Genetic algorithm for non linear model optimisation

Hello everyone

Dealing with clinical data; I try to optimize a non-linear model with a genetic algorithm. Indeed, after identifying a satisfactory non-linear model (IDNLARX with 2 inputs and 4 outputs), I try to identify the most favorable conditions in terms of input (Synchro_input) for drug consumption (Synchro_output (:, 2) named 'NAD') to ensure a high blood pressure values (Synchro_output (1), named 'PAM'). My fitness function is to minimise the ratio of NAD/PAM.

The algorithm did not function well and here is the warning: ----------------------------------------

    Warning: You have more channels than data.
    Check if data matrix should be transposed.
    > In @iddata\private\datachk at 26
      In iddata.pvset at 141
      In iddata.set at 142
      In iddata.subsasgn at 72
      In idnlarx.sim at 327
      In IDNLARX_fitness at 14
      In gads\private\validate>@(x)fitness(x,FitnessFcnArgs{:}) at 119
      In gads\private\fcnvectorizer at 12
      In gads\private\stepGA at 45
      In gads\private\galincon at 63
      In ga at 306
      In gads\private\gaguirun at 38
      In gadsswitchyard at 13

---------------------------- here is the fitness function:

    function y = IDNLARX_fitness(x)
    Synchro_input=[0.710280000000000,0.526234000000000;0.710280000000000,0.526234000000000;0.710280000000000,0.526234000000000;0.710280000000000,0.526234000000000;0.710280000000000,0.360519000000000;0.728972000000000,0.360519000000000;0.710280000000000,0.360519000000000;0.598131000000000,0.360519000000000;0.448598000000000,0.360519000000000;0.366355000000000,0.360519000000000;0.411215000000000,0.360519000000000;0.443258000000000,0.360519000000000;0.448598000000000,0.360519000000000;0.444444000000000,0.360519000000000;0.456075000000000,0.315065000000000;0.455395000000000,0.315065000000000;0.464174000000000,0.315065000000000;0.477354000000000,0.315065000000000;0.474479000000000,0.315065000000000;0.471603000000000,0.315065000000000;0.489097000000000,0.315065000000000;0.501558000000000,0.315065000000000;0.507788000000000,0.315065000000000;0.467290000000000,0.315065000000000;0.439252000000000,0.315065000000000;0.411215000000000,0.719394000000000;0.386293000000000,0.719394000000000;0.370433000000000,0.719394000000000;0.356839000000000,0.719394000000000;0.336449000000000,0.719394000000000;0.303219000000000,0.719394000000000;0.252336000000000,0.719394000000000;0.197597000000000,0.719394000000000;0.197597000000000,0.719394000000000;0.186916000000000,0.719394000000000;0.192256000000000,0.719394000000000;0.213618000000000,0.719394000000000;0.229640000000000,1;0.277704000000000,1;0.336449000000000,1;0.373832000000000,1;0.406542000000000,1;0.431983000000000,1;0.452336000000000,1;0.492778000000000,1;0.526480000000000,1;0.554996000000000,1;0.603882000000000,1;0.652768000000000,1;0.687275000000000,0.963636000000000;0.707405000000000,0.963636000000000;0.718907000000000,0.963636000000000;0.733285000000000,0.963636000000000;0.750539000000000,0.963636000000000;0.741912000000000,0.963636000000000;0.724659000000000,0.963636000000000;0.710280000000000,0.963636000000000;0.687275000000000,0.963636000000000;0.658519000000000,0.963636000000000;0.626887000000000,0.963636000000000;0.598131000000000,0.963636000000000;0.578001000000000,0.948918000000000;0.563863000000000,0.948918000000000;0.582555000000000,0.948918000000000;0.598131000000000,0.948918000000000;0.601246000000000,0.948918000000000;0.613707000000000,0.948918000000000;0.641745000000000,0.948918000000000;0.676012000000000,0.948918000000000;0.707165000000000,0.948918000000000;0.725857000000000,0.948918000000000;0.747664000000000,0.948918000000000;0.769470000000000,0.948918000000000;0.791277000000