A novel life choice-based optimizer

Abstract

This paper presents a novel metaheuristic algorithm named as life choice-based optimizer (LCBO) developed on the typical decision-making ability of humans to attain their goals while learning from fellow members. LCBO is investigated on 29 popular benchmark functions which included six CEC-2005 functions, and its performance has been benchmarked against seven optimization techniques including recent ones. Further, different abilities of LCBO optimization algorithm such as exploitation, exploration and local minima avoidance were also investigated and have been reported. In addition to this, scalability is tested for several benchmark functions where dimensions have been varied till 200. Furthermore, two engineering optimization benchmark problems, namely pressure vessel design and cantilever beam design, were also optimized using LCBO and the results have been compared with recently reported other algorithms. The obtained comparative results in all the above-mentioned experimentations revealed the clear superiority of LCBO over the other considered metaheuristic optimization algorithms. Therefore, based on the presented investigations, it is concluded that LCBO is a potential optimizer for engineering problems.

Appendix

The engineering problems used in this paper are pressure vessel design and cantilever beam design. The mathematical details of these engineering problems have been presented. The mathematical equations of constraints, range space and cost function to be minimized are given below.

1.1 Pressure vessel design

The objective of this problem is to minimize the total cost consisting of material, forming and welding of a cylindrical vessel as in Fig. 6. Both ends of the vessel are capped, and the head has a hemispherical shape. There are four variables in this problem, namely thickness of the shell ($T_{s}$), thickness of the head ($T_{h}$), inner radius ($R$) and length of the cylindrical section without considering the head ($L$). The function $f\left( {T_{s} ,T_{h} ,R,L} \right)$ is to be minimized subjected to the following four constraints $g1$, $g2$, $g3$ and $g4$ and variable ranges:

Fig. 6

Pressure vessel design problem

$$ f\left( {T_{s} ,T_{h} ,R,L} \right) = 0.6224\;T_{s} RL + 1.7781\;T_{h} R^{2} + 3.1661\;{\text{T}}_{s}^{2} L + T_{h} + 19.84\;T_{h}^{2} L $$

$$ g1 = - T_{h} + 0.0193\;R \le 0 $$

$$ g2 = - T_{h} + 0.0095\;R \le 0 $$

$$ g3 = - \pi R^{2} L - \frac{4}{3}\pi R^{3} + 1296000 \le 0 $$

$$ g4 = L - 240 \le 0 $$

$$ 1*0.0625 \le T_{s} ,T_{h} \le 99*0.0625 \;{\text{and}}\;10 \le R,\;L \le 200 $$

1.2 Cantilever beam design

The cantilever beam shown in Fig. 7 is made of five elements, each having a hollow cross section with constant thickness. There is external force acting at the free end of the cantilever. The weight of the beam is to be minimized while assigning an upper limit on the vertical displacement of the free end. The design variables are the heights (or widths) $x_{i}$ of the cross section of each element. Another interesting requirement is the lower bounds on these design variables are very small and the upper bounds very large so they do not become active in the problem. The problem is formulated using classical beam theory as follows:

Fig. 7

Cantilever beam design problem

$$ f\left( x \right) = 0.0624*\left( {x_{1} + x_{2} + x_{3} + x_{4} + x_{5} } \right) $$

subjected to the following constraint and range of variables:

$$ \begin{aligned} & g\left( x \right) = \frac{61}{{x_{1}^{3} }} + \frac{37}{{x_{2}^{3} }} + \frac{19}{{x_{3}^{3} }} + \frac{7}{{x_{4}^{3} }} + \frac{1}{{x_{5}^{3} }} - 1 \le 0 \\ & 0.01 \le {\text{x}}_{1} , {\text{x}}_{2} ,{\text{x}}_{3} ,x_{4} ,x_{5 } \le 100 \\ \end{aligned} $$