrogate model improves the relative performance of DE for most test-problems, specially when using r-nearest neighbors with r = 0.001 and a DE parameter F = 0.7.

The proposed methods have no limitations and can be applied to solve constrained optimization problems in general, and structural ones in particular.

The proposed techniques can be used to solve real-world problems in engineering. Also, the performance of the proposals is examined using structural engineering problems.

The main contributions of this work are to introduce and to evaluate additional local surrogate models; to evaluate the effect of the value of DE’s parameter F (which scales the differences between components of candidate solutions) upon each surrogate model; and to perform a more complete set of experiments covering continuous as well as discrete design variables.

The purpose of this paper is to evaluate the performance of social spider algorithm (SSA) to solve constrained structural optimisation problems and to compare its results with others algorithms such as genetic algorithm, particle swarm optimisation, differential evolution and artificial bee colony.

To handle the constraints of the problems, this paper couples to the SSA an efficient selection criteria proposed in the literature that promotes a tournament between two solutions in which the feasible or less infeasible solution wins. The discussion is conducted on the competitiveness of the SSA with other algorithms as well as its performance in constrained problems.

SSA is a population algorithm proposed for global optimisation inspired by the foraging of social spiders. A spider moves on the web towards the position of the prey, guided by vibrations that occur around it in different frequencies. The SSA was proposed to solve problems without constraints, but these are present in most of practical problems. This paper evaluates the performance of SSA to solve constrained structural optimisation problems and compares its results with other algorithms such as genetic algorithm, particle swarm optimisation, differential evolution and artificial bee colony.

The proposed algorithm has no limitations, and it can be applied in other classes of constrained optimisation problems.

This paper evaluated the proposed algorithm with a benchmark of constrained structural optimisation problems intensely used in the literature, but it can be applied to solve real constrained optimisation problems in engineering and others areas.

This is the first paper to evaluate the performance of SSA in constrained problems and to compare its results with other algorithms traditional in the literature.

The first order reliability method requires optimization algorithms to find the minimum distance from the origin to the limit state surface in the normal space. The purpose of this paper is to develop an improved version of the new metaheuristic algorithm inspired from echolocation behaviour of bats, namely, the bat algorithm (BA) dedicated to perform structural reliability analysis.

Modifications have been embedded to the standard BA to enhance its efficiency, robustness and reliability. In addition, a new adaptive penalty equation dedicated to solve the problem of the determination of the reliability index and a proposition on the limit state formulation are presented.

The comparisons between the improved bat algorithm (iBA) presented in this paper and other standard algorithms on benchmark functions show that the iBA is highly efficient, and the application to structural reliability problems such as the reliability analysis of overhead crane girder proves that results obtained with iBA are highly reliable.

A new iBA and an adaptive penalty equation for handling equality constraint are developed to determine the reliability index. In addition, the low computing time and the ease implementation of this method present great advantages from the engineering viewpoint.

The purpose of this paper is to improve and to extend the use of original rank‐niche evolution strategy (RNES) algorithm to solve constrained and unconstrained multiobjective optimization problems.

A new mutation step size is developed for evolution strategy. A mixed ranking procedure is used to improve the quality of the fitness function. A self‐adaptive sharing radius is developed to save computational time. Four constraint‐treating methods are developed to solve constrained optimization problems. Two of them do not use penalty function approach.

The improved RNES algorithm finds better quality Pareto‐optimal solutions more efficiently than the previous version. For most test problems, the solutions obtained by improved RNES are better than, or at least can be compared with, results from other papers.

The application of any evolutionary algorithm to real structural optimization problems would face a problem of spending huge computational time. Some approximate analysis method needs to be incorporated with RNES to solve practical problems.

This paper provides an easier approach to find Pareto‐optimal solutions using an evolutionary algorithm. The algorithm can be used to solve both unconstrained and constrained problems.

The purpose of this paper is to present the application of an adaptive bacterial foraging (BF) algorithm for the design optimization of an energy efficient induction motor.

