In nature, the eastern North American monarch population is known for its southward migration during the late summer/autumn from the northern USA and southern Canada to Mexico, covering thousands of miles. By simplifying and idealizing the migration of monarch butterflies, a new kind of nature-inspired metaheuristic algorithm, called monarch butterfly optimization (MBO), a first of its kind, is proposed in this paper. In MBO, all the monarch butterfly individuals are located in two distinct lands, viz. southern Canada and the northern USA (Land 1) and Mexico (Land 2). Accordingly, the positions of the monarch butterflies are updated in two ways. Firstly, the offsprings are generated (position updating) by migration operator, which can be adjusted by the migration ratio. It is followed by tuning the positions for other butterflies by means of butterfly adjusting operator. In order to keep the population unchanged and minimize fitness evaluations, the sum of the newly generated butterflies in these two ways remains equal to the original population. In order to demonstrate the superior performance of the MBO algorithm, a comparative study with five other metaheuristic algorithms through thirty-eight benchmark problems is carried out. The results clearly exhibit the capability of the MBO method toward finding the enhanced function values on most of the benchmark problems with respect to the other five algorithms. Note that the source codes of the proposed MBO algorithm are publicly available at GitHub (
 https://github.com/ggw0122/Monarch-Butterfly-Optimization
 , C++/MATLAB) and MATLAB Central (
 http://www.mathworks.com/matlabcentral/fileexchange/50828-monarch-butterfly-optimization
 , MATLAB).

Monarch butterfly optimization

Because of successful implementations and high intensity, metaheuristic research has been extensively reported in literature, which covers algorithms, applications, comparisons, and analysis. Though, little has been evidenced on insightful analysis of metaheuristic performance issues, and it is still a “black box” that why certain metaheuristics perform better on specific optimization problems and not as good on others. The performance related analyses performed on algorithms are mostly quantitative via performance validation metrics like mean error, standard deviation, and co-relations have been used. Moreover, the performance tests are often performed on specific benchmark functions—few studies are those which involve real data from scientific or engineering optimization problems. In order to draw a comprehensive picture of metaheuristic research, this paper performs a survey of metaheuristic research in literature which consists of 1222 publications from year 1983 to 2016 (33 years). Based on the collected evidence, this paper addresses four dimensions of metaheuristic research: introduction of new algorithms, modifications and hybrids, comparisons and analysis, and research gaps and future directions. The objective is to highlight potential open questions and critical issues raised in literature. The work provides guidance for future research to be conducted more meaningfully that can serve for the good of this area of research.

Metaheuristic research: a comprehensive survey

A survey on new generation metaheuristic algorithms

Review of applications of algorithms in bio-inspired computing.Brief description of algorithms without mathematical notations.Brief description of scope of applications of the algorithms.Identification of algorithms whose applications may be explored.Identification of algorithms on which theory development may be explored. With the explosion of data generation, getting optimal solutions to data driven problems is increasingly becoming a challenge, if not impossible. It is increasingly being recognised that applications of intelligent bio-inspired algorithms are necessary for addressing highly complex problems to provide working solutions in time, especially with dynamic problem definitions, fluctuations in constraints, incomplete or imperfect information and limited computation capacity. More and more such intelligent algorithms are thus being explored for solving different complex problems. While some studies are exploring the application of these algorithms in a novel context, other studies are incrementally improving the algorithm itself. However, the fast growth in the domain makes researchers unaware of the progresses across different approaches and hence awareness across algorithms is increasingly reducing, due to which the literature on bio-inspired computing is skewed towards few algorithms only (like neural networks, genetic algorithms, particle swarm and ant colony optimization). To address this concern, we identify the popularly used algorithms within the domain of bio-inspired algorithms and discuss their principles, developments and scope of application. Specifically, we have discussed the neural networks, genetic algorithm, particle swarm, ant colony optimization, artificial bee colony, bacterial foraging, cuckoo search, firefly, leaping frog, bat algorithm, flower pollination and artificial plant optimization algorithm. Further objectives which could be addressed by these twelve algorithms have also be identified and discussed. This review would pave the path for future studies to choose algorithms based on fitment. We have also identified other bio-inspired algorithms, where there are a lot of scope in theory development and applications, due to the absence of significant literature.

Bio inspired computing - A review of algorithms and scope of applications

The behavior of natural phenomena has become one of the most popular sources for researchers to design optimization algorithms for scientific, computing and engineering fields. As a result, a lot of nature-inspired algorithms have been proposed in the last decades. Due to the numerous issues of the global optimization process, new algorithms are always welcome in this research field. This paper introduces the Coyote Optimization Algorithm (COA), which is a population based metaheuristic for optimization inspired on the canis latrans species. It contributes with a new algorithmic structure and mechanisms for balancing exploration and exploitation. A set of boundary constrained real parameter optimization benchmarks is tested and a comparative study with other nature-inspired metaheuristics is provided to investigate the performance of the COA. Numerical results and non-parametric statistical significance tests indicate that the COA is capable of locating promising solutions and it outperforms other metaheuristics on most tested functions.

