Frederico G. Guimarães

A clonal selection algorithm for optimization in electromagnetics

This paper proposes the real-coded clonal selection algorithm (RCSA) for use in electromagnetic design optimization. Some features of the algorithm, such as the number of clones, mutation range, and the fraction of the population selected each generation are discussed. The TEAM Workshop problem 22 is investigated, in order to illustrate the performance of the algorithm in a real electromagnetic problem. The results obtained, a set of optimal solutions representing a broader range of options for the designer, are compared with those achieved by a genetic algorithm, showing the efficiency of the RCSA in practical optimization problems.

Electric Distribution Network Expansion Under Load-Evolution Uncertainty Using an Immune System Inspired Algorithm

This paper addresses the problem of electric distribution network expansion under condition of uncertainty in the evolution of node loads in a time horizon. An immune-based evolutionary optimization algorithm is developed here, in order to find not only the optimal network, but also a set of suboptimal ones, for a given most probable scenario. A Monte-Carlo simulation of the future load conditions is performed, evaluating each such solution within a set of other possible scenarios. A dominance analysis is then performed in order to compare the candidate solutions, considering the objectives of: smaller infeasibility rate, smaller nominal cost, smaller mean cost and smaller fault cost. The design outcome is a network that has a satisfactory behavior under the considered scenarios. Simulation results show that the proposed approach leads to resulting networks that can be rather different from the networks that would be found via a conventional design procedure: reaching more robust performances under load evolution uncertainties

A modified immune network algorithm for multimodal electromagnetic problems

Some optimization algorithms based on theories from immunology have the feature of finding an arbitrary number of optima, including the global solution. However, this advantage comes at the cost of a large number of objective function evaluations, in most cases, prohibitive in electromagnetic design. This paper proposes a modified version of the artificial immune network algorithm (opt-AINet) for electromagnetic design optimization. The objective of this modified AINet (m-AINet) is to reduce the computational effort required by the algorithm, while keeping or improving the convergence characteristics. Another improvement proposed is to make it more suitable for constrained problems through the utilization of a specific constraint-handling technique. The results obtained over an analytical problem and the design of an electromagnetic device show the applicability of the proposed algorithm

Optimization of Cost Functions Using Evolutionary Algorithms with Local Learning and Local Search

Evolutionary algorithms can benefit from their association with local search operators, giving rise to hybrid or memetic algorithms. The cost of the local search may be prohibitive, particularly when dealing with computationally expensive functions. We propose the use of local approximations in the local search phase of memetic algorithms for optimization of cost functions. These local approximations are generated using only information already collected by the algorithm during the evolutionary process, requiring no additional evaluations. The local search improves some individuals of the population, hence speeding up the overall optimization process. We investigate the design of a loudspeaker magnet with seven variables. The results show the improvement achieved by the proposed combination of local learning and search within evolutionary algorithms

Multiobjective approaches for robust electromagnetic design

Robust optimization problems are inherently multiobjective, because the designer searches for compromise solutions between the mathematical model and possible uncertainties when constructing the physical device. We propose a novel formulation that consists of the employment of a multiobjective approach for robust design. The proposed methodology is applied to two practical problems: the design of a loudspeaker and the design of a superconducting magnetic storage device. The results provide more alternatives to the decision maker, confirming the usefulness and benefit of the approach

Local search with quadratic approximations into memetic algorithms for optimization with multiple criteria

This paper proposes a local search optimizer that, employed as an additional operator in multiobjective evolutionary techniques, can help to find more precise estimates of the Pareto-optimal surface with a smaller cost of function evaluation. The new operator employs quadratic approximations of the objective functions and constraints, which are built using only the function samples already produced by the usual evolutionary algorithm function evaluations. The local search phase consists of solving the auxiliary multiobjective quadratic optimization problem defined from the quadratic approximations, scalarized via a goal attainment formulation using an LMI solver. As the determination of the new approximated solutions is performed without the need of any additional function evaluation, the proposed methodology is suitable for costly black-box optimization problems.

A Meshless Method for Electromagnetic Field Computation Based on the Multiquadric Technique

A meshless method for electromagnetic field computation is developed based on the multiquadric interpolation technique. A global approximation to the solution is built based only on the discretization of the domain in nodes and the differential equations describing the problem in the domain and its boundary. An attractive characteristic of the multiquadric solution is that it is continuous and it has infinitely continuous derivatives. This is particularly important to obtain field quantities in electromagnetic analysis. The method is also capable of dealing with physical discontinuities present at the interface between different materials. The formulation is presented in the Cartesian and polar coordinates, which can be extended to other systems. We applied the formulation in the analysis of an electrostatic micromotor and a microstrip. The results demonstrate good agreement with other numerical technique, showing the adequacy of the proposed methodology for electromagnetic analysis

Pareto cone ε-dominance: improving convergence and diversity in multiobjective evolutionary algorithms

Relaxed forms of Pareto dominance have been shown to be the most effective way in which evolutionary algorithms can progress towards the Pareto-optimal front with a widely spread distribution of solutions. A popular concept is the e-dominance technique, which has been employed as an archive update strategy in some multiobjective evolutionary algorithms. In spite of the great usefulness of the e-dominance concept, there are still difficulties in computing an appropriate value of e that provides the desirable number of nondominated points. Additionally, several viable solutions may be lost depending on the hypergrid adopted, impacting the convergence and the diversity of the estimate set. We propose the concept of cone e-dominance, which is a variant of the e-dominance, to overcome these limitations. Cone e-dominance maintains the good convergence properties of e-dominance, provides a better control over the resolution of the estimated Pareto front, and also performs a better spread of solutions along the front. Experimental validation of the proposed cone e-dominance shows a significant improvement in the diversity of solutions over both the regular Pareto-dominance and the e-dominance.

Using differential evolution for combinatorial optimization: A general approach

The Differential Evolution (DE) algorithm was initially proposed for continuous numerical optimization, but it has been applied with success in many combinatorial optimization problems, particularly permutation-based integer combinatorial problems. In this paper, a new and general approach for combinatorial optimization is proposed using the Differential Evolution algorithm. The proposed approach aims at preserving its interesting search mechanism for discrete domains, by defining the difference between two candidate solutions as a differential list of movements in the search space. Thus, a more meaningful and general differential mutation operator for the context of combinatorial optimization problems can be produced. We discuss three alternatives for using the differential list of movements within the differential mutation operation. We present results on instances of the Traveling Salesman Problem (TSP) and the N-Queen Problem (NQP) to illustrate the adequacy of the proposed approach for combinatorial optimization.

Overview of artificial immune systems for multi-objective optimization

Evolutionary algorithms have become a very popular approach for multiobjective optimization in many fields of engineering. Due to the outstanding performance of such techniques, new approaches are constantly been developed and tested to improve convergence, tackle new problems, and reduce computational cost. Recently, a new class of algorithms, based on ideas from the immune system, have begun to emerge as problem solvers in the evolutionary multiobjective optimization field. Although all these immune algorithms present unique, individual characteristics, there are some trends and common characteristics that, if explored, can lead to a better understanding of the mechanisms governing the behavior of these techniques. In this paper we propose a common framework for the description and analysis of multiobjective immune algorithms.