000,0.960173000000000;0.803738000000000,0.960173000000000;0.796549000000000,0.960173000000000;0.787922000000000,0.960173000000000;0.785047000000000,0.960173000000000;0.759166000000000,0.960173000000000;0.747664000000000,0.960173000000000;0.759166000000000,0.960173000000000;0.756290000000000,0.960173000000000;0.756290000000000,0.960173000000000;0.744788000000000,0.960173000000000;0.739037000000000,0.960173000000000;0.733285000000000,0.960173000000000;0.730410000000000,0.960173000000000;0.721783000000000,0.960173000000000;0.710280000000000,0.960173000000000;0.698778000000000,0.960173000000000;0.704529000000000,0.960173000000000;0.716032000000000,0.960173000000000;0.687275000000000,0.960173000000000;0.655643000000000,0.960173000000000;0.644141000000000,0.960173000000000;0.626887000000000,0.960173000000000;0.621136000000000,0.479654000000000;0.612509000000000,0.479654000000000;0.647017000000000,0.479654000000000;0.644860000000000,0.479654000000000;0.644860000000000,0.479654000000000;0.652506000000000,0.479654000000000;0.618522000000000,0.479654000000000;0.594393000000000,0.479654000000000;0.598131000000000,0.479654000000000;0.589823000000000,0.479654000000000;0.610592000000000,0.479654000000000;0.623053000000000,0.479654000000000;0.618899000000000,0.352900000000000;0.618899000000000,0.352900000000000;0.621495000000000,0.352900000000000;0.551402000000000,0.352900000000000;0.560748000000000,0.352900000000000;0.564901000000000,0.352900000000000;0.557009000000000,0.352900000000000;0.575701000000000,0.352900000000000;0.557349000000000,0.352900000000000;0.542056000000000,0.352900000000000;0.542056000000000,0.352900000000000;0.529595000000000,0.352900000000000;0.510903000000000,0.352900000000000;0.507788000000000,0.352900000000000;0.510903000000000,0.352900000000000;0.520489000000000,0.352900000000000;0.529116000000000,0.352900000000000;0.534867000000000,0.352900000000000;0.531991000000000,0.352900000000000;0.537743000000000,0.352900000000000;0.554996000000000,0.352900000000000;0.569375000000000,0.352900000000000;0.598131000000000,0.352900000000000;0.612509000000000,0.352900000000000;0.632638000000000,0.352900000000000;0.652768000000000,0.352900000000000;0.655643000000000,0.352900000000000;0.655643000000000,0.352900000000000;0.649892000000000,0.352900000000000;0.644141000000000,0.352900000000000;0.644141000000000,0.352900000000000;0.661395000000000,0.352900000000000;0.672897000000000,0.352900000000000;0.675773000000000,0.352900000000000;0.684400000000000,0.352900000000000;0.675773000000000,0.352900000000000;0.678648000000000,0.352900000000000;0.655643000000000,0.352900000000000;0.644141000000000,0.352900000000000;0.655643000000000,0.352900000000000;0.667146000000000,0.352900000000000;0.681524000000000,0.352900000000000;0.687275000000000,0.352900000000000;0.690151000000000,0.352900000000000;0.681524000000000,0.352900000000000;0.678648000000000,0.352900000000000;0.675773000000000,0.352900000000000;0.675773000000000,0.352900000000000;0.672897000000000,0.352900000000000;0.672897000000000,0.352900000000000;];
    Synchro_output=[0.931001000000000,0.146341000000000,0.191587000000000,0.362782000000000;0.968681000000000,0.146341000000000,0.193229000000000,0.367078000000000;0.986543000000000,0.146341000000000,0.206679000000000,0.371375000000000;1,0.146341000000000,0.220130000000000,0.380773000000000;0.992510000000000,0.150094000000000,0.233580000000000,0.390172000000000;0.979679000000000,0.153846000000000,0.247030000000000,0.399570000000000;0.966883000000000,0.157598000000000,0.260480000000000,0.408969000000000;0.960455000000000,0.161351000000000,0.264495000000000,0.418367000000000;0.955368000000000,0.171357000000000,0.268510000000000,0.427766000000000;0.947107000000000,0.181363000000000,0.272525