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Swarm Intelligence Algorithm Based on Competitive Predators with Dynamic Virtual Teams JAISCR, 2017, Vol. 7, No. 2, pp. 87 – 101 10.1515/jaiscr-2017-0006 SWARM INTELLIGENCE ALGORITHM BASED ON COMPETITIVE PREDATORS WITH DYNAMIC VIRTUAL TEAMS Shiqin Yang, Yuji Sato Graduate School of Computer and Information Sciences,Hosei University 3-7-2 Kajino-cho Koganei-shi, Tokyo, Japan Abstract In our previous work, Fitness Predator Optimizer (FPO) is proposed to avoid premature convergence for multimodal problems. In FPO, all of the particles are seen as predators. Only the competitive, powerful predator that are selected as an elite could achieve the limited opportunity to update. The elite generation with roulette wheel selection could increase individual independence and reduce rapid social collaboration. Experimental re- sults show that FPO is able to provide excellent performance of global exploration and local minima avoidance simultaneously. However, to the higher dimensionality of multi- modal problem, the slow convergence speed becomes the bottleneck of FPO. A dynamic team model is utilized in FPO, named DFPO to accelerate the early convergence rate. In this paper, DFPO is more precisely described and its variant, DFPO-r is proposed to im- prove the performance of DFPO. A method of team size selection is proposed in DFPO-r to increase population diversity. The population diversity is one of the most important factors that determines the performance of the optimization algorithm. A higher degree of population diversity is able to help DFPO-r alleviate a premature convergence. The strategy of selection is to choose team size according to the higher degree of population diversity. Ten well-known multimodal benchmark functions are used to evaluate the solu- tion capability of DFPO and DFPO-r. Six benchmark functions are extensively set to 100 dimensions to investigate the performance of DFPO and DFPO-r compared with LBest PSO, Dolphin Partner Optimization and FPO. Experimental results show that both DFPO and DFPO-r could demonstrate the desirable performance. Furthermore, DFPO-r shows better robustness performance compared with DFPO in experimental study. Keywords: swarm intelligence, sitness predator optimizer, dynamic virtual team, popu- lation diversity 1 Introduction of swarm intelligence are Ant Colony Optimiza- tion (ACO) [9], Particle Swarm Optimization (PSO) Swarm Intelligence (SI) is a relatively new in- [10], Artificial Bee Colony (ABC) [12], Stochas- terdisciplinary field of research, which has gained tic Diffusion Search (SDS) [2], [25] and bacterial huge popularity these days. It is study of compu- foraging algorithm [20]. Recently, there are many tational systems, which draw inspiration from the other nature-inspired meta-heuristic algorithms that collective intelligence emerging from the behav- proposed as extensions of SI, such as firefly algo- ior of groups of simple agents (like bees, ants and rithm [34], fireworks algorithm [32], wasp swarm birds). The most well-known paradigms in the area algorithm [26], Glowworm Swarm Optimization 88 Shiqin Yang, Yuji Sato (GSO) [21], [22], Gravitational Search Algorithm ticles’ movement to avoid premature convergence. (GSA) [27] and so on. The experimental results show that the PPO has a A major problem with most swarm intelligence better performance than the traditional PSO [13], algorithms in multimodal optimization is premature [16] in regard to multimodal functions. However, convergence, which results in great performance the parameters of the PPO were empirically defined, loss and sub-optimal solutions [1]. Generally, the which greatly influence the robust performance of fast social collaboration between particles seems to the algorithm. be the reason for loss of population diversity. Di- Generally, most of swarm intelligence algo- versity declines rapidly in the later iteration period, rithms, such as cuckoo search [36], brain storm op- leaving the optimization algorithm with great diffi- timization algorithm [28], bacterial foraging opti- culties of escaping the local optima. Consequently, mization algorithm [8], focus on social collabora- the clustering particles with fitness stagnation fur- tion of population while they seldom concentrate ther exacerbates the premature convergence situa- on the individual competition and independent self tion. An accepted hypothesis is that maintenance awareness. The skills of individual competition are of high diversity is crucial for preventing premature effective methods for inspiration to develop intelli- convergence in multimodal optimization. gent systems and provide solutions to multimodal Many kinds of optimization algorithms are pro- problems. We assume that the individual competi- posed to improve the diversity of the population tion is more efficient for reducing