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The purpose of this paper is to apply a hybrid algorithm based on the combination of two heuristics inspired by artificial life to the solution of optimization problems.

The flock‐of‐starlings optimization (FSO) and the bacterial chemotaxis algorithm (BCA) were adapted to implement a hybrid and parallel algorithm: the FSO has been powerfully employed for exploring the whole space of solutions, whereas the BCA has been used to refine the FSO‐found solutions, thanks to its better performances in local search.

A good solution of the 8‐th parameters version of the TEAM problem 22 is obtained by using a maximum 200 FSO steps combined with 20 BCA steps. Tests on an analytical function are presented in order to compare FSO, PSO and FSO+BCA algorithms.

The development of an efficient method for the solution of optimization problems, exploiting the different characteristic of the two heuristic approaches.

The paper shows the combination and the interaction of stochastic methods having different exploration properties, which allows new algorithms able to produce effective solutions of multimodal optimization problems, with an acceptable computational cost, to be defined.

The paper aims to present a new methodology for hybrid genetic algorithms (GA) in the solution of electromagnetic optimization problems.

This methodology can be seen as a local search operator which uses local quadratic approximations for each objective and constraint function in the problem. In the local search phase, these approximations define an associated local search problem that is efficiently solved using a formulation based on linear matrix inequalities.

The paper illustrates the proposed methodology comparing the performance of the hybrid GA against the basic GA in two analytical problems and in the well‐known TEAM benchmark Problem 22. For the analytical problems, 30 independent runs for each algorithm were considered whereas for Problem 22, ten independent runs for each algorithm were taken.

For the analytical problems, the hybrid GA enhanced both the convergence speed, in terms of the number of function evaluations, and the accuracy of the final result. For Problem 22, the hybrid GA was able to reach a better solution, with a better value of the standard deviation with less CPU time.

The paper could be useful both for device designers and researchers involved optimization in computational electromagnetics.

The hybrid GA proposed enhanced the convergence speed, in terms of the number of function evaluations, representing a faster and robust algorithm for practical optimization problems.

This paper aims to show on a widely used benchmark problem that chaotic sequences can improve the search ability of evolution strategies (ES).

The Lozi map is used to generate new individuals in the framework of ES algorithms. A quasi‐Newton (QN) method is also used within the iterative loop to improve the solution's quality locally.

It is shown that the combined use of chaotic sequences and QN methods can provide high‐quality solutions with small standard deviation on the selected benchmark problem.

Although the benchmark is considered to be representative of typical electromagnetic problems, different test cases may give less satisfactory results.

The proposed approach appears to be an efficient general purpose optimizer for electromagnetic design problems.

This paper introduces the use of chaotic sequences in the area of electromagnetic design optimization.

An effective approach to the optimal design of electromagnetic devices should take into account the effect of mechanical tolerances on the actual devices performance. A possible approach could be to match a Pareto optimality study with a Monte Carlo analysis by randomly varying the constructive parameters. In this paper it is shown how such an analysis can be used to allow an expert designer to select among different Pareto optimal designs.

The purpose of this paper is to present a new multi‐objective clonal selection algorithm (MCSA) for the solution of electromagnetic optimization problems.

The method performs the somatic hypermutation step using different probability distributions, balancing the local search in the algorithm. Furthermore, it includes a receptor editing operator that implicitly realizes a dynamic search over the landscape.

In order to illustrate the efficiency of MCSA, its performance is compared with the nondominated sorting genetic algorithm II (NSGA‐II) in some analytical problems and in the well‐known TEAM benchmark Problem 22. Three performance evaluation techniques are used in the comparison, and the effect of each operator of the MCSA in its accomplishment is estimated.

In the analytical problems, the MCSA enhanced both the extension and uniformity in its solutions, providing better Pareto‐optimal sets than the NSGA‐II. In the Problem 22, the MCSA also outperformed the NSGA‐II. The MCSA was not dominated by the NSGA‐II in the three variables case and clearly presented a better convergence speed in the eight variables problem.

This paper could be useful for researchers who deal with multi‐objective optimization problems involving high‐computational cost.

The new operators incorporated in the MCSA improved both the extension, uniformity and the convergence speed of the solutions, in terms of the number of function evaluations, representing a robust tool for real‐world optimization problems.

The purpose of this paper is to show, on a widely used benchmark problem, that adaptive mutation factors and attractive/repulsive phases guided by population diversity can improve the search ability of differential evolution (DE) algorithms.

An adaptive mutation factor and attractive/repulsive phases guided by population diversity are used within the framework of DE algorithms.

The paper shows that the combined use of adaptive mutation factors and population diversity in order to guide the attractive/repulsive behavior of DE algorithms can provide high‐quality solutions with small standard deviation on the selected benchmark problem.

Although the chosen benchmark is considered to be representative of typical electromagnetic problems, different test cases may give less satisfactory results.

The proposed approach appears to be an efficient general purpose stochastic optimizer for electromagnetic design problems.

This paper introduces the use of population diversity in order to guide the attractive/repulsive behavior of DE algorithms.

To establish a statistical formulation of robust design optimization and to develop a fast optimization algorithm for the solution of the statistical design problem.

Existing formulations and methods for statistical robust design are reviewed and compared. A consistent problem formulation in terms of statistical parameters of the involved variables is introduced. A novel algorithm for statistical optimization is developed. It is based on the unscented transformation, a fast method for the propagation of random variables through nonlinear functions. The prediction performance of the unscented transformation is demonstrated and compared with other methods by means of an analytical test function. The validity of the proposed approach is shown through the design of the superconducting magnetic energy storage device of the TEAM workshop problem 22.

Provides a consistent formulation of statistical robust design optimization and an efficient and accurate method for the solution of practical problems.

The proposed approach can be applied to all kinds of design problems and allows to account for the inevitable effects of tolerances and parameter variations occuring in practical realizations of designed devices.

Discusses the combined use of a modified version of the global optimization technique simulated annealing and a deterministic optimizer based on Shor’s method. Describes the features of the proposed technique and reports on some results regarding a standard benchmark problem.

The purpose of this paper is to propose a multi-objective optimization algorithm, which can improve both the performance robustness and the constraint feasibility when the uncertainty in design variables is considered.

Multi-objective robust optimization by gradient index combined with the reliability-based design optimization (RBDO).

It is shown that searching for the optimal design of the TEAM problem 22, which can minimize the magnetic stray field by keeping the target system energy (180 MJ) and improve the feasibility of superconductivity constraint (quenching condition), is possible by using the proposed method.

RBDO method applied to the electromagnetic problem cooperated with the design sensitivity analysis by the finite element method.

The purpose of this paper is to develop a novel multi‐objective optimization algorithm which takes into account the uncertainty in design parameters by using a reduced resolution for their representation, thus implementing a simple form of robustness. Additionally, the number of function evaluations should be minimized.

The proposed approach is based on an elitist evolutionary algorithm coupled with a reduction in the number of significant figures used to represent design parameters. In effect, this becomes a filter in the optimization process and allows the system to avoid extremely sharp optima within the search space. By reducing the resolution of the search and maintaining a full archive of previous solutions, the number of evaluations of the objective functions, each of which may require an expensive numerical solution, is reduced.

The algorithm was tested both on an algebraic test function and on two TEAM Workshop Problems (22 and 25). The results demonstrated that it is stable; can emerge from deceptive fronts; and find optimal solutions which match those previously published at a relatively low‐computational cost.

The originality of this paper lies in the concept of using a low‐resolution representation of the design parameters. This results in a finite size search space and increases the speed of the algorithm while avoiding non‐manufacturable solutions.