Helon Vicente Hultmann Ayala

Tuning of PID controller based on a multiobjective genetic algorithm applied to a robotic manipulator

Highlights? Multiobjective optimization finds a set of solutions called non-dominated solutions. ? The NSGA-II approach is evaluated. ? This algorithm is tested in PID tuning using a robotic manipulator of two-degree-of-freedom. Most controllers optimization and design problems are multiobjective in nature, since they normally have several (possibly conflicting) objectives that must be satisfied at the same time. Instead of aiming at finding a single solution, the multiobjective optimization methods try to produce a set of good trade-off solutions from which the decision maker may select one. Several methods have been devised for solving multiobjective optimization problems in control systems field. Traditionally, classical optimization algorithms based on nonlinear programming or optimal control theories are applied to obtain the solution of such problems. The presence of multiple objectives in a problem usually gives rise to a set of optimal solutions, largely known as Pareto-optimal solutions. Recently, Multiobjective Evolutionary Algorithms (MOEAs) have been applied to control systems problems. Compared with mathematical programming, MOEAs are very suitable to solve multiobjective optimization problems, because they deal simultaneously with a set of solutions and find a number of Pareto optimal solutions in a single run of algorithm. Starting from a set of initial solutions, MOEAs use iteratively improving optimization techniques to find the optimal solutions. In every iterative progress, MOEAs favor population-based Pareto dominance as a measure of fitness. In the MOEAs context, the Non-dominated Sorting Genetic Algorithm (NSGA-II) has been successfully applied to solving many multiobjective problems. This paper presents the design and the tuning of two PID (Proportional-Integral-Derivative) controllers through the NSGA-II approach. Simulation numerical results of multivariable PID control and convergence of the NSGA-II is presented and discussed with application in a robotic manipulator of two-degree-of-freedom. The proposed optimization method based on NSGA-II offers an effective way to implement simple but robust solutions providing a good reference tracking performance in closed loop.

A self-adaptive chaotic differential evolution algorithm using gamma distribution for unconstrained global optimization

Evolutionary algorithms (EAs) have yielded promising results for solving nonlinear, non-differentiable and multi-modal optimization problems. Due to its population-based nature, EAs can avoid being trapped in a local optimum, and consequently have the ability to find global optimal solutions. As a novel evolutionary technique, differential evolution (DE) has received increasing attention and wide applications in a variety of fields. DE algorithm uses an efficient way of self-adapting mutation using small populations for function optimization over continuous spaces. The potentialities of DE are its simple structure, easy use, convergence property, quality of solution, and robustness. In this paper, an effective self-adaptive DE algorithm based on Gaussian probability distribution, gamma distribution and chaotic sequence (DEGC) for solving continuous global optimization problems is proposed. The proposed DEGC algorithm is tested on several benchmark functions from the usual literature. Numerical results comparisons with a classical DE approach and a self-adaptive DE approach demonstrate the effectiveness and efficiency of the proposed DEGC algorithm.

Image thresholding segmentation based on a novel beta differential evolution approach

An improved beta differential evolution algorithm is proposed.The improved differential evolution is applied to image threholding segmentation.Simulation results demonstrate that the proposed differential evolution is superior to FODPSO. Image segmentation is the process of partitioning a digital image into multiple regions that have some relevant semantic content. In this context, histogram thresholding is one of the most important techniques for performing image segmentation. This paper proposes a beta differential evolution (BDE) algorithm for determining the n-1 optimal n-level threshold on a given image using Otsu criterion. The efficacy of BDE approach is illustrated by some results when applied to two case studies of image segmentation. Compared with a fractional-order Darwinian particle swarm optimization (PSO), the proposed BDE approach performs better, or at least comparably, in terms of the quality of the final solutions and mean convergence in the evaluated case studies.

A Multiobjective Gaussian Particle Swarm Approach Applied to Electromagnetic Optimization

The development of optimization techniques for multiobjective problems in electromagnetics has been flourishing in the last decade. This paper proposes an improved multiobjective particle swarm optimization approach and applies it to the multiobjective version of TEAM workshop problem 22. Simulation results show that this improved version of the algorithm finds a better Pareto-optimal front with respect to more classical PSO methods while maintaining a better spread of nondominated solutions along the front. Furthermore, the proposed algorithm is compared with the widely used Nondominated Sorting Genetic Algorithm-II (NSGA-II) method highlighting a strongly different behaviour of these strategies.

Harmony Search Approach Based on Ricker Map for Multi-Objective Transformer Design Optimization

Harmony search (HS) algorithm is an evolutionary optimization algorithm developed in an analogy with an improvisation process where musicians try to polish their pitches to obtain a better harmony. In this paper, a modified HS (MHS) algorithm is adapted to multi-objective optimization using external archiving, ranking with crowding distance, and control parameters tuning based on Ricker map to solve a transformer design optimization (TDO) problem with two competing objectives. Simulations applied to a TDO problem demonstrate the effectiveness of the proposed multi-objective MHS algorithm. Results indicate that, compared with other multi-objective HS algorithm, in terms of output quality, the proposed MHS is able to find competitive solutions with a good tradeoff between the design objectives.

