Krill Herd Algorithm Research Articles

Application of the bio-inspired Krill Herd optimization technique to phase equilibrium calculations

The Krill Herd optimization technique, which is based on the simulated herding behaviour of the krill crustacean, is applied to calculations involving phase equilibrium and phase stability, as the application of this emerging technique is extremely limited in the literature. In this work, the Krill Herd algorithm (KH)11Krill Herd algorithm. and the modified Lévy-flight Krill Herd algorithm (LKH)22Lévy-flight Krill Herd algorithm. has been applied to phase stability (PS)33Phase stability. and phase equilibrium calculations in non-reactive (PE)44Phase equilibrium. and reactive (rPE)55Reactive phase equilibrium. systems, where global minimization of the total Gibbs energy is necessary. Several phase stability and phase equilibrium systems were considered for the analysis of the performance of the technique that includes both vapour and liquid phase conditions.The Krill Herd algorithm was found to reliably determine the desired global optima in PS, PE and rPE problems with generally higher success rates and lower computing time requirements than previously applied metaheuristic techniques such as those involving swarm intelligence and genetic and evolutionary algorithms.

Comparative Study of Krill Herd, Firefly and Cuckoo Search Algorithms for Unimodal and Multimodal Optimization

Today, in computer science, a computational challenge exists in finding a globally optimized solution from an enormously large search space. Various metaheuristic methods can be used for finding the solution in a large search space.These methods can be explained as iterative search processes that efficiently perform the exploration and exploitation in the solution space. In this context, three such nature inspired metaheuristic algorithms namely Krill Herd Algorithm (KH), Firefly Algorithm (FA) and Cuckoo search Algorithm (CS) can be used to find optimal solutions of various mathematical optimization problems. In this paper, the proposed algorithms were used to find the optimal solution of fifteen unimodal and multimodal benchmark test functions commonly used in the field of optimization and then compare their performances on the basis of efficiency, convergence, time and conclude that for both unimodal and multimodal optimization Cuckoo Search Algorithm via Levy flight has outperformed others and for multimodal optimization Krill Herd algorithm is superior than Firefly algorithm but for unimodal optimization Firefly is superior than Krill Herd algorithm.

Optimal power flow using krill herd algorithm

In this article, an efficient optimization procedure based on herding behavior of krill individuals, krill herd algorithm (KHA), for the solution of multi-objective optimal power flow (OPF) with the objective of fuel cost minimization, voltage deviation minimization and voltage stability improvement is proposed. This algorithm is based on the effect of the influence of a teacher on the output of learners in a class. The proposed KHA approach is carried out on the standard IEEE 30-bus, IEEE 57-bus and IEEE 118-bus systems to solve different single and multi-objective OPF problems. Simulation results of the proposed approach are compared to differential evolution (DE), modified DE (MDE), multi-objective DE (MODE), evolving ant direction DE (EADDE), particle swarm optimization (PSO), improved genetic algorithm (IGA), gradient method, biogeography-based optimization (BBO), PSO with inertia weight approach (PSOIWA), PSO with constriction factor approach (PSOCFA), real-coded GA (RGA), artificial bee colony (ABC), general passive congregation PSO (GPAC), local passive congregation PSO (LPAC), coordinated aggregation (CA), interior point method (IPM) and quantum-inspired evolutionary algorithm (QEA). The comparison demonstrates the superiority of the proposed approach and confirms its potential to solve multi-objective OPF problems. Copyright © 2014 John Wiley & Sons, Ltd.

