Multi-objective Extremal Optimization Research Articles

Optimal design of robust resilient automatic voltage regulators

Uncertainties in the plant model parameters and perturbations in the controller gains imposed by implementation errors represent a challenge to ensure robust stability and controller non-fragility simultaneously. Optimal design of robust non-fragile proportional–integral–derivative (PID) controller is presented for an automatic voltage regulator (AVR). The PID design relies basically on Kharitonov theorem and optimization by future search algorithm (FSA). The proposed algorithm has low computational complexity and fast convergence rate because it utilizes both local and global search methods. Further, FSA can improve the exploration characteristic and prevent trapping in local optima by updating its random initial. The PID controller is optimized by FSA to cope with expected parametric uncertainties of the plant model and tolerate its gain perturbations such that robust stability and controller non-fragility are simultaneously met. An interval plant model is suggested to account for model uncertainties where only eight extreme plants derived by Kharitonov theorem are considered in design. FSA-based PID optimization is constrained by the stability conditions of Kharitonov’s plants derived using Routh–Hurwitz. A new figure-of-demerit (FoD) based performance index is suggested to enforce simultaneous minimization of the time domain specifications. The suggested objective function is represented by a weighted sum of FoD of nominal response and the sum of reciprocals of the perturbation radii of PID gains. The output results of the recommended design are compared to that of artificial bee colony (ABC) algorithm and teaching–learning based optimization (TLBO) algorithm, multi-objective extremal optimization (MOEO), and non-dominated sorting genetic algorithm II (NSGA II). The results can confirm better response of the suggested technique measured up to other techniques where robustness and non-fragility are simultaneously ensured.

Optimization of Fractional Order Controllers for AVR System Using Distance and Levy-Flight Based Crow Search Algorithm

ABSTRACT This paper proposes a Distance and Levy-flight based Crow Search Algorithm (DLCSA) for optimization of three Fractional-order controllers: Fractional Order Proportional-Integral-Derivative (FOPID), Fractional Order Proportional-Integral (FOPI) and Fractional Order Proportional-Derivative (FOPD) controllers. Novelties of the proposed method are fourfold; (a) distance-based Flight length (Dfl)to improve the convergence rate, (b) Levy-flight based evasion to improve the efficiency of the algorithm, (c)adaptive awareness probability(AP) to set a tradeoff between local and global search and (d) Fuzzy based adaptive objective function to adjust the solution weights automatically. With such adaptations, the new approach preserves solution diversity and improves the convergence to global optima. To demonstrate the effectiveness of the contributions, proposed methods: DLCSA-FOPID, DLCSA-FOPI, and DLCSA-FOPD are implemented on an Automatic Voltage Regulator system and results are compared with few other well-established techniques like Zeigler–Nichols (Z-N), Artificial Bee Colony (ABC) Optimization (ACO), Multi-Objective Extremal Optimization (MOEO), Genetic Algorithm (GA), Chaos Ant Swarm (CAS) algorithm, Real Coded Extremal Optimization (RCEO), etc. Further to investigate robustness of proposed methods, the results are obtained for set-point tracking, noise suppression, load disturbance rejection, control effort, and modeling errors. The results demonstrate the better performance of the proposed method as compared to other state of the art techniques.

A new hybrid memetic multi-objective optimization algorithm for multi-objective optimization

To deal with the multi-objective optimization problems (MOPs), a meta-heuristic based on an improved shuffled frog leaping algorithm (ISFLA) which belongs to memetic evolution is presented. For the MOPs, both diversity maintenance and searching effectiveness are crucial for algorithm evolution. In this work, modified calculation of crowding distance to evaluate the density of a solution, memeplex clustering analyses based on a grid to divide the population, and new selection measure of global best individual are proposed to ensure the diversity of the algorithm. A multi-objective extremal optimization procedure (MEOP) is also introduced and incorporated into ISFLA to enable the algorithm to evolve more effectively. Finally, the experimental tests on thirteen unconstrained MOPs and DTLZ many-objective problems show that the proposed algorithm is flexible to handle MOPs and many-objective problems. The effectiveness and robustness of the proposed algorithm are also analyzed in detail.

