Lucas S. Batista

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.

A Distributed Clonal Selection Algorithm for Optimization in Electromagnetics

This paper proposes the real-coded distributed clonal selection algorithm (DCSA) for use in electromagnetic design optimization. This algorithm employs different types of probability distributions for the mutation of the clones. In order to illustrate the efficiency of this algorithm in practical optimization problems, we compare the results obtained by DCSA with other immune and genetic algorithms over analytical problems and for the TEAM Workshop Problem 22 for the 3 and 8 variables versions. The results indicate that the DCSA is a suitable optimization tool in terms of accuracy and performance.

A comparison of dominance criteria in many-objective optimization problems

In this paper, we analyze four dominance criteria in terms of their ability to adequately order sets of points in multi-and many-objective optimization problems. The use of relaxed and alternative dominance relationships has been an important tool for improving the performance of multiobjective evolutionary optimization algorithms, and their ordering ability is among the most important characteristics responsible for such improvement. Three relaxed formulations of dominance are investigated, along with the traditional Pareto ordering, in order to provide a comparison baseline. The results obtained show that all three relaxed dominance approaches presented greater robustness to the increase in the number of objectives, and are therefore more appropriate for use in many-objective optimization algorithms.

A Differential Mutation operator for the archive population of multi-objective evolutionary algorithms

The Differential Evolution (DE) algorithm is a simple and efficient evolutionary algorithm that has been applied to solve many optimization problems mainly in continuous search domains. In the last few years, many implementations of multi-objective versions of DE have been proposed in the literature, combining the traditional differential mutation operator as the variation mechanism and some form of Pareto-ranking based fitness. In this paper, we propose the utilization of the differential mutation operator as an additional operator to be used within any multi-objective evolutionary algorithm that employs an archive (offline) population. The operator is applied for improving the high-quality solutions stored in the archive, working both as a local search operator and a diversity operator depending on the points selected to build the differential mutation. In order to illustrate the use of the operator, it is coupled with the NSGA-II and the multi-objective DE (MODE), showing promising results.

An evolutionary approach for the demand side management optimization in smart grid

An important function of a Smart Grid (SG) is the Demand Side Management (DSM), which consists on controlling loads at customers side, aiming to operate the system with major efficiency and sustainability. The main advantages of this technique are (i) the decrease of demand curves peak, that results on smoother load profile and (ii) the reduction of both operational costs and the requirement of new investments in the system. The customer can save money by using loads on schedules with lower taxes instead of schedules with higher taxes. In this context, this work proposes a simple metaheuristic to solve the problem of DSM on smart grid. The suggested approach is based on the concept of day-ahead load shifting, which implies on the exchange of the use schedules planned for the next day and aims to obtain the lowest possible cost of energy. The demand management is modeled as an optimization problem whose solution is obtained by using an Evolutionary Algorithm (EA). The experimental tests are carried out considering a smart grid with three distinct demand areas, the first with residential clients, other one with commercial clients and a third one with industrial clients, all of them possessing a major number of controllable loads of diverse types. The obtained results were significant in all three areas, pointing substantial cost reductions for the customers, mainly on the industrial area.

Dynamic Multiobjective Clonal Selection Algorithm for Engineering Design

We propose a Multiobjective Clonal Selection Algorithm (MCSA) with dynamic variation of its main parameters for the solution of engineering design problems. The MCSA performs a cloning process using different probability distributions, in which the mutation strengths are guided based on a logarithmic rule and on information implicitly created by a simple differential evolution technique. This feature results in a self-adapting search in the algorithm. The efficiency of the MCSA is studied comparing its performance with the Nondominated Sorting Genetic Algorithm II (NSGA-II) in analytical test problems and also in the design of a microwave heating device. The MCSA has outperformed the NSGA-II in all problems investigated.

Ant colony optimization for the topological design of interior permanent magnet (IPM) machines

Purpose – The purpose of this paper is to apply an Ant colony optimization approach for the solution of the topological design of interior permanent magnet (IPM) machines. Design/methodology/approach – The IPM motor design domain is discretized into a suitable equivalent graph representation and an Ant System (AS) algorithm is employed to achieve an efficient distribution of materials into this graph. Findings – The single-objective problems associated with the maximization of the torque and with the maximization of the shape smoothness of the IPM are investigated. The rotor of the device is discretized into a 9×18 grid in both cases, and three different materials are considered: air, iron and permanent magnet. Research limitations/implications – The graph representation used enables the solution of topological design problems with an arbitrary number of materials, which is relevant for 2 and 3D problems. Originality/value – From the numerical experiments, the AS algorithm was able to achieve reasonable s...

Multi‐domain topology optimization with ant colony systems

Purpose – The purpose of this paper is to present a graph representation of the design space that is suitable for the ant colony optimization (ACO) method in topology optimization (TO) problems.Design/methodology/approach – The ACO is employed to obtain optimal routes in an equivalent graph representation of the discretized design space, with each route corresponding to a given distribution of material.Findings – The problem associated with the maximization of the torque of a c‐core magnetic actuator is investigated, in which part of the yoke is discretized into a 16×8 grid and can assume three different materials: air, pure iron and a magnetic material.Research limitations/implications – The results of the c‐core magnetic actuator problem, which are in agreement with literature available, show the adequacy of the proposed approach to TO of electromagnetic devices.Practical implications – The graph representation of the design space permits the solution of topological design problems with an arbitrary num...

Multi-objective Topology Optimization with Ant Colony Optimization and Genetic Algorithms

In this work, we present a multi-objective approach for Topology Optimization applied to the design of devices with several materials. The first stage consists of applying a Multi-Objective Ant Colony Optimization (MOACO) to find tradeoff topologies with different material distributions. In the second stage, we parameterize the boundaries of the topologies found by using NURBS. A Multi-objective Genetic Algorithm is applied as a heuristic optimization engine to optimize the control points, weights and knots of the curves in order to smooth and refine the boundaries of the topology. The main advantage of a multi-objective approach is that the designer can identify, explore and refine a number of tradeoff topologies. The proposed methodology is illustrated in the design of a C-core magnetic actuator.

A new self-adaptive approach for evolutionary multiobjective optimization

We propose in this paper a new strategy for self-adaptation in multiobjective evolutionary algorithms, which is based on information obtained from the implicit distribution created by a chaotic differential mutation operator. This technique is used to develop a self-adaptive evolutionary algorithm for multiobjective optimisation, and its efficiency is evaluated by means of a comparative study using well-known benchmark problems. The statistical analysis of the results shows that the proposed algorithm was able to outperform the NSGA-II in fourteen of the seventeen problems used. These results represent evidence for the adequacy of the proposed technique in solving the classes of multiobjective optimisation problems represented in the benchmark suites used.