Opposition-based krill herd algorithm with Cauchy mutation and position clamping

Abstract

Krill herd (KH) has been proven to be an efficient algorithm for function optimization. For some complex functions, this algorithm may have problems with convergence or being trapped in local minima. To cope with these issues, this paper presents an improved KH-based algorithm, called Opposition Krill Herd (OKH). The proposed approach utilizes opposition-based learning (OBL), position clamping (PC) and Cauchy mutation (CM) to enhance the performance of basic KH. OBL accelerates the convergence of the method while both PC and heavy-tailed CM help KH escape from local optima. Simulations are implemented on an array of benchmark functions and two engineering optimization problems. The results show that OKH has a good performance on majority of the considered functions and two engineering cases. The influence of each individual strategy (OBL, CM and PC) on KH is verified through 25 benchmarks. The results show that the KH with OBL, CM and PC operators, has the best performance among different variants of OKH.

Introduction

Inspired by nature, a variety of modern intelligent algorithms have been developed and applied to solve optimization problems. Some of them, like cuckoo search (CS) [1], [2], [3], [4], [5], biogeography-based optimization (BBO) [6], [7], [8], [9], [10], [11], [12], [13], artificial bee colony (ABC) [14], [15], genetic algorithm (GA) [16], genetic programming (GP) [17], stud GA (SGA) [18], [19], differential evolution (DE) [20], [21], [22], [23], [24], [25], ant lion optimizer (ALO) [26], chicken swarm optimization (CSO) [27], wolf search algorithm (WSA) [28], multi-verse optimizer (MVO) [29], earthworm optimization algorithm (EWA) [30], grey wolf optimizer (GWO) [31], [32], firefly algorithm (FA) [33], [34], [35], dragonfly algorithm (DA) [36], harmony search (HS) [37], [38], [39], [40], [41], bird swarm algorithm (BSO) [42], moth-flame optimization (MFO) [43], animal migration optimization (AMO) [44], particle swarm optimization (PSO) [45], [46], [47], [48], ant colony optimization (ACO) [49], bat algorithm (BA) [50], [51], [52], [53], [54], have solved several complicated challenging problems that are hard to deal with by traditional optimization techniques. Among these algorithms, krill herd (KH) method [55], [56], [57] has been studied extensively due to its promising performance for solving most complex problems. KH was first proposed by Gandomi and Alavi by the idealization of communicating and foraging behaviors of krill swarms [55]. KH performed well on various optimization problems [55]. However, in some cases, it might not be capable of escaping from local minima. In order to decrease the influence of this problem for KH, this paper proposes different variants of KH algorithm using opposition-based learning (OBL), position clamping (PC) and Cauchy mutation (CM). The main idea of OBL is to search for a better candidate solution through the simultaneous consideration of a solution and its opposite that is closer to the global optimum. OBL can successfully handle this task by updating the other half krill according to the previous ones following its basic theory. Consequently, a faster convergence can be provided for the KH method. The heavy-tailed CM and PC help the krill not trap into the local optima. Through different experiments, the KH together with OBL, CM and PC operators performs the best among various OKHs. Experimental simulations on 25 benchmark functions and two engineering optimization problems show that OKH performs well on the majority of benchmark functions and engineering problems.

The remainder of this paper is organized as follows. The next section introduces the main process of the basic KH and OBL theory. Section 3 proposes an improved OKH model by combination of KH, CM operator and PC operator. Then, in Section 4, a series of comparison experiments on various benchmarks and two engineering cases are conducted. The final section provides our concluding remarks and points out our future work orientation.