this link may be help you

https://www.mathworks.com/matlabcentral/fileexchange/81253-improved-grey-wolf-optimizer-i-gwo?s_tid=srchtitle

Tsipianitis A, Tsompanakis Y. Improved Cuckoo Search algorithmic variants for constrained nonlinear optimization. Advances in Engineering Software. 2020 Nov 1;149:102865.

An example article is here

You should be aware that new metaheuristic algorithms often do not introduce novel mechanisms. Rather, they tend to come up with new arrangements of existing metaheuristic concepts. See this paper: Preprint Mitigating Metaphors: A Comprehensible Guide to Recent Natur...

Hello Seyed,

You can check recent work on using pattern mining mechanisms to enhance metaheuristics. This is a technical contribution that applies to many kinds of methods and problems, regardless of the terminology (or metaphor) adopted.

Preprint PILS: Exploring high-order neighborhoods by pattern mining a...

Article MineReduce: An approach based on data mining for problem siz...

For a technical description and survey of the most common metaheuristic mechanisms you may also find these papers interesting:

Article Metaheuristics in Combinatorial Optimization: Overview and C...

Article Heuristics for Multi-Attribute Vehicle Routing Problems : A ...

Finally, I recommend to focus on a technical description of the methods, independent of biological concepts, as already discussed in several previous papers:

Article Metaheuristics -- the metaphor exposed

Good luck with your research!

The following paper may help you

https://www.sciencedirect.com/science/article/pii/S1875510020305497

It is completely false to claim that metaheuristics are not dependent on starting point. You can easily observe it in the following paper in topology optimization (I have also the experience):

https://www.tandfonline.com/doi/abs/10.1080/13588265.2017.1331493

Also, a method cannot claim to be good due to not using sensitivity information. Because, you may need to pay a huge computational cost for discovering the result instead! Besides, note that the heuristics will all fail when the dimensions are increased. For example, in topology optimization the design variables will go up to 2 million! A group search in large scales for global optimum with metaheuristics is same as searching for a lost key in all over the New York with a group of your friends! :-)

Metaheuristics have no mathematical background and can never guarantee the globality of the designs. The best idea is to move to the superior method which is mathematical programming. But if you like to stay in metaheuristics, proposing a “novel tired panda algorithm” or “zombie bat algorithm” will never help you. In my opinion, a good idea might be empowering metaheuristics with mathematical programming. One of the most interesting implementations of such methods is present in the following dissertation which has coupled math opt, heuristics, and surrogate modeling for a black box optimization. The PDF is available here:

http://tuprints.ulb.tu-darmstadt.de/6861/

I can also reference to some other effective implementations as follows:

https://ieeexplore.ieee.org/abstract/document/7748335

https://link.springer.com/article/10.1007/s10409-020-00942-7

I am speaking about continuous optimization and specifically structural optimization which you are involved in.

You can check the MTDE algorithm implemented by a multi-trial vector approach (MTV) which is a new and effective mechanism to improve metaheuristic algorithms. The MTDE and its full source code are available here:

Article MTDE: An effective multi-trial vector-based differential evo...

I recommend you to check also the CCSA algorithm implemented by a Conscious Neighborhood-based approach which is an effective mechanism to improve other metaheuristic algorithms as well. The CCSA and its full source code are available here:

Article CCSA: Conscious Neighborhood-based Crow Search Algorithm for...

One of the most efficient approaches is using hierarchical clustering with the next multilevel macromodelling. Pls. see my papers:

1. The optimal circuit reduction method as an effective tool to solve large and very large size intractable combinatorial VLSI physical design problems.

2. Power System Islanding by the Hierarchical Clustering.

3. MACROMODELING FOR VLSI PHYSICAL DESIGN AUTOMATION PROBLEMS

4. A Parallel Ring Method for Solving a Large-scale Traveling Salesman Problem.

5. Algorithms for software clustering and modularization.

6. The analysis and optimization algorithms of the electronic circuits design.

7. Partitioning Optimization by Iterative Reassignment of the Hierarchically Built Clusters with Border Elements.

8. Partitioning Optimization by Iterative Reassignment of the Hierarchically Built Clusters with Border Elements.

9. The methodology and algorithms for solving the very large-scale physical design automation problems: Partitioning, packaging, placement and routing.

10. Partitioning Optimization by Recursive Moves of Hierarchically Built Clusters.

11. “Hierarchical clustering – efficient approach to solve nonpolynomial large-scale combinatorial problems of circuit types”..

12. The optimal circuit reduction method as an effective tool to solve large and very large size intractable combinatorial VLSI physical design problems.

13. Circuit Partitioning for FPGAs by the Optimal Circuit Reduction Method.

14. VLSI and PCB elements placement optimization using hierarchical scanning area method.

Prof. Roman Bazylevych

What i understood, equations of exploration and exploitation constants can be modified to enhance the performance.

However, i noticed that, GWO has the tendency to deliver very insignificant results one or two times if you run it multiple times.

In addtion, nowadays researchers usuing levy flight mechanism in most of the algorithms.