Comparative Study of Krill Herd, Firefly and Cuckoo Search Algorithms for Unimodal and Multimodal Optimization

Today, in computer science, a computational challenge exists in finding a globally optimized solution from an enormously large search space. Various metaheuristic methods can be used for finding the solution in a large search space.These methods can be explained as iterative search processes that efficiently perform the exploration and exploitation in the solution space. In this context, three such nature inspired metaheuristic algorithms namely Krill Herd Algorithm (KH), Firefly Algorithm (FA) and Cuckoo search Algorithm (CS) can be used to find optimal solutions of various mathematical optimization problems. In this paper, the proposed algorithms were used to find the optimal solution of fifteen unimodal and multimodal benchmark test functions commonly used in the field of optimization and then compare their performances on the basis of efficiency, convergence, time and conclude that for both unimodal and multimodal optimization Cuckoo Search Algorithm via Levy flight has outperformed others and for multimodal optimization Krill Herd algorithm is superior than Firefly algorithm but for unimodal optimization Firefly is superior than Krill Herd algorithm.

A novel sufficient bio-inspired optimisation method based on modified krill herd algorithm to solve the economic load dispatch

Economic dispatch (ED) is a noteworthy and valuable plan in the power grids for providing balance between the load and generation in a commercial manner. Actually, the practical ED is a non-convex nonlinear optimisation problem with some equality and inequality limits. Mathematically, the practical ED entails a prevailing solver to find the optimal solution. In this way, this article proposes a new bio-inspired algorithm called krill herd (KH) to resolve the practical ED problem incorporating different types of constraints such as valve-loading effects, prohibited operating zone, spinning reserve and multi-fuel option. In order to improve the overall search skill of the algorithm, a new modification method based on Levy Flight motion and crossover operator is employed. The proposed modified KH (MKH) algorithm is examined on three test systems to validate its satisfying performance.

Chaotic Krill Herd Optimization Algorithm

The Krill Herd (KH) optimization algorithm is one of the most recent heuristic optimization techniques. This algorithm mimics the lifecycle of krill in oceans. Despite high performance of KH, stagnation in local optima and slow convergence speed are two probable problems in solving challenging optimization problems. This work enhances the performance of the KH algorithm by the chaos theory. To be exact, three one-dimensional chaotic maps (Circle, Sine, and Tent) are integrated into KH. The results prove that the proposed chaotic KH algorithms are able to show superior results compared to KH in terms of local optima avoidance and convergence speed.

Economic load dispatch using krill herd algorithm

Economic load dispatch (ELD) is an important topic in the operation of power plants which can help to build up effective generating management plans. The practical ELD problem has non-smooth cost function with nonlinear constraints which make it difficult to be effectively solved. This paper presents, a new and efficient krill herd algorithm (KHA) to solve both convex and non-convex ELD problems of thermal power units considering valve point loading, multiple fuel operation, transmission losses and constraints such as ramp rate limits and prohibited operating zones. To enhance the overall performance and effectiveness of the proposed algorithm, the crossover and mutation operation of differential evolution (DE) are integrated with the proposed method. The different versions of KHA are successfully applied to small, medium, and large-scale power systems for solving six different ELD problems. The simulation results obtained by the proposed algorithms are compared with the results obtained using other recently develop methods available in the literature. From numerical results, it is found that the proposed KHA with crossover and mutation operators approach is able to provide better solution than other reported techniques in terms of fuel cost. Furthermore, this algorithm is better in terms of robustness than most of the existing algorithms used in this study.

An effective krill herd algorithm with migration operator in biogeography-based optimization

Krill herd (KH) is a novel search heuristic method. To improve its performance, a biogeography-based krill herd (BBKH) algorithm is presented for solving complex optimization tasks. The improvement involves introducing a new krill migration (KM) operator when the krill updating to deal with optimization problems more efficiently. The KM operator emphasizes the exploitation and lets the krill cluster around the best solutions at the later run phase of the search. The effects of these enhancements are tested by various well-defined benchmark functions. Based on the experimental results, this novel BBKH approach performs better than the basic KH and other optimization algorithms.

