Manta ray foraging and Gaussian mutation-based elephant herding optimization for global optimization

The elephant herding optimization (EHO) algorithm is a novel metaheuristic optimizer inspired by the clan renewal and separation behaviors of elephant populations. Although it has few parameters and is easy to implement, it suffers from a lack of exploitation, leading to slow convergence. This paper proposes an improved EHO algorithm called manta ray foraging and Gaussian mutation-based EHO for global optimization (MGEHO). The clan updating operator in the original EHO algorithm is replaced by the somersault foraging strategy of manta rays, which aims to optimally adjust patriarch positions. Additionally, a dynamic convergence factor is set to balance exploration and exploitation. The gaussian mutation is adopted to enhance the population diversity, enabling MGEHO to maintain a strong local search capability. To evaluate the performances of different algorithms, 33 classical benchmark functions are chosen to verify the superiority of MGEHO. Also, the enhanced paradigm is compared with other advanced metaheuristic algorithms on 32 benchmark functions from IEEE CEC2014 and CEC2017. Furthermore, a scalability test, convergence analysis, statistical analysis, diversity analysis, and running time analysis demonstrate the effectiveness of MGEHO from various aspects. The results illustrate that MGEHO is superior to other algorithms in terms of solution accuracy and stability. Finally, MGEHO is applied to solve three real engineering problems. The comparison results show that this method is a powerful auxiliary tool for handling complex problems.

Running Time Analysis of Broadcast Consensus Protocols

Broadcast consensus protocols (BCPs) are a model of computation, in which anonymous, identical, finite-state agents compute by sending/receiving global broadcasts. BCPs are known to compute all number predicates in $$\mathsf {NL}=\mathsf {NSPACE}(\log n)$$ NL = NSPACE ( log n ) where n is the number of agents. They can be considered an extension of the well-established model of population protocols. This paper investigates execution time characteristics of BCPs. We show that every predicate computable by population protocols is computable by a BCP with expected $$\mathcal {O}(n \log n)$$ O ( n log n ) interactions, which is asymptotically optimal. We further show that every log-space, randomized Turing machine can be simulated by a BCP with $$\mathcal {O}(n \log n \cdot T)$$ O ( n log n · T ) interactions in expectation, where T is the expected runtime of the Turing machine. This allows us to characterise polynomial-time BCPs as computing exactly the number predicates in $$\mathsf {ZPL}$$ ZPL , i.e. predicates decidable by log-space, randomised Turing machine with zero-error in expected polynomial time where the input is encoded as unary.

Running Time Analysis of MOEA/D with Crossover on Discrete Optimization Problem

Decomposition-based multiobjective evolutionary algorithms (MOEAs) are a class of popular methods for solving multiobjective optimization problems (MOPs), and have been widely studied in numerical experiments and successfully applied in practice. However, we know little about these algorithms from the theoretical aspect. In this paper, we present a running time analysis of a simple MOEA with crossover based on the MOEA/D framework (MOEA/D-C) on four discrete optimization problems. Our rigorous theoretical analysis shows that the MOEA/D-C can obtain a set of Pareto optimal solutions to cover the Pareto front of these problems in expected running time apparently lower than the one without crossover. Moreover, the MOEA/D-C only needs to decompose an MOP into a few scalar optimization subproblems according to several simple weight vectors. This result suggests that the use of crossover in decomposition-based MOEA can simplify the setting of weight vector for different problems and make the algorithm more efficient. This study theoretically explains why some decomposition-based MOEAs work well in computational experiments and provides insights in design of MOEAs for MOPs in future research.