Coyote Optimization Algorithm: A New Metaheuristic for Global Optimization Problems

A new bio-inspired algorithm, Chicken Swarm Optimization (CSO), is proposed for optimization applications. Mimicking the hierarchal order in the chicken swarm and the behaviors of the chicken swarm, including roosters, hens and chicks, CSO can efficiently extract the chickens’ swarm intelligence to optimize problems. Experiments on twelve benchmark problems and a speed reducer design were conducted to compare the performance of CSO with that of other algorithms. The results show that CSO can achieve good optimization results in terms of both optimization accuracy and robustness. Future researches about CSO are finally suggested.

A New Bio-inspired Algorithm: Chicken Swarm Optimization

A new bio-inspired algorithm, namely Bird Swarm Algorithm (BSA), is proposed for solving optimisation applications. BSA is based on the swarm intelligence extracted from the social behaviours and social interactions in bird swarms. Birds mainly have three kinds of behaviours: foraging behaviour, vigilance behaviour and flight behaviour. Birds may forage for food and escape from the predators by the social interactions to obtain a high chance of survival. By modelling these social behaviours, social interactions and the related swarm intelligence, four search strategies associated with five simplified rules are formulated in BSA. Simulations and comparisons based on eighteen benchmark problems demonstrate the effectiveness, superiority and stability of BSA. Some proposals for future research about BSA are also discussed.

A new bio-inspired optimisation algorithm: Bird Swarm Algorithm

Habitat selection and compensation for Doppler effect are incorporated into algorithm.Algorithm possesses the quantum search operator and mechanical search operator.Self-adaptive local search is proposed.Algorithm shows significant performance in comparison with more than 20 methods. A novel bat algorithm (NBA) is proposed for optimization in this paper, which focuses on further mimicking the bats' behaviors and improving bat algorithm (BA) in view of biology. The proposed algorithm incorporates the bats' habitat selection and their self-adaptive compensation for Doppler effect in echoes into the basic BA. The bats' habitat selection is modeled as the selection between their quantum behaviors and mechanical behaviors. Having considered the bats' self-adaptive compensation for Doppler effect in echoes and the individual's difference in the compensation rate, the echolocation characteristics of bats can be further simulated in NBA. A self-adaptive local search strategy is also embedded into NBA. Simulations and comparisons based on twenty benchmark problems and four real-world engineering designs demonstrate the effectiveness, efficiency and stability of NBA compared with the basic BA and some well-known algorithms, and suggest that to improve algorithm based on biological basis should be very efficient. Further research topics are also discussed.

A novel bat algorithm with habitat selection and Doppler effect in echoes for optimization

A new bio-inspired algorithm: Chicken swarm optimization

Neural architecture search (NAS) is a challenging problem in the design of deep learning due to its nonconvexity. To address this problem, an adaptive scalable NAS method (AS-NAS) is proposed based on the reinforced I-Ching divination evolutionary algorithm (IDEA) and variable-architecture encoding strategy. First, unlike the typical reinforcement learning (RL)-based and evolutionary algorithm (EA)-based NAS methods, a simplified RL algorithm is developed and used as the reinforced operator controller to adaptively select the efficient operators of IDEA. Without the complex actor–critic parts, the reinforced IDEA based on simplified RL can enhance the search efficiency of the original EA with lower computational cost. Second, a variable-architecture encoding strategy is proposed to encode neural architecture as a fixed-length binary string. By simultaneously considering variable layers, channels, and connections between different convolution layers, the deep neural architecture can be scalable. Through the integration with the reinforced IDEA and variable-architecture encoding strategy, the design of the deep neural architecture can be adaptively scalable. Finally, the proposed AS-NAS are integrated with the ${L}_{1/2}$ regularization to increase the sparsity of the optimized neural architecture. Experiments and comparisons demonstrate the effectiveness and superiority of the proposed method.

Xian-Bing Meng

Papers

A New Bio-inspired Algorithm: Chicken Swarm Optimization

A new bio-inspired optimisation algorithm: Bird Swarm Algorithm

A novel bat algorithm with habitat selection and Doppler effect in echoes for optimization

A new bio-inspired algorithm: Chicken swarm optimization

AS-NAS: Adaptive Scalable Neural Architecture Search With Reinforced Evolutionary Algorithm for Deep Learning