# Price's Transistor Modelling Problem

I. Mathematical Expression:

$$f(X)=\gamma^2(X)+\sum_{k=1}^{4}\left(\alpha^2_k(X)+\beta^2_k(X)\right)$$

where:

$$\bullet$$ $$\alpha_k(X)=\left(1-x_1x_2\right)x_3\left[e^{\displaystyle x_5\left(g_{1,k}-g_{3,k} \ x_7 \times 10^{-3} -g_{5,k} \ x_8 \times 10^{-3}\right)}-1\right]-g_{5,k}+g_{4,k} \ x_2$$

$$\bullet$$ $$\beta_k(X)=\left(1-x_1x_2\right)x_4\left[e^{\displaystyle x_6\left(g_{1,k}-g_{2,k}-g_{3,k} \ x_7 \times 10^{-3} +g_{4,k} \ x_9 \times 10^{-3}\right)}-1\right]-g_{5,k} \ x_1+g_{4,k}$$

$$\bullet$$ $$\gamma(X)=x_1x_3-x_2x_4$$

$$\bullet$$ The values of $$g$$ are tabulated in Table 1

$$\bullet$$ $$-10\leq x_i\leq 10$$ , $$i=1,2,\cdots,9$$

$$\bullet$$ $$f_{min}(X^*)=0$$

$$\bullet$$ $$x^*_i=(0.9,0.45,1,2,8,8,5,1,2)$$

II. References:

[1] M. M. Ali, C. Khompatraporn, and Z. B. Zabinsky, "A Numerical Evaluation of Several Stochastic Algorithms on Selected Continuous Global Optimization Test Problems," Journal of Global Optimization, vol. 31, no. 4, pp. 635-672, Apr. 2005.
[2] Ali R. Alroomi, "The Farm of Unconstrained Benchmark Functions," University of Bahrain, Electrical and Electronics Department, Bahrain, Oct. 2013. [Online]. Available: http://www.al-roomi.org/cv/publications