the rapid social for preventing premature convergence. Some of collaboration and increase the ability of being out them are inspired by the social behavior of swarms of the local optimum for the swarm. This motivated and herds in nature. Moreover, hunting and search our attempt to present a new swarm intelligence op- behavior of predators are implemented by more timization, the Fitness Predator Optimizer (FPO) and more researchers and proved to be an effective [33] that implements hunting and search behavior method. For instance, the basic idea of Artificial of predators, but also emphasizes on the individual Fish-Swarm Algorithm (AFSA) [23] is to imitate competition and independent self awareness. fish behavior such as preying, swarming, follow- In an FPO system, all of the individuals are seen ing with local search of individual fish for reach- as predators. Only the competitive, powerful indi- ing the global optimum. The Grey Wolf Optimizer viduals selected as elites can achieve the limited op- (GWO) [24] algorithm mimics the leadership hier- portunity to update. The elite team reduces the risk archy and hunting mechanism of grey wolves in na- of all of the individuals moving towards the same ture. The Dolphin Partner Optimization (DPO) [30] place. However, in regards to the higher dimension- mimics the hunting mechanism of dolphins in na- ality of multimodal problem, the slow convergence ture. Bat-inspired Algorithm (BA) [35] based on speed in the early iteration becomes the bottleneck the echolocation behavior of bats. Bats use a type to restrict the improvement of the Fitness Predator of sonar, called, echolocation to detect prey, avoid Optimizer. In order to resolve this problem, we try obstacles and locate their roosting crevices in the to design a superior topology structure of FPO in dark. Krill Herd (KH) [11] is based on the simula- this paper. tion of the herding of the krill swarms in response Many investigations about the swarm paradigm to specific biological and environmental processes. [14], [17] have found that the gbest type converges The most closely associated algorithm with our pro- quickly on problem solutions but has a weakness for posed method is the Predator-Prey Optimizer (PPO) becoming trapped in the local optima, while lbest [31]. It is a form of particle swarm optimization populations are able to escape from local optima, as where new particles called predators are introduced. subpopulations explore different regions. In [15], The objective of predator is to pursue the best in- [18], Kennedy theorized that heterogeneous popu- dividual in the swarm. The fear probability is the lation structures, with some subsets of the popula- probability of a particle changing its velocity due to tion tightly connected and others relatively isolated, the presence of the predator. When all of the parti- could provide the benefits of both lbest and gbest cles tend to move toward the best global particle, sociometries. Motivated by the heterogeneous pop- a predator particle nearby will disturb these par- ulation structure, a modified dynamic virtual team Shiqin Yang, Yuji Sato SWARM INTELLIGENCE ALGORITHM BASED . 89 (GSO) [21], [22], Gravitational Search Algorithm ticles’ movement to avoid premature convergence. is presented in this paper with the aim of acceler- To most swarm intelligence algorithms, all par- (GSA) [27] and so on. The experimental results show that the PPO has a ating the early convergence rate and improving the ticles in a swarm get an equal opportunity to update A major problem with most swarm intelligence better performance than the traditional PSO [13], global searching capability for FPO. Dynamic vir- during each iteration. Unlike most swarm intelli- algorithms in multimodal optimization is premature [16] in regard to multimodal functions. However, tual team, which was first presented by the Dolphin gence algorithms, FPO practices a limited number convergence, which results in great performance the parameters of the PPO were empirically defined, Partner Optimization (DPO) [30] mimics the hunt- of updates for each iteration. This greatly stimulates loss and sub-optimal solutions [1]. Generally, the which greatly influence the robust performance of ing mechanism of dolphins in nature. The perfor- the competition among the particles in a swarm. fast social collaboration between particles seems to the algorithm. mance of DPO with the virtual team model is eval- Principle 1 means that a particle with a better fitness be the reason for loss of population diversity. Di- Generally, most of swarm intelligence algo- uated on several benchmark functions. Experiments function value, that had a prior possibility to update versity declines rapidly in the later iteration period, rithms, such as cuckoo search [36], brain storm op- show that it
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