eq1 = y3 + Log[y1/y2];
eq2 = y3 - y1 - 1;
eq3 = y2 + y1 + 2 y3^2;
f = (eq1)^2 + (eq2)^2 + (eq3)^2;

yvars={y1,y2,y3};

yrules={0<=y1<=1, 0<=y2<=1, 0<=y3<=1};

methods={"DifferentialEvolution","NelderMead","RandomSearch","SimulatedAnnealing"};

(*This will run NMinimize using the specified method: specified as an index into the methods list above. It will output the Method name, result of running NMinimize and time taken*)

nm1[method_, suppress_:0]:=Module[{r, TIMESTART, TIMEFINISH, RUNTIME, OUT},
 TIMESTART=Date[];
 If[suppress==0,{Print["Using ", methods[[method]]," :"]}]; 
 OUT=Timing[r=NMinimize[{f,yrules},yvars,Method->methods[[method]]]]; 
 RUNTIME=OUT[[1]];
 If[suppress==0,{Print[r]}];
 TIMEFINISH=Date[];
 If[suppress==0,{Print["Total Run time: ", RUNTIME]}];
 Return[Append[r, RUNTIME]];
]



nm1a[]:=Module[{ct1, ResList},
 ct1=0;
 ResList={};
 Label[o1];
 ct1=ct1+1;	
 r=nm1[ct1,1];
 AppendTo[ResList,r];
 If[ct1==1, SMALLEST=1];
 If[ResList[[ct1]][[1]]<ResList[[SMALLEST]][[1]], SMALLEST=ct1];
 If[ct1<Length[methods], Goto[o1]];

 ct1=0; 
 Print["***************"];
 Print[" Final Results:"];
 Label[o2];
 ct1=ct1+1;
 Print[methods[[ct1]]," : ",ResList[[ct1]][[1]]];
 Print[ResList[[ct1]][[2]]];
 Print["Time: ",ResList[[ct1]][[3]]];
 Print["________________________________________"];
 If[ct1<Length[methods],Goto[o2]];
 
 Print["Best: ", methods[[SMALLEST]]];

 Return[ResList[[SMALLEST]]];
]