The elephant herding optimization (EHO) algorithm is a relatively novel population-based optimization technique, which mimics herding behavior and can be modeled into two operators: clan updating operators and separating operators. Also, in the literature, EHO has received a great deal of attention from researchers since it was proposed applied to many application fields for its advantages of excellent global optimization ability and ease of implementation. However, there is still an insufficiency in the EHO algorithm regarding its lack of exploitation, which leads to slow convergence. In this paper, we propose three enhanced versions of EHO based on the γ value termed EEHO15, EEHO20, and EEHO25 to overcome the problems of fast unjustified convergence toward the origin of the basic EHO. The exploration/exploitation abilities of the EEHO algorithms are achieved by the updating of the two operators (clan and separation operator). To tackle this drawback, a constant function is used as a benchmark for inspecting the biased convergence of evolutionary algorithms in general. Moreover, we utilize CEC'17 test suite benchmark functions to test the performance of the proposed three versions of EEHO against EHO, particle swarm optimization (PSO), bird swarm algorithm (BSA), and ant lion optimizer (ALO) algorithms. Eventually, the experimental results revealed that the proposed EEHO algorithms extremely obtained better results compared with other competitive algorithms.

Purpose The purpose of this paper is to propose an enhanced elephant herding optimization (EEHO) algorithm by improving the exploration phase to overcome the fast-unjustified convergence toward the origin of the native EHO. The exploration and exploitation of the proposed EEHO are achieved by updating both clan and separation operators. Design/methodology/approach The original EHO shows fast unjustified convergence toward the origin specifically, a constant function is used as a benchmark for inspecting the biased convergence of evolutionary algorithms. Furthermore, the star discrepancy measure is adopted to quantify the quality of the exploration phase of evolutionary algorithms in general. Findings In experiments, EEHO has shown a better performance of convergence rate compared with the original EHO. Reasons behind this performance are: EEHO proposes a more exploitative search method than the one used in EHO and the balanced control of exploration and exploitation based on fixing clan updating operator and separating operator. Operator γ is added to EEHO assists to escape from local optima, which commonly exist in the search space. The proposed EEHO controls the convergence rate and the random walk independently. Eventually, the quantitative and qualitative results revealed that the proposed EEHO outperforms the original EHO. Research limitations/implications Therefore, the pros and cons are reported as follows: pros of EEHO compared to EHO – 1) unbiased exploration of the whole search space thanks to the proposed update operator that fixed the unjustified convergence of the EHO toward the origin and the proposed separating operator that fixed the tendency of EHO to introduce new elephants at the boundary of the search space; and 2) the ability to control exploration–exploitation trade-off by independently controverting the convergence rate and the random walk using different parameters – cons EEHO compared to EHO: 1) suitable values for three parameters (rather than two only) have to be found to use EEHO. Originality/value As the original EHO shows fast unjustified convergence toward the origin specifically, the search method adopted in EEHO is more exploitative than the one used in EHO because of the balanced control of exploration and exploitation based on fixing clan updating operator and separating operator. Further, the star discrepancy measure is adopted to quantify the quality of exploration phase of evolutionary algorithms in general. Operator γ that added EEHO allows the successive local and global searching (exploration and exploitation) and helps escaping from local minima that commonly exist in the search space.

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Finding all possible triangulations of convex polygon is a highly time and memory space consuming combinatorial problem. Therefore, it is very important to develop algorithms for generating triangulations as efficiently as possible. This paper presents a new method for generating triangulations of a convex polygon, called Orbiting triangle method (OTM). The method is based on using the set of (n − 1)-gon triangulations during the set of n-gon triangulations creation. The main feature of the OTM algorithm is the use of the Catalan triangle to identify valid triangulations, so that the algorithm spends almost no time to eliminate duplicates. In this way, the method possesses small complexity and saves the computational time required for detecting and eliminating duplicates.