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Modified Leader-Advocate-Believer Algorithm with Clustering-Based Search Space Reduction Method for Solving Engineering Design Problems

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Abstract

A Modified Leader-Advocate-Believer (LAB) algorithm is introduced in this paper. It builds upon the original LAB algorithm (Reddy et al. 2023), which is a socio-inspired algorithm that models competitive and learning behaviours within a group, establishing hierarchical roles. The proposed algorithm incorporates the roulette wheel approach and a reduction factor introducing inter-group competition and iteratively narrowing down the sample space. The algorithm is validated by solving the benchmark test problems from CEC 2005 and CEC 2017. The solutions are validated using standard statistical tests such as two-sided and pairwise signed rank Wilcoxon test and Friedman rank test. The algorithm exhibited improved and superior robustness as well as search space exploration capabilities. Furthermore, a Clustering-Based Search Space Reduction (C-SSR) method is proposed, making the algorithm capable to solve constrained problems. The C-SSR method enables the algorithm to identify clusters of feasible regions, satisfying the constraints and contributing to achieve the optimal solution. This method demonstrates its effectiveness as a potential alternative to traditional constraint handling techniques. The results obtained using the Modified LAB algorithm are then compared with those achieved by other recent metaheuristic algorithms.

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Data Availability

The source codes and datasets will be made available on request.

Abbreviations

\({\psi }^{l}\) :

Lower bound

\({\psi }^{u}\) :

Upper bound

\(P\) :

Population of society

\(G\) :

Total number of groups

\({A}_{g}\) :

Advocate associated to the leader of the \(g\) th group \(\left(g=1,...., G\right)\)

\({B}_{j}\left(g\right)\) :

j th believer associated to the leader of the \(g\) th group \(\left(j = 1, \dots ,n-2\right)\)

\({L}^{*}\) :

Best global leader

\({L}_{g}\) :

Leader for the \({g}^{th}\) group

\(N\) :

Number of dimensions

\(e\) :

Number of equidistant points in each dimension

\(point\_combinations\) :

Representative set of points

\({P}_{i}\) :

Set of equidistant points in the ith dimension

\(|\) :

Cartesian product

\({c}_{i}\) :

\({i}^{th}\) Constraint

\({n}_{i}\) :

Total number of points satisfying \({c}_{i}\)

\(t\) :

Total number of constraints

\({x}_{j}^{k}\) :

\({k}^{th}\) point in \(satisfying\_value{s}_{j}\)

\(combined\_points\) :

Set of points where optimal solution exists

\(MinPts\) :

Minimum number of neighbours for DBSCAN

\(eps\) :

Epsilon for DBSCAN

\(C\) :

Cluster formed using DBSCAN

Ω:

Search space updation factor for advocates and leaders

σ:

Step size factor for updating global leader value

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Authors and Affiliations

  1. Institute of Artificial Intelligence, Dr Vishwanath Karad MIT World Peace University, 124 Paud Road, Kothrud, Pune, MH, 411038, India

    Ruturaj Reddy, Utkarsh Gupta, Ishaan R. Kale, Apoorva Shastri & Anand J. Kulkarni

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  1. Ruturaj Reddy
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  2. Utkarsh Gupta
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  3. Ishaan R. Kale
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Contributions

Ruturaj Reddy: Implementation and testing of modified algorithm, and manuscript preparation. Utkarsh Gupta: Formulation and testing of the constrained approach, and manuscript preparation. Ishaan Kale: Formulation of the modified algorithm, and manuscript preparation. Apoorva Shastri: Statistical analysis and validation of the algorithm, and manuscript preparation. Anand J Kulkarni: Conceptualization of the method and review.

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Correspondence to Ishaan R. Kale.

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Reddy, R., Gupta, U., Kale, I.R. et al. Modified Leader-Advocate-Believer Algorithm with Clustering-Based Search Space Reduction Method for Solving Engineering Design Problems. SN COMPUT. SCI. 5, 376 (2024). https://doi.org/10.1007/s42979-024-02716-5

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