Multiobjective Krill Herd Algorithm for Electromagnetic Optimization

Metaheuristics have recently become the forefront of the current research as a powerful way to deal with many electromagnetic optimization problems. Based on the simulation of the herding behavior of krill individuals, a krill herd (KH) algorithm was recently proposed to solve optimization problems. In order to extend the classical mono-objective KH algorithm approach, this paper proposes a new multiobjective KH (MOKH) algorithm and a modified MOKH approach using the beta distribution in the inertia weight tuning. Numerical results on a multiobjective constrained brushless direct current motor design problem show that the evaluated MOKH algorithms present a promising performance.

Multiobjective Cuckoo Search Applied to Radial Basis Function Neural Networks Training for System Identification

Abstract In the present work we introduce a system identification framework where no a priori information on the system to be identified is available. Focusing in the specific case of radial basis functions neural networks models, we insert the choice of the model complexity and its inputs in the optimization procedure together with the model parameters, aiming at accuracy, model validity and regularization in a multiobjective approach. The multicriteria problem is solved by means of the multiobjective cuckoo search, which is based on an archiving technique and the crowding distance metric. Simulation results are promising when the methodology is applied to identify a robot arm given solely input and output data.

Multiobjective Gaussian Particle Swarm Approach Applied to Multi-loop PI Controller Tuning of a Quadruple-Tank System

The use of PI (Proportional-Integral), PD (Proportional-Derivative) and PID (Proportional-Integral-Derivative)controllers have a long history in control engineering and are acceptable for most of real applications because of their simplicity in architecture and their performances are quite robust for a wide range of operating conditions. Unfortunately, it has been quite difficult to tune properly the gains of PI, PD, and PID controllers because many industrial plants are often burdened with problems such as high order, time delays, and non-linearities. Recently, several metaheuristics, such as evolutionary algorithms, swarm intelligence and simulated annealing, have been proposed for the tuning of mentioned controllers. In this context, different metaheuristics have recently received much interest for achieving high efficiency and searching global optimal solution in problem space.Multi-objective evolutionary and swarm intelligence approaches often find effectively a set of diverse and mutually competitive solutions. A multi-loop PI control scheme based on a multi-objective particle swarm optimization approach with updating of velocity vector using Gaussian distribution (MGPSO) for multi-variable systems is proposed in this chapter.Particle swarm optimization is a simple and efficient population-based optimization method motivated by social behavior of organisms such as fish schooling and bird flocking. The proposal of PSO algorithm was put forward by several scientists who developed computational simulations of the movement of organisms such as flocks of birds and schools of fish. Such simulations were heavily based on manipulating the distances between individuals, i.e., the synchrony of the behavior of the swarm was seen as an effort to keep an optimal distance between them. In theory, at least, individuals of a swarm may benefit from the prior discoveries and experiences of all the members of a swarm when foraging. The fundamental point of developing PSO is a hypothesis in which the exchange of information among creatures of the same species offers some sort of evolutionary advantage. PSO demonstrates good performance in many function optimization problems and parameter optimization problems in recent years. Application of the proposed MGPSO using concepts of Pareto optimality to a multi-variable quadruple-tank process is investigated in this paper. Compared to a classical multi-objective PSO algorithm which is applied to the same process, the MGPSO shows considerable robustness and efficiency in PI control tuning.

Multi-objective symbiotic search algorithm approaches for electromagnetic optimization

Optimization metaheuristics are a powerful way to deal with many electromagnetic optimization problems. Recently, the symbiotic organisms search (SOS) algorithm was proposed to solve single-objective optimization problems. SOS mimics the symbiotic relationship among the living beings. In order to extend the classical mono-objective SOS algorithm approach, this paper proposes a new multi-objective SOS (MOSOS) and an improved IMOSOS. Results on a multi-objective constrained brushless direct current (DC) motor design show that the MOSOS and IMOSOS present promising performance.

Multiobjective Symbiotic Search Algorithm Approaches for Electromagnetic Optimization

Optimization metaheuristics is a powerful way to deal with many electromagnetic optimization problems. Their main advantages are that they don’t require gradient computation, they are more likely to give a global optimum solution and have a higher degree of exploration and exploitation ability. Recently, the symbiotic organisms search (SOS) algorithm was proposed to solve single-objective optimization problems. SOS mimics the symbiotic relationship among the living beings. In order to extend the classical mono-objective SOS algorithm approach, this paper proposes a new multiobjective SOS (MOSOS) based on nondominance and crowding distance criterion. Furthermore, an improved MOSOS (IMOSOS) based on normal (Gaussian) probability distribution function also was proposed and evaluated. Results on a multiobjective constrained brushless direct current (dc) motor design show that the MOSOS and IMOSOS present promising performance.