$(1)$ Solve the attached problems $($Problem $1,$ Problem $2$ and Problem $3)$ by using the algorithm you chose. For each problem, you must follow the following steps:

Step$1$: Try to find a best parameter set $($i$.$e$.$ population size, iteration limit$,$ etc.$).$

Step$2$: By using the parameters obtained in step $1,$ solve the problem for $25$ times $($Note: Values of the objective function and decision variables must be displayed on the command window at the end of each trial$).$

Step$3$: Give the best, worst and average solutions among the $25$ trials. Besides, compute the standard deviation of those.

Step$4$: For the best solution among the $25$ trials, give the values of decision variables and prove that this solution is feasible.

$(2)$ Prepare a project report including followings;

An introducton section $($briefly exlain what you've done in this project$).$

A summary of the algorithm you used in your Project $($basic explanations, algorithm steps, flow$-$charts, etc$)$

A section including all results obtained in Step$1,$ Step$2,$ Step$3$ and Step$4$ given above for each problem.

A Conclusion Section

References

$(3)$ Upload the followings to the assignment published on ESOGU UZEM in a single $.$rar file with a name of $151220xxxxx\_$project.rar.

Project Report

MATLAB folders for each Problem, seperately.

Name each folder as Problem$1,$ Problem$2$ and Problem$3.$

In each folder, a script file with a name "main$\_$ProblemX.m$"$ must be exist.

Your algorithm must solve the corresponding problem when this script is run.

After a solution is obtained, values of the objective function and decision variables must be displayed on the command window.

This problem solve Reptile Search Method use Matlab cofe

The Paper in which your algorithm is proposed.Problem $3$:

minf$(x_1,x_2,x_3,x_4,x_5,x_6,x_7,x_8,x_9,x_{10},x_{11},x_{12})=0\mathrm{.}15{\displaystyle \underset{i=1}{\overset{6}{}}}\frac{x_i}{(\frac{K_i}{T_i{x}_{i+6}}{)}^{0\mathrm{.}025}-1}$

Subject To

$x_i^{\text{m}\text{i}\text{n}}{x}_i{x}_i^{\text{m}\text{a}\text{x}},$AAi$=1,2,$dots,$12$

$\frac{0\mathrm{.}15x_1}{(\frac{K_1}{T_1{x}_7}{)}^{0\mathrm{.}025}-1}+0\mathrm{.}26\frac{0\mathrm{.}14x_5}{(\frac{S_5}{T_5{x}_{11}}{)}^{0\mathrm{.}020}-0\mathrm{.}95}$

$\frac{0\mathrm{.}15x_2}{(\frac{K_2}{T_2{x}_8}{)}^{0\mathrm{.}025}-1}+0\mathrm{.}25\frac{0\mathrm{.}14x_4}{(\frac{S_4}{T_4{x}_{10}}{)}^{0\mathrm{.}020}-0\mathrm{.}95}$

$\frac{0\mathrm{.}15x_3}{(\frac{K_3}{T_3{x}_9}{)}^{0\mathrm{.}025}-1}+0\mathrm{.}27\frac{0\mathrm{.}14x_1}{(\frac{S_1}{T_1{x}_7}{)}^{0\mathrm{.}020}-0\mathrm{.}95}$

$\frac{0\mathrm{.}15x_4}{(\frac{K_4}{T_4{x}_{10}}{)}^{0\mathrm{.}025}-1}+0\mathrm{.}30\frac{0\mathrm{.}14x_6}{(\frac{S_6}{T_6{x}_{12}}{)}^{0\mathrm{.}020}-0\mathrm{.}95}$

$\frac{0\mathrm{.}15x_5}{(\frac{K_5}{T_5{x}_{11}}{)}^{0\mathrm{.}025}-1}+0\mathrm{.}29\frac{0\mathrm{.}14x_3}{(\frac{S_3}{T_3{x}_9}{)}^{0\mathrm{.}020}-0\mathrm{.}95}$

$\frac{0\mathrm{.}15x_6}{(\frac{K_6}{T_6{x}_{12}}{)}^{0\mathrm{.}025}-1}+0\mathrm{.}28\frac{0\mathrm{.}14x_2}{(\frac{S_2}{T_2{x}_8}{)}^{0\mathrm{.}020}-0\mathrm{.}95}$

Where

$x_i^{\text{m}\text{i}\text{n}}=0\mathrm{.}9,$AAi$=1,2,$dots,$6$

$x_i^{\text{m}\text{a}\text{x}}=1\mathrm{.}2,$AAi$=1,2,$dots,$6$

$x_i^{\text{m}\text{i}\text{n}}=0\mathrm{.}015,$AAi$=6,7,$dots,$12$

$x_i^{\text{m}\text{a}\text{x}}=2,$AAi$=6,7,$dots,$12$

$\backslash$table$[[i,1,2,3,4,5,6],[T_i,60,40,40,60,40,80],[K_i,1978\mathrm{.}90,1525\mathrm{.}70,1683\mathrm{.}90,1815\mathrm{.}40,1499\mathrm{.}60,1766\mathrm{.}30],[S_i,175\mathrm{.}00,545\mathrm{.}00,617\mathrm{.}22,466\mathrm{.}17,384\mathrm{.}00,145\mathrm{.}34]]$