000000000,0.437164000000000;0.933988000000000,0.247029000000000,0.276540000000000,0.446563000000000;0.926743000000000,0.312695000000000,0.288347000000000,0.478518000000000;0.921752000000000,0.378361000000000,0.300155000000000,0.510473000000000;0.898625000000000,0.444028000000000,0.334501000000000,0.538937000000000;0.885814000000000,0.509694000000000,0.368848000000000,0.567401000000000;0.876496000000000,0.575360000000000,0.403194000000000,0.595865000000000;0.864517000000000,0.641026000000000,0.437540000000000,0.624329000000000;0.863851000000000,0.702939000000000,0.460078000000000,0.652793000000000;0.845882000000000,0.764853000000000,0.482617000000000,0.681257000000000;0.830242000000000,0.826767000000000,0.505156000000000,0.709721000000000;0.823088000000000,0.888680000000000,0.527694000000000,0.738185000000000;0.828745000000000,0.944340000000000,0.550233000000000,0.766649000000000;0.814769000000000,1,0.572771000000000,0.795113000000000;0.801458000000000,1,0.595310000000000,0.816058000000000;0.796633000000000,1,0.617848000000000,0.831096000000000;0.779163000000000,1,0.662524000000000,0.846133000000000;0.764355000000000,0.988118000000000,0.707200000000000,0.861171000000000;0.748383000000000,0.976235000000000,0.751875000000000,0.876208000000000;0.739731000000000,0.964353000000000,0.774012000000000,0.891246000000000;0.735072000000000,0.952470000000000,0.796149000000000,0.906284000000000;0.735405000000000,0.940588000000000,0.818286000000000,0.921321000000000;0.736570000000000,0.928705000000000,0.840423000000000,0.936359000000000;0.730580000000000,0.916823000000000,0.862560000000000,0.951396000000000;0.720597000000000,0.879300000000000,0.884698000000000,0.966434000000000;0.715772000000000,0.841776000000000,0.906835000000000,0.981472000000000;0.713942000000000,0.804253000000000,0.928972000000000,1;0.707619000000000,0.777361000000000,0.951109000000000,0.995972000000000;0.699799000000000,0.750469000000000,0.967406000000000,0.991944000000000;0.693643000000000,0.723577000000000,0.983703000000000,0.987916000000000;0.678835000000000,0.708568000000000,1,0.983888000000000;0.658870000000000,0.693558000000000,0.994160000000000,0.979860000000000;0.653046000000000,0.678549000000000,0.988320000000000,0.975832000000000;0.651216000000000,0.663540000000000,0.982480000000000,0.971805000000000;0.652214000000000,0.648530000000000,0.976640000000000,0.967777000000000;0.649053000000000,0.633521000000000,0.970800000000000,0.963749000000000;0.649219000000000,0.611007000000000,0.964960000000000,0.959721000000000;0.655542000000000,0.604753000000000,0.959120000000000,0.955693000000000;0.664859000000000,0.598499000000000,0.953280000000000,0.945220000000000;0.672014000000000,0.592245000000000,0.947440000000000,0.942266000000000;0.674010000000000,0.575360000000000,0.936655000000000,0.939313000000000;0.681997000000000,0.558474000000000,0.925869000000000,0.936359000000000;0.684326000000000,0.536585000000000,0.915083000000000,0.933405000000000;0.688153000000000,0.514697000000000,0.910138000000000,0.930451000000000;0.700465000000000,0.492808000000000,0.905192000000000,0.927497000000000;0.708784000000000,0.470919000000000,0.900246000000000,0.924544000000000;0.717103000000000,0.449031000000000,0.895301000000000,0.921590000000000;0.722926000000000,0.427142000000000,0.890355000000000,0.918636000000000;0.736237000000000,0.395247000000000,0.885409000000000,0.915682000000000;0.749547000000000,0.370857000000000,0.880464000000000,0.912728000000000;0.762192000000000,0.355847000000000,0.875518000000000,0.901719000000000;0.780328000000000,0.340838000000000,0.870572000000000,0.887218000000000;0.796633000000000,0.318324000000000,0.864951000000000,0.872718000000000;0.802124000000000,0.295810000000000,0.859330000000000,0.858217000000000