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This question tests the student's ability to solve Integer Programming problems applying Population-based Metaheuristics.

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P-{k}{kx}{k5}{k7}{k8}{a}{b}

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Solve the following Integer Programming problem:

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Maximize: $f(x,y) = \\simplify{{kx} x + {ky} y}$

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Subject to

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$\\simplify{{k5} x - y} \\ge \\var{k6}$

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$\\simplify{100*{k2} x + 100*{k1} y} \\le \\var{100*s}$

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$\\simplify{x^2 + y^2} \\le \\var{s4}$

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$\\simplify{100*{k11}/{a} x^2+(100*{k22}-100*{k11}*2) x + 100*{k11}y} \\le \\simplify{100*{ss} - 100*{k11*a}}$

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$x \\in [0,\\var{aup}],~~y \\in [0,\\var{bup}]$

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1. Click on \"End Exam\" and then \"Print this results summary\" (your problem will be extracted as pdf with all the necessary information/data). Do not worry about the \"Total 0/0 (0%)\" score, this pdf is only for generating a LP problem).
2. \n
3. Create your own implementation of a Population-based algorithm, in the language of your choice, and solve your problem and print the output.
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5. For the OnTrack task - submit the pdf from NAMBAS (i.e. your problem), your code and your best solution obtained; that is:
6. \n
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(i) Best soultion found is $(x, y) = (\\cdots, \\cdots)$

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(ii) Objevtive function value $f(x,y) = \\cdots$ (expected to be $\\ge \\var{tol}$)

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(iii) Checking all the constraints:

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$\\simplify{{k5} x - y} = \\cdots$ (expected to be $\\ge \\var{k6}$)

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$\\simplify{100*{k2} x + 100*{k1} y} = \\cdots$ (expected to be $\\le \\var{100*s}$)

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$\\simplify{x^2 + y^2} = \\cdots$ (expected to be $\\le \\var{s4}$)

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$\\simplify{100*{k11}/{a} x^2+(100*{k22}-100*{k11}*2) x + 100*{k11}y} = \\cdots$  (expected to be $\\le \\simplify{100*{ss} - 100*{k11*a}}$)

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