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gams:a_gams_implementation_of_the_example_model_mentioned_in_an_overview_of_genetic_algorithms_for_the_solution_of_optimisation_problems

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gams:a_gams_implementation_of_the_example_model_mentioned_in_an_overview_of_genetic_algorithms_for_the_solution_of_optimisation_problems [2007/09/27 05:08] (current)
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 +====== A MINLP GAMS implementation of the example model mentioned in "An overview of genetic algorithms for the solution of optimisation problems"​ ======
 +<​code>​
 +$ontext
 +An overview of genetic algorithms for the solution of optimisation problems
  
 +Simon Mardle and Sean Pascoe
 +University of Portsmouth
 +
 +http://​www.economicsnetwork.ac.uk/​cheer/​ch13_1/​ch13_1p16.htm
 +$offtext
 +
 +Set i boat class /i1*i3/
 +    j fish species /j1*j3/
 +
 +Parameter
 +    P(j) Price of fish species j / j1 2.5, j2 2, j3 1.5 /
 +    F(i) Fixed Costs of boat class i / i1 1, i2 0.8, i3 0.8 /
 +    V(i) Variable Costs of boat class i / i1 0.01, i2 0.008, i3 0.008 /
 +    K(j) Carrying capacity of fish species j / j1 2000, j2 2500, j3 4000 /
 +    R(j) Growth rate of fish species j / j1 0.1, j2 0.5, j3 0.3 /
 +    ue(i) upper bound on effort / i1 275, i2 160, i3 200 /;
 +
 +Table Q(i,j) Catchability coefficient of fish species j by boat class i
 +   ​j1 ​      ​j2 ​     j3
 +i1 0.0002 ​  ​0.0001
 +i2          0.0002 ​ 0.00005
 +i3                  0.0002
 +;
 +
 +Variable
 +    z     ​profit
 +    xb(i) boats
 +    xe(i) effort
 +    xf(j) fishing mortality
 +    xc(j) catch
 +    xl(j) landings;
 +Positive Variables xe,​xf,​xc,​xl;​
 +Integer Variables xb;
 +
 +Equation
 +    obj   ​revenue from landings minus the fixed and variable costs of the fishing
 +    e1(j) fishing mortality
 +    e2(j) evaluates catch from this fishing mortality rate
 +    e3(j) constrains landings to be no greater than catch;
 +
 +obj..       z =e= sum(j, P(j)*xl(j)) - sum(i, F(i)*xb(i) + V(i)*xe(i)*xb(i));​
 +e1(j).. xf(j) =e= sum(i, Q(i,​j)*xe(i)*xb(i));​
 +e2(j).. xc(j) =e= K(j)*xf(j) - K(j)/​R(j)*sqr(xf(j));​
 +e3(j).. xl(j) =l= xc(j);
 +
 +model fish /all/;
 +option optcr=0;
 +xe.up(i) = ue(i);
 +xl.up(j) = 500;
 +
 +xb.l(i)=uniform(1,​10);​
 +xe.l(i)=uniform(100,​200);​
 +
 +solve fish max z using rminlp;
 +fish.optcr=0; ​
 +solve fish max z using minlp;
 +</​code>​
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