Hybrid krill herd algorithm with differential evolution for global numerical optimization

In order to overcome the poor exploitation of the krill herd (KH) algorithm, a hybrid differential evolution KH (DEKH) method has been developed for function optimization. The improvement involves adding a new hybrid differential evolution (HDE) operator into the krill, updating process for the purpose of dealing with optimization problems more efficiently. The introduced HDE operator inspires the intensification and lets the krill perform local search within the defined region. DEKH is validated by 26 functions. From the results, the proposed methods are able to find more accurate solution than the KH and other methods. In addition, the robustness of the DEKH algorithm and the influence of the initial population size on convergence and performance are investigated by a series of experiments.

A chaotic particle-swarm krill herd algorithm for global numerical optimization

Purpose – To improve the performance of the krill herd (KH) algorithm, in this paper, a series of chaotic particle-swarm krill herd (CPKH) algorithms are proposed for solving optimization tasks within limited time requirements. The paper aims to discuss these issues. Design/methodology/approach – In CPKH, chaos sequence is introduced into the KH algorithm so as to further enhance its global search ability. Findings – This new method can accelerate the global convergence speed while preserving the strong robustness of the basic KH. Originality/value – Here, 32 different benchmarks and a gear train design problem are applied to tune the three main movements of the krill in CPKH method. It has been demonstrated that, in most cases, CPKH with an appropriate chaotic map performs superiorly to, or at least highly competitively with, the standard KH and other population-based optimization methods.

Lévy-Flight Krill Herd Algorithm

To improve the performance of the krill herd (KH) algorithm, in this paper, a Lévy-flight krill herd (LKH) algorithm is proposed for solving optimization tasks within limited computing time. The improvement includes the addition of a new local Lévy-flight (LLF) operator during the process when updating krill in order to improve its efficiency and reliability coping with global numerical optimization problems. The LLF operator encourages the exploitation and makes the krill individuals search the space carefully at the end of the search. The elitism scheme is also applied to keep the best krill during the process when updating the krill. Fourteen standard benchmark functions are used to verify the effects of these improvements and it is illustrated that, in most cases, the performance of this novel metaheuristic LKH method is superior to, or at least highly competitive with, the standard KH and other population-based optimization methods. Especially, this new method can accelerate the global convergence speed to the true global optimum while preserving the main feature of the basic KH.

Incorporating mutation scheme into krill herd algorithm for global numerical optimization

Recently, Gandomi and Alavi proposed a robust meta-heuristic optimization algorithm, called Krill Herd (KH), for global optimization. To improve the performance of the KH algorithm, harmony search (HS) is applied to mutate between krill during the process of krill updating instead of physical diffusion used in KH. A novel hybrid meta-heuristic optimization approach HS/KH is proposed to solve global numerical optimization problem. HS/KH combines the exploration of harmony search (HS) with the exploitation of KH effectively, and hence, it can generate the promising candidate solutions. The detailed implementation procedure for this improved meta-heuristic method is also described. Fourteen standard benchmark functions are applied to verify the effects of these improvements, and it is demonstrated that, in most cases, the performance of this hybrid meta-heuristic method (HS/KH) is superior to, or at least highly competitive with, the standard KH and other population-based optimization methods, such as ACO, BBO, DE, ES, GA, HS, KH, PSO, and SGA. The effect of the HS/FA parameters is also analyzed.

Krill herd: A new bio-inspired optimization algorithm

In this paper, a novel biologically-inspired algorithm, namely krill herd (KH) is proposed for solving optimization tasks. The KH algorithm is based on the simulation of the herding behavior of krill individuals. The minimum distances of each individual krill from food and from highest density of the herd are considered as the objective function for the krill movement. The time-dependent position of the krill individuals is formulated by three main factors: (i) movement induced by the presence of other individuals (ii) foraging activity, and (iii) random diffusion. For more precise modeling of the krill behavior, two adaptive genetic operators are added to the algorithm. The proposed method is verified using several benchmark problems commonly used in the area of optimization. Further, the KH algorithm is compared with eight well-known methods in the literature. The KH algorithm is capable of efficiently solving a wide range of benchmark optimization problems and outperforms the exciting algorithms.