Therefore, exploration and exploitation constants and levy flight can be used.

Normally we can improve meta heuristic optimization algorithms with the help of exploration and exploitation section along with different initialization role or exploration and exploitation search section.

This may help you:

https://www.sid.ir/en/journal/ViewPaper.aspx?id=494476

Multiple approaches are normally being adopted to improve the performance of meta heuristic algorithms that includes initialization methods, tweeks in positions updating equations, introducing new phenomenon from different domain, merging concepts from different algorithms and optimizing parameters plus initialization method of these algorithms.

However, I personally do agree with @Pooya Rostami in connection to extensive efforts going on in this area instead of looking for a breakthrough.

Kindly refer to this:

S. Sharma, R. Kapoor and S. Dhiman, "A Novel Hybrid Metaheuristic Based on Augmented Grey Wolf Optimizer and Cuckoo Search for Global Optimization,"2021 2nd International Conference on Secure Cyber Computing and Communications (ICSCCC), 2021, pp. 376-381, doi: 10.1109/ICSCCC51823.2021.9478142.

Or refer to the same paper at the following address:

https://www.researchgate.net/publication/353403100_A_Novel_Hybrid_Metaheuristic_Based_on_Augmented_Grey_Wolf_Optimizer_and_Cuckoo_Search_for_Global_Optimization

Article An Optimization Based Power Usage Scheduling Strategy Using ...

This can be done through application simulation software

You can try operators, like OBL, QOBL, LV, Cauchi Parator, Cultural Algothim etc. Combining this operators too can yield a more positive result.

MH are programs that seek global Optimus and are inspired in nature. You can do some steps to improve them:

1) Clean and make as short as possible the code. Talking about new algorithms. The expertise of new researchers can be confuse. A clean and objective code improves computational cost.

2) Tuning of parameters. The parameters of any MH very impacts yours exploration and exploitations capabilities. Some methods can be useful, but the best way to tune parameters is still a open problem... Some ways are: Design of experiments (DOE), Hyper-heuristics, etc.

3) All MH use in some point a random value, generally between 0 and 1. Some researchers improve significantly their algorithms using different theories for to generate these values, as caos theory and levy flights. There is no theory that can be the best for all algorithms. Each one can be improved with one of these theories and yet, for a specific problem.

You can incorporate cellular automata concept for hybridization.

I would like to invite you to have a look on the following links.

SSO: https://www.mathworks.com/matlabcentral/fileexchange/92150-sperm-swarm-optimization-sso

HSSOGSA: https://www.mathworks.com/matlabcentral/fileexchange/92130-hssogsa?s_tid=srchtitle

MOSFP: https://github.com/sh7adeh1990/MOSFP

One of very efficient approach to improve the performance of meta heuristic algorithms for NP-hard large-scale optimization problems is using hioerarchical clustering (botton-up) witn building macro-models at every level and next mustistep optimization at every level in going down step. At aevery level of opimazation we use macromodels of every cluster as well as local optimization algorithms with macro-models. Please, see my paper:

R. Bazylevych, MACROMODELING FOR VLSI PHYSICAL DESIGN AUTOMATION PROBLEMS.

January 2011. In book: G.Setlak, K.Markov. Business and engineering applications of intelligent and information systems.Publisher: ITHEAEditors: G.Setlak, K.Markov.

Prof. Roman Bazylevych

Please go through this paper. It may help you. One of the latest metaheuristic techniques is Bonobo Optimizer (BO). It has been published in the reputed Journal named Applied Intelligence (A. K. Das and D. K. Pratihar, "Bonobo optimizer (BO): an intelligent heuristic with self-adjusting parameters over continuous spaces and its applications to engineering problems," Applied Intelligence, pp 1-33, 2021. doi:https://doi.org/10.1007/s10489-021-02444-w).

The source code of BO is available at:

https://in.mathworks.com/matlabcentral/fileexchange/92703-bonobo-optimizer-bo

How to define the meta heuristic algorithm?

Use tangent flight mecanism :pure step=tan(rand*pi) or small step=sign(-,1)tan(rand*pi/2.5)

X=X+step

Layeb, A. (2022). Tangent search algorithm for solving optimization problems. Neural Computing and Applications, 1-32.

Hi,

This book chapter might help when it comes to generating new ideas on hybridization:

Chapter Hybrid Metaheuristic Algorithms: Past, Present, and Future

You can incorporate a statistical regeneration mechanism for improving metaheuristic optimization algorithms.

Article An enhanced Shuffled Shepherd Optimization Algorithm for opt...

You can apply Elite Opposition based Learning and hybridization

a comprehensive statistical comparison has been done in the following paper:

"Optimal design of truss structures with frequency constraints: a comparative study of DE, IDE, LSHADE, and CMAES algorithms"

link:Article Optimal design of truss structures with frequency constraint...

this can be a criterion for choosing an appropriate metaheuristic algorithm among some most powerful algorithm in the literature.

Check out the following links for further information.

https://ieeexplore.ieee.org/abstract/document/9344597

https://www.degruyter.com/document/doi/10.1515/jisys-2020-0117/html