;0.813604000000000,0.273296000000000,0.853709000000000,0.843716000000000;0.822921000000000,0.255785000000000,0.853034000000000,0.829216000000000;0.835400000000000,0.233896000000000,0.852359000000000,0.814715000000000;0.846548000000000,0.212008000000000,0.851684000000000,0.800215000000000;0.856198000000000,0.190119000000000,0.851008000000000,0.785714000000000;0.868510000000000,0.168230000000000,0.850333000000000,0.771214000000000;0.880157000000000,0.146341000000000,0.849658000000000,0.756713000000000;0.886313000000000,0.153221000000000,0.848983000000000,0.747046000000000;0.875498000000000,0.160100000000000,0.848307000000000,0.737379000000000;0.880989000000000,0.166979000000000,0.847632000000000,0.734157000000000;0.889640000000000,0.173859000000000,0.835624000000000,0.730934000000000;0.894465000000000,0.172608000000000,0.823615000000000,0.727712000000000;0.906944000000000,0.171357000000000,0.811607000000000,0.724490000000000;0.917759000000000,0.170106000000000,0.800274000000000,0.721267000000000;0.930237000000000,0.168856000000000,0.788941000000000,0.718045000000000;0.929572000000000,0.171982000000000,0.777607000000000,0.714823000000000;0.931735000000000,0.175109000000000,0.766274000000000,0.711600000000000;0.932899000000000,0.188868000000000,0.754941000000000,0.708378000000000;0.939056000000000,0.202627000000000,0.743608000000000,0.705156000000000;0.935894000000000,0.210757000000000,0.732275000000000,0.703276000000000;0.932255000000000,0.205754000000000,0.720942000000000,0.701396000000000;0.924109000000000,0.190744000000000,0.703568000000000,0.707573000000000;0.917350000000000,0.175735000000000,0.686194000000000,0.713749000000000;0.907991000000000,0.160725000000000,0.668820000000000,0.719925000000000;0.909377000000000,0.156348000000000,0.651446000000000,0.726101000000000;0.905044000000000,0.151970000000000,0.645406000000000,0.732277000000000;0.904525000000000,0.147592000000000,0.639365000000000,0.738453000000000;0.903658000000000,0.143215000000000,0.633324000000000,0.744629000000000;0.900192000000000,0.138837000000000,0.627284000000000,0.750806000000000;0.899152000000000,0.135084000000000,0.621243000000000,0.756982000000000;0.893259000000000,0.120700000000000,0.615202000000000,0.763158000000000;0.889273000000000,0.106316000000000,0.609161000000000,0.770408000000000;0.885807000000000,0.0975610000000000,0.603121000000000,0.772825000000000;0.894299000000000,0.0888055000000000,0.589634000000000,0.775242000000000;0.896899000000000,0.0900563000000000,0.576147000000000,0.777658000000000;0.901578000000000,0.0856785000000000,0.562661000000000,0.780075000000000;0.896725000000000,0.0813008000000000,0.555215000000000,0.782492000000000;0.890139000000000,0.0819262000000000,0.547769000000000,0.784909000000000;0.880954000000000,0.0825516000000000,0.540323000000000,0.787325000000000;0.874021000000000,0.0831770000000000,0.532877000000000,0.789742000000000;0.870728000000000,0.0838024000000000,0.525431000000000,0.792159000000000;0.861889000000000,0.0844278000000000,0.517985000000000,0.794576000000000;0.857037000000000,0.0838024000000000,0.510539000000000,0.796992000000000;0.843171000000000,0.0819262000000000,0.503093000000000,0.787057000000000;0.847712000000000,0.0787992000000000,0.495647000000000,0.775779000000000;0.848877000000000,0.0756723000000000,0.500557000000000,0.764501000000000;0.850541000000000,0.0669168000000000,0.505466000000000,0.753222000000000;0.847213000000000,0.0581614000000000,0.510375000000000,0.741944000000000;0.847546000000000,0.0550344000000000,0.522730000000000,0.730666000000000;0.850707000000000,0.0519074000000000,0.535085000000000,0.719388000000000;0.854368000000000,0.0487805000000000,0.547440000000000,0.708110000000000;0.856697000000000,0.0456535000000000,0.559796000000000