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A new adaptive tuned Social Group Optimization (SGO) algorithm with sigmoid-adaptive inertia weight for solving engineering design problems

  • 1203: Applications of Advanced Artificial Intelligence in Multimedia and Information Security
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Abstract

Evolutionary algorithms have found enormous applications in solving real-world problems due to their stochastic nature. They have a set of control parameters, which are used to perform certain operations to induce randomness, scalar displacement etc. Various works have been done for tuning these parameters, as appropriate parameter tuning can enhance the performance of algorithm greatly. Inertia weights based parameter tuning is one of the widely used techniques for this purpose. In this paper, we have reviewed some of the inertia weight strategies and applied them to Social Group Optimization (SGO) to study the changes in its performance and have performed a thorough analysis on the same. Following the analysis, the need of a more generalized inertia weight strategy was felt which could be used in parameter tuning for different variety of problems and hence Sigmoid adaptive inertia weight have been proposed. SGO with sigmoid-adaptive inertia weight (SGOSAIW) has been simulated on twenty-seven benchmark functions suite and further simulated on few mechanical and chemical engineering problems and compared to other similar algorithms for performance analysis. In eight-benchmark function suite, SGOSAIW obtained better minima except one i.e. ‘Schwefel 2.26’ with respect to other algorithms investigated in this work. In nineteen-benchmark function suite, SGOSAIW obtained better minima except one i.e. ‘Noisy function’. Thus, the proposed algorithm yielded promising results which are well represented with suitable tables and graphs in the paper.

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Authors and Affiliations

  1. School of Computer Engineering, Kalinga Institute of Industrial Technology, Bhubaneswar, India

    Junali Jasmine Jena & Suresh Chandra Satapathy

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  1. Junali Jasmine Jena
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Appendix

Appendix

1.1 Problem-1 Three Bar Truss

Minimize: \(\mathrm{f}\left(\mathrm{x},\mathrm{y}\right)=\left(2\sqrt{2}\mathrm{x}+\mathrm{y}\right)\mathrm{L}\)

Subject to :

$$\mathrm{g}1\left(\mathrm{x},\mathrm{y}\right)=\left(\sqrt{2\mathrm{x}}+\mathrm{y}\right)\mathrm{P}-\upsigma (\sqrt{2}{\mathrm{x}}^{2}+2\mathrm{xy})\le 0$$
$$\mathrm{g}2\left(\mathrm{x},\mathrm{y}\right)=\mathrm{yP}-\upsigma (\sqrt{2}{\mathrm{x}}^{2}+2\mathrm{xy})\le 0$$
$$\mathrm{g}3\left(\mathrm{x},\mathrm{y}\right)=\mathrm{P}-\upsigma (\sqrt{2}\mathrm{y}+\mathrm{x})\le 0$$

Where :

$$0\le \mathrm{x},\mathrm{y}\le 1,$$
$$\mathrm{L}=100\mathrm{cm},\mathrm{ P}=2\mathrm{KN}/{\mathrm{cm}}^{2},\upsigma =2\mathrm{KN}/{\mathrm{cm}}^{2}$$

1.2 Problem-2 Cantilever Beam

Minimize: \(\mathrm{f}\left(\mathrm{a},\mathrm{b},\mathrm{c},\mathrm{d},\mathrm{e}\right)=0.0624(\mathrm{a}+\mathrm{b}+\mathrm{c}+\mathrm{d}+\mathrm{e})\)

Subject to : \(\mathrm{g}\left(\mathrm{a},\mathrm{b},\mathrm{c},\mathrm{d},\mathrm{e}\right)=\frac{61}{{\mathrm{a}}^{3}}+\frac{37}{{\mathrm{b}}^{3}}+\frac{19}{{\mathrm{c}}^{3}}+\frac{7}{{\mathrm{d}}^{3}}+\frac{1}{{\mathrm{e}}^{3}}\le 1\)

Where : \(0.01\le \mathrm{a},\mathrm{b},\mathrm{c},\mathrm{d},\mathrm{e}\le 100\)

1.3 Problem-3 Process Synthesis Problem

Minimize : \(\mathrm{f}\left(\mathrm{x},\mathrm{y}\right)=\mathrm{x}+2\mathrm{xy}\)

Subject to : \(\mathrm{g}1\left(\mathrm{x},\mathrm{y}\right)=1.25-{\mathrm{x}}^{2}-\mathrm{y}\le 0\)

$$\mathrm{g}2\left(\mathrm{x},\mathrm{y}\right)=\mathrm{x}+\mathrm{y}-1.6\le 0$$

Where : \(0\le \mathrm{x}\le 1.6,\mathrm{ y}\in \{\mathrm{0,1}\}\)

1.4 Problem-4 Process Synthesis and Design Problem

Minimize : \(\mathrm{f}\left(\mathrm{a},\mathrm{b},\mathrm{c}\right)=2\mathrm{a}+\mathrm{b}-\mathrm{c}\)

Subject to : \(\mathrm{g}1\left(\mathrm{a},\mathrm{b}\right)=\mathrm{a}-2{\mathrm{e}}^{-\mathrm{b}}=0\)

$$\mathrm{g}2\left(\mathrm{a},\mathrm{b},\mathrm{c}\right)=\mathrm{c}+\mathrm{b}-\mathrm{a}\le 0$$

Where : \(0.5\le \mathrm{a},\mathrm{b}\le 1.4,\mathrm{ c}\in \{\mathrm{0,1}\}\)

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Jena, J.J., Satapathy, S.C. A new adaptive tuned Social Group Optimization (SGO) algorithm with sigmoid-adaptive inertia weight for solving engineering design problems. Multimed Tools Appl 83, 3021–3055 (2024). https://doi.org/10.1007/s11042-021-11266-4

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