A Multi-Cohort Intelligence (Multi-CI) metaheuristic algorithm in emerging socio-inspired optimization domain is proposed. The algorithm implements intra-group and inter-group learning mechanisms. It focusses on the interaction amongst different cohorts. The performance of the algorithm is validated by solving 75 unconstrained test problems with dimensions up to 30. The solutions were comparing with several recent algorithms such as Particle Swarm Optimization, Covariance Matrix Adaptation Evolution Strategy, Artificial Bee Colony, Self-adaptive differential evolution algorithm, Comprehensive Learning Particle Swarm Optimization, Backtracking Search Optimization Algorithm and Ideology Algorithm. The Wilcoxon signed rank test was carried out for the statistical analysis and verification of the performance. The proposed Multi-CI outperformed these algorithms in terms of the solution quality including objective function value and computational cost, i.e. computational time and functional evaluations. The prominent feature of the Multi-CI algorithm along with the limitations are discussed as well. In addition, an illustrative example is also solved and every detail is provided.
Several nature-inspired optimization algorithms have been developed so far. The notable algorithms are Evolutionary Algorithms (EAs), Genetic Algorithms (GAs), Swarm Optimization (SO) techniques, etc. These methods have proven their superiority in terms of solution quality and computational time over the traditional (exact) methods for solving a wide variety of problem classes. In agreement with the no-free-lunch theorem, certain modifications and supportive techniques are required to be incorporated into these methods when applying for solving a variety of class of problems. This motivated the researchers to resort to development of new optimization methods. An Artificial Intelligence (AI) based socio-inspired optimization methodology referred to as Cohort Intelligence (CI) was proposed by Kulkarni et al. in 2013. It is inspired from the interactive and competitive social behaviour of individual candidates in a cohort. Every candidate exhibits self-interested behaviour and tries to improve it by learning from the other candidates in the cohort. The learning refers to following/adopting the qualities associated with the behaviour of the other candidates. The candidates iteratively follow one another based on certain probability and the cohort is considered saturated/converged when no further improvement in the behaviour of any of the candidates is possible for considerable number of attempts.
The CI methodology was validated by solving several unconstrained test problems (Kulkarni et al. 2013). The algorithm performed better as compared to several versions of the Particle Swarm Optimization (PSO) such as Chaos-PSO (CPSO) and Linearly Decreasing Weight PSO (LDWPSO) (Liu et al. 2010) as well as Robust Hybrid PSO (RHPSO) (Xu et al. 2013). Then was applied for solving a combinatorial problem such as Knapsack problem (Kulkarni and Shabir2016). The algorithm yielded comparable solutions as compared to the Integer programming (IP), Harmony Search (HS) (Zou et al. 2011;Geem et al. 2001), Improved HS (IHS) (Zou et al. 2011;Mahdavi et al. 2007), Novel Global HS (NGHS) (Zou et al. 2011;Layeb 2011Layeb , 2013)), Quantum Inspired HS Algorithm (QIHSA) (Layeb 2013) and Quantum Inspired Cuckoo Search Algorithm (QICSA) (Layeb 2011).The combinatorial problems from healthcare domain as well as complex large sized Supply Chain problems such as Sea-Cargo problem and Selection of Cross-Border Shippers were also solved (Kulkarni et al. 2016). Furthermore, CI contributed in design of fractional PID controller (Shah and Kulkarni, 2017). CI was applied for solving mechanical engineering problems such as discrete and mixed variable engineering problems (Kale and Kulkarni, 2017) and cup forming design problems (Kulkarni, Kulkarni, Kulkarni, Kakandikar 2016). Recently several variations of CI were proposed by Patankar and Kulkarni (2018). In addition, CI with Cognitive Computing (CICC) was applied for solving steganography problems by (Sarmah andKulkarni, 2017, 2018). The CI performance was better as compared to the IP solutions as well as specially developed Multi Random Start Local Search (MRSLS) method. In these problems, constraints were handled using a specially developed probability based constraint handling approach. In addition, Traveling Salesman Problem (TSP) was also solved (Kulkarni et al. 2017). The approach was further adopted for solving continuous constrained test problems (Shastri et al. 2016, Kulkarni et al 2016). In addition, complex problem of heat exchanger was also solved using CI method (Dhavale et al. 2016). The solutions were comparable to the techniques such as Differential Evolution (DE) (Price et al. 2005) and GA (Deb et al. 2000).Furthermore, a modified version of CI referred to as MCI as well as its hybridized version with K-means performed better as compared to K-means, K-means++ as well as Genetic Algorithm (GA) (Maulik and Bandyopadhyay 2000), Simulated Annealing (SA) (Niknam and Amiri 2010; Selim and Alsultan 1991), Tabu Search (TS) (Niknam and Amiri 2010), Ant Colony Optimization (ACO) (Shelokar et al. 2004), Honeybee Mating Optimization (HBMO) (Fathian and Amiri 2008) and Particle Swarm Optimization (PSO) (Kao et al. 2008).
It is important to mention here that in the current version of CI (including MCI in which a mutation approach was used for sampling) the candidates learn from the candidates of the same cohort. As the selection is based on roulette wheel approach it is not necessary that the candidate will follow the best candidate in every learning attempt. Even though this helps the candidates jump out of local minima, learning options are limited as only intra-group learning exists. In the society several cohorts exist which interact and compete with one another which could be referred to as inter-group learning. This makes the candidates learn from the candidates within the cohort as well as the candidates from other cohorts. In the proposed Multi-Cohort Intelligence (Multi-CI) approach intr
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