,0.696831000000000;0.854201000000000,0.0425266000000000,0.572151000000000,0.685553000000000;0.861688000000000,0.0393996000000000,0.584506000000000,0.674275000000000;0.860191000000000,0.0362727000000000,0.596861000000000,0.662997000000000;0.861356000000000,0.0337711000000000,0.609216000000000,0.654135000000000;0.860191000000000,0.0325203000000000,0.621571000000000,0.644200000000000;0.867844000000000,0.0325203000000000,0.634839000000000,0.634264000000000;0.868676000000000,0.0325203000000000,0.648107000000000,0.624329000000000;0.870839000000000,0.0325203000000000,0.661374000000000,0.614393000000000;0.865848000000000,0.0325203000000000,0.662287000000000,0.604458000000000;0.872503000000000,0.0325203000000000,0.663199000000000,0.594522000000000;0.872503000000000,0.0325203000000000,0.664112000000000,0.584586000000000;0.865016000000000,0.0325203000000000,0.665024000000000,0.574651000000000;0.865182000000000,0.0325203000000000,0.665937000000000,0.564715000000000;0.864018000000000,0.0325203000000000,0.666849000000000,0.554780000000000;0.868344000000000,0.0325203000000000,0.667762000000000,0.544844000000000;0.870174000000000,0.0325203000000000,0.668674000000000,0.545918000000000;0.879325000000000,0.0325203000000000,0.669587000000000,0.559345000000000;0.879990000000000,0.0325203000000000,0.660480000000000,0.572771000000000;0.881488000000000,0.0325203000000000,0.651373000000000,0.586198000000000;0.887977000000000,0.0325203000000000,0.642267000000000,0.599624000000000;0.896129000000000,0.0325203000000000,0.632247000000000,0.613050000000000;0.900122000000000,0.0325203000000000,0.622228000000000,0.626477000000000;0.901786000000000,0.0325203000000000,0.612209000000000,0.639903000000000;0.900122000000000,0.0325203000000000,0.602190000000000,0.653330000000000;0.901121000000000,0.0325203000000000,0.592171000000000,0.666756000000000;0.909273000000000,0.0325203000000000,0.582152000000000,0.680183000000000;0.908608000000000,0.0325203000000000,0.572132000000000,0.693609000000000;0.913433000000000,0.0325203000000000,0.562113000000000,0.697637000000000;0.914598000000000,0.0325203000000000,0.552094000000000,0.699248000000000;0.919922000000000,0.0325203000000000,0.543060000000000,0.700859000000000;0.915929000000000,0.0325203000000000,0.534027000000000,0.702470000000000;0.911103000000000,0.0325203000000000,0.524993000000000,0.708244000000000;0.907110000000000,0.0325203000000000,0.525979000000000,0.714519000000000;0.906278000000000,0.0325203000000000,0.526964000000000,0.721365000000000;0.903783000000000,0.0325203000000000,0.527950000000000,0.728863000000000;0.903284000000000,0.0325203000000000,0.528935000000000,0.737111000000000;0.913433000000000,0.0325203000000000,0.529921000000000,0.746226000000000;0.909273000000000,0.0325203000000000,0.530906000000000,0.756355000000000;0.903783000000000,0.0325203000000000,0.531892000000000,0.767675000000000;0.899457000000000,0.0325203000000000,0.532877000000000,0.780411000000000;0.895131000000000,0.0325203000000000,0.533863000000000,0.776495000000000;0.894965000000000,0.0325203000000000,0.539849000000000,0.772019000000000;0.892469000000000,0.0325203000000000,0.545834000000000,0.766855000000000;];
    S_ECLS = iddata(Synchro_output(1:80,:), Synchro_input(1:80,:), 300,'Name','S_ECLS');
    S_ECLS.InputName={'PAPd','PCT'};
    S_ECLS.OutputName={'PAM','NAD','CRP','Xray'};
    S_ECMO = iddata(Synchro_output(81:158,:), Synchro_input(81:158,:), 300, 'Name', 'S_ECMO');
    S_ECMO.InputName={'PAPd','PCT'};
    S_ECMO.OutputName={'PAM','NAD','CRP','Xray'};
    nk=[1 1;1 1;1 1;1 1];
    nb=[2 2;2 2;2 2;2 2];
    na=[2 0 0 0;0 2 0 0;0 0 2 0;0 0 0 2];
    SynchroNLARX = nlarx(S_ECLS,[na nb nk], wavenet);
    t=sim(SynchroNLARX,[x(1) x(2)]);
    y=min((t(:,2)+0.1)./(t(:,1)+0.1));