The induction motor design problem is formulated as a mixed integer nonlinear optimization problem. A set of nine independent variables is selected, and to make the machine feasible and practically acceptable, six constraints are imposed on the design. Two different objective functions are considered, namely, the annual active material cost, and the sum of the annual active material cost, annual cost of the active power loss of the motor and annual energy cost required to supply such power loss. A new adaptive BF algorithm is used for solving the optimization problem. A generic penalty function method, which does not require any penalty coefficient, is employed for constraint handling.

The adaptive BF algorithm is validated for two sample motors and benchmarked with the genetic algorithm, particle swarm optimization, simple BF algorithm, and conventional design methods. The results show that the proposed algorithm outperforms the other methods in both the solution quality and convergence rate. The annual cost of the induction motor is remarkably reduced when designed on the basis of minimizing its annual total cost, instead of minimizing its material cost only.

To the best of the knowledge, none of the existing work has applied the BF algorithms for electrical machine design problems. Therefore, the solution to this problem constitutes the main contribution of the paper. According to the huge number of induction motors operating all over the world, the BF techniques used in their design, on minimum annual cost basis, will lead to a tremendous saving in global energy consumption.

The purpose of this paper is to present a new method for solving parametric programming problems; a new scheme of constraints fuzzification. In the proposed approach, constraints are learned based on deductive learning.

Adaptive neural‐fuzzy inference system (ANFIS) is used for constraint learning by generating input and output membership functions and suitable fuzzy rules.

The experimental results show the ability of the proposed approach to model the set of constraints and solve parametric programming. Some notes in the proposed method are clustering of similar constraints, constraints generalization and converting crisp set of constraints to a trained system with fuzzy output. Finally, this idea for modeling of constraint in the support vector machine (SVM) classifier is used and shows that this approach can obtain a soft margin in the SVM.

Properties of the new scheme such as global view of constraints, constraints generalization, clustering of similar constraints, creation of real fuzzy constraints, study of constraint strength and increasing the degree of importance to constraints are different aspects of the proposed method.

The purpose of this paper is to propose a new scheme for obtaining acceptable solutions for problems of continuum topology optimization of structures, regarding the distribution and limitation of discretization errors by considering h-adaptivity.

The new scheme encompasses, simultaneously, the solution of the optimization problem considering a solid isotropic microstructure with penalization (SIMP) and the application of the h-adaptive finite element method. An analysis of discretization errors is carried out using an a posteriori error estimator based on both the recovery and the abrupt variation of material properties. The estimate of new element sizes is computed by a new h-adaptive technique named “Isotropic Error Density Recovery”, which is based on the construction of the strain energy error density function together with the analytical solution of an optimization problem at the element level.

Two-dimensional numerical examples, regarding minimization of the structure compliance and constraint over the material volume, demonstrate the capacity of the methodology in controlling and equidistributing discretization errors, as well as obtaining a great definition of the void–material interface, thanks to the h-adaptivity, when compared with results obtained by other methods based on microstructure.

This paper presents a new technique to design a mesh made with isotropic triangular finite elements. Furthermore, this technique is applied to continuum topology optimization problems using a new iterative scheme to obtain solutions with controlled discretization errors, measured in terms of the energy norm, and a great resolution of the material boundary. Regarding the computational cost in terms of degrees of freedom, the present scheme provides approximations with considerable less error if compared to the optimization process on fixed meshes.

A new surface error calculation method for layered manufacturing processes is proposed in this paper. The developed method is used to generate the layers by adaptively varying the thickness of the layers based on the surface approximation errors. Traditionally, the surface errors are calculated using local approximation techniques. In this paper, the surface approximation errors are calculated more accurately by marching through the surface points and determining the distances between layers and the surface points. Using the calculated distances, the adaptive layers are generated for both traditional two‐dimensional layer and ruled‐layer approximation methods. It has been shown that layered manufacturing (rapid prototyping) processes can achieve better accuracy and efficiency using the proposed surface error calculation and the adaptive ruled layer approximation methods. Computer implementation and illustrative examples are also presented in this paper.