Design of a Fractional Order Frequency PID Controller for an Islanded Microgrid: A Multi-Objective Extremal Optimization Method

Fractional order proportional-integral-derivative(FOPID) controllers have attracted increasing attentions recently due to their better control performance than the traditional integer-order proportional-integral-derivative (PID) controllers. However, there are only few studies concerning the fractional order control of microgrids based on evolutionary algorithms. From the perspective of multi-objective optimization, this paper presents an effective FOPID based frequency controller design method called MOEO-FOPID for an islanded microgrid by using a Multi-objective extremal optimization (MOEO) algorithm to minimize frequency deviation and controller output signal simultaneously in order to improve finally the efficient operation of distributed generations and energy storage devices. Its superiority to nondominated sorting genetic algorithm-II (NSGA-II) based FOPID/PID controllers and other recently reported single-objective evolutionary algorithms such as Kriging-based surrogate modeling and real-coded population extremal optimization-based FOPID controllers is demonstrated by the simulation studies on a typical islanded microgrid in terms of the control performance including frequency deviation, deficit grid power, controller output signal and robustness.

Design of fractional order PID controller for automatic regulator voltage system based on multi-objective extremal optimization

Design of an effective and efficient fractional order PID (FOPID) controller, as a generalization of a standard PID controller based on fractional order calculus, for an industrial control system to obtain high-quality performances is of great theoretical and practical significance. From the perspective of multi-objective optimization, this paper presents a novel FOPID controller design method based on an improved multi-objective extremal optimization (MOEO) algorithm for an automatic regulator voltage (AVR) system. The problem of designing FOPID controller for AVR is firstly formulated as a multi-objective optimization problem with three objective functions including minimization of integral of absolute error (IAE), absolute steady-state error, and settling time. Then, an improved MOEO algorithm is proposed to solve this problem by adopting individual-based iterated optimization mechanism and polynomial mutation (PLM). From the perspective of algorithm design, the proposed MOEO algorithm is relatively simpler than NSGA-II and single-objective evolutionary algorithms, such as genetic algorithm (GA), particle swarm optimization (PSO), chaotic anti swarm (CAS) due to its fewer adjustable parameters. Furthermore, the superiority of proposed MOEO-FOPID controller to NSGA-II-based FOPID, single-objective evolutionary algorithms-based FOPID controllers, MOEO-based and NSGA-II-based PID controllers is demonstrated by extensive experimental results on an AVR system in terms of accuracy and robustness.

A novel elitist multiobjective optimization algorithm: Multiobjective extremal optimization

Recently, a general-purpose local-search heuristic method called extremal optimization (EO) has been successfully applied to some NP-hard combinatorial optimization problems . This paper presents an investigation on EO with its application in numerical multiobjective optimization and proposes a new novel elitist (1 + λ ) multiobjective algorithm, called multiobjective extremal optimization (MOEO). In order to extend EO to solve the multiobjective optimization problems , the Pareto dominance strategy is introduced to the fitness assignment of the proposed approach. We also present a new hybrid mutation operator that enhances the exploratory capabilities of our algorithm. The proposed approach is validated using five popular benchmark functions . The simulation results indicate that the proposed approach is highly competitive with the state-of-the-art multiobjective evolutionary algorithms . Thus MOEO can be considered a good alternative to solve numerical multiobjective optimization problems.

Multiobjective extremal optimization with applications to engineering design

In this paper, we extend a novel unconstrained multiobjective optimization algorithm, so-called multiobjective extremal optimization (MOEO), to solve the constrained multiobjective optimization problems (MOPs). The proposed approach is validated by three constrained benchmark problems and successfully applied to handling three multiobjective engineering design problems reported in literature. Simulation results indicate that the proposed approach is highly competitive with three state-of-the-art multiobjective evolutionary algorithms, i.e., NSGA-II, SPEA2 and PAES. Thus MOEO can be considered a good alternative to solve constrained multiobjective optimization problems.