------------- Thanks for any help.

[Matt J]

Seems doubtful that you've shown your actual code. This line

 SynchroNLARX = nlarx(S_ECLS,[na nb nk], wavenet);

should have given an error, since 'wavenet' is not enclosed in quotes.

[Matt J]

Abdelmoumen Commented

Hello Really, there's nothing doubtful, but the only trouble is to find help by allowing anyone to manipulate data whose usefulness remains confidential.The only warnings were those declared above. The wavenet doesn't generate a special error.

[Matt J]

I have run your code, and I get

Undefined function or variable 'wavenet'.

Error in test>IDNLARX_fitness (line 19)
    SynchroNLARX = nlarx(S_ECLS,[na nb nk], wavenet);

So, I still don't think you have provided code that let's one reproduce your issue.

In any case, the warning you see is coming from sim(), not from ga() itself. You could use "dbstop if warning" to trap the occurence of the warning and to examine what exactly is being fed to sim at that point in the code.

[Matt J]

Abdelmoumen Commented

Thanks Matt for reply, I have changed my code as follow:

SynchroNLARX = nlarx(S_ECLS,[na nb nk],'wavenet');
t=sim(SynchroNLARX,[x(1) x(2) x(3) x(4) x(5) x(6) x(7) x(8) x(9) x(10);x(11) x(12) x(13) x(14) x(15) x(16) x(17) x(18) x(19) x(20)]');
t(1:2,:)=[] remove the two first lines;
y=min((t(:,2)+0.1)./(t(:,1)+0.1));

The only remaining error is: Error using ==> makeState at 55 Your fitness function must return a scalar value.

any suggestions will be helpfull.

Answer 1

[Matt J]

The only remaining error is: Error using makeState at 55 Your fitness function must return a scalar value. any suggestions will be helpfull.

Modify your code as follows and re-run. If it stops at the K>> prompt and displays a value for y and size_t, tell us what's displayed.

 t(1:2,:)=[]; %remove the two first lines;

 y=min((t(:,2)+0.1)./(t(:,1)+0.1));

 if ~isscalar(y) | ~isfinite(y)

    size_t=size(t),
    y,
    keyboard

 end

Answer 2

[Abdelmoumen]

Relocated to Comment by Matt J

Answer 3

[Abdelmoumen]

Relocated to Comment by Matt J

Answer 4

[Abdelmoumen]

Thanks Matt you for your all. I changed the code as you suggested me, and It does not work. The error results in fact from an error in the number of variables i indicated (2) witch does not correspond to the real number of variables (20) in the sim line, x (1) ... x (20). ..............

t = sim (SynchroNLARX, [x (1) x (2) x (3) x (4) x (5) x (6) x (7) x (8) x (9) x (10) x (11) x (12) x (13) x (14) x (15) x (16) x (17) x (18) x (19) x (20)] ')

............

It works well now

The genetic algorithm is surprising.