I.J. Intelligent Systems and Applications, 2016, 11, 34-50 Published Online November 2016 in MECS (http://www.mecs-press.org/) DOI: 10.5815/ijisa.2016.11.05 Copyright © 2016 MECS I.J. Intelligent Systems and Applications, 2016, 11, 34-50 Improved Krill Herd Algorithm with Neighborhood Distance Concept for Optimization Pras un Kumar Agrawal 1 , Manjaree Pandit 1 , Hari Mohan Dubey *1 Department of Electrical Engineering, 1 M.I.T.S, Gwalior, India *Corresponding Author, Tel.+91-0751-2665962, +91-0751-2409348, E-mail: harimohandubeymits@gmail.com Abstract —Krill herd algorithm (KHA) is a novel nature inspired (NI) optimization technique that mimics the herding behavior of krill, which is a kind of fish found in nature. The mathematical model of KHA is based on three phenomena observed in the behavior of a herd of krills, which are, moment induced by other krill, foraging motion and random physical diffusion. These three key features of the algorithm provide a good balance between global and local search capability, which makes the algorithm very powerful. The objective is to minimize the distance of each krill from the food source and also from the point of highest density of the herd, which helps in convergence of population around the food source. Improvisation has been made by introducing neighborhood distance concept along with genetic reproduction mechanism in basic KH Algorithm. KHA with mutation and crossover is called as (KHAMC) and KHA with neighborhood distance concept is referred here as (KHAMCD). This paper compares the performance of the KHA with its two improved variants KHAMC and KHAM CD. The performance of the three algorithms is compared on eight benchmark functions and also on two real world economic load dispatch (ELD) problems of power system. Results are also compared with recently reported methods to establish robustness, validity and superiority of the KHA and its variant algorithms. Index Terms—Krill Herd Algorithm (KHA), mutation and crossover, neighborhood distance concept, unimodal function, multimodal function, economic load dispatch. I. INT RODUCT ION Optimization is basically a spontaneous process that plays an important role in real world application. Its objective is to compute a set of variables that either minimize or maximize the objectives function within given constraints. For solution of a given model or an objective function, there is a need of efficient optimization techniques which can either be conventional (deterministic) or have a stochastic, evolutionary approach. Conventional techniques include nonlinear programming, linear programming, quadratic programming, Newton’s method etc. Deterministic approaches generally require an initial guess which has a vital impact on the final solution. Considering practical utility of optimization there is need of robust and efficient algorithms which are free from this limitation. Generally the practical problems are much complex and also have many constraints which cannot be solved by conventional approaches. On the other hand, nature inspired methods which are basically population based stochastic search techniques often provides quick and reasonable solution; though a careful tuning of parameters is required to prevent solution from getting trapped in local minima. In the recent years various population based evolutionary techniques have been developed for solution of problems related to real world application. Among evolutionary algorithms genetic algorithm (GA) is probably the most popular algorithm based on Darwinian evolution concept proposed by Holland in 1992[1]. Simple concepts are involved in it and involvement of stochastic operators may be the key point for popularity of this algorithm. After GA various nature inspired algorithms have been proposed such as Particle Swarm Optimization(PSO)[7], Ant Colony Optimization(ACO)[8], Harmony Search Algorithm (HSA)[9], Artificial Bee Colony Algorithm(ABC)[15], Gravitational Search Algorithm(GSA)[16] etc, which may be based on natural concepts of evolution, collective behavior, ecology or physical science [2-26] listed in Table 1. Each algorithm has its own advantage. But the key points associated with evolutionary algorithms which make them popular for solution of complex constrained problem in comparison to conventional approach are depicted in Table 2. In fact there is no optimization technique has been developed that can capable to solve all types of optimization problems [27]. A comparative study of NI algorithms for unimodal and multimodal optimization problem is presented in ref. [55]. Among NI algorithms krill herd algorithm (KHA) is novel optimization techniques that inspired by herding behavior of krill herd. KHA implemented to solve different types of real world optimization problems either by hybridizing with other evolutionary algorithm to improve the basic KHA or by adding some mathematical concept [28-38]. Variant of KHA proposed till date is depicted in Fig. 1. In this paper KHA with neighborhood distance concept is proposed and their performances were analyzed using benchmark functions and practical complex constrained problems related to economic load dispatch (ELD) of power system. This paper organized as below: section I deals with introduction to optimization techniques, section II presents krill herd algorithm and its variants. The