How to solve multi-objective optimization problem of a single variable that can take only integer values?

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Vamshi Krishna Gudipati 2018-9-2

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/417208-how-to-solve-multi-objective-optimization-problem-of-a-single-variable-that-can-take-only-integer-va

评论： Vamshi Krishna Gudipati 2018-9-17

Hi,

I am trying to solve a multi-objective optimization problem where I only have a single variable that can take integer values. I tried the code provided by the Mathworks support team for imposing integer constraints which is written for two variables. I was able to use the functions provided in exampleIntGAMULTIOBJ.zip: @int_pop, @int_mutation, @int_crossoverarithmetic for solving problem with two variables. However, it doesn't work for the case of a single variable. What changes should I make to the functions provided to be able to make it work for single variable? Below is the link for the functions

https://www.mathworks.com/matlabcentral/answers/103369-is-it-possible-to-solve-a-mixed-integer-multi-objective-optimization-problem-using-global-optimizati

Thanks.

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Vamshi Krishna Gudipati 2018-9-11

在 MATLAB Online 中打开

function y = HB_RegionalLoss_InitialCost(x)
[sec_prop,~] = xlsread('AISC_Shapes_Database.xls','Database v14.1');
Upload1 = importdata('PGA_short.txt');  
Upload2 = importdata('Annual_exceedance_rate_short.txt');
PGA = Upload1.data;   % Discretized PGA values (same PGA range that is used to develop neural network )
ARE = Upload2.data;   % Annual rate of exceedance
% Probability of a pga value
PPGA(1) = 1-(1-exp(-0.528973));  % 0.528973 corresponds to 0.005 pga from the hazard curve
for i = 2:length(PGA)
    PPGA(i) = (1-exp(-ARE(i-1)))-(1-exp(-ARE(i)));
end
PPGA = PPGA';
r = 0.05; % discount rate
N = 50; % control period in years
%%Hospital Building
[HB_Designs,~] = xlsread('HB_Designs_sorted_short.xlsx');
HB_IC = xlsread('HB_Initial_Cost_short.xlsx');
HB_Initial_Cost = HB_IC(x(1)); % 2016 Cost Estimate
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Expected Failure Cost
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
Upload1 = importdata('1Drift.txt');
Upload2 = importdata('1Damage_ratio.txt');
Drift_vs_Damage =  [Upload1.data Upload2.data];
Upload1 = importdata('HB_2Damage_ratio.txt');
Upload2 = importdata('HB_2Recovery_time.txt');
Damage_vs_Recovery =  [Upload1.data Upload2.data];
Upload1 = importdata('3Damage_ratio.txt');
Upload2 = importdata('3Minor_injury_rate.txt');
Damage_vs_Minor_injury =  [Upload1.data Upload2.data];
Upload1 = importdata('4Damage_ratio.txt');
Upload2 = importdata('4Major_injury_rate.txt');
Damage_vs_Major_injury =  [Upload1.data Upload2.data];
Upload1 = importdata('5Damage_ratio.txt');
Upload2 = importdata('5Fatality_rate.txt');
Damage_vs_Fatality =  [Upload1.data Upload2.data];
Upload1 = importdata('HB_PWMinor_drift.txt');
Upload2 = importdata('HB_PWMinor_prob.txt');
Drift_vs_PWMinor_Damage =  [Upload1.data Upload2.data];
Upload1 = importdata('HB_PWModerate_drift.txt');
Upload2 = importdata('HB_PWModerate_prob.txt');
Drift_vs_PWModerate_Damage =  [Upload1.data Upload2.data];
Upload1 = importdata('HB_PWExtensive_drift.txt');
Upload2 = importdata('HB_PWExtensive_prob.txt');
Drift_vs_PWExtensive_Damage =  [Upload1.data Upload2.data];
Upload1 = importdata('HB_PWComplete_drift.txt');
Upload2 = importdata('HB_PWComplete_prob.txt');
Drift_vs_PWComplete_Damage =  [Upload1.data Upload2.data];
% fraction converted from one level of injury to other
Upload1 = importdata('11Damage_ratio.txt');
Upload2 = importdata('11Min_Maj_transfer.txt');
Damage_vs_Min_to_Maj_injury =  [Upload1.data Upload2.data];
Upload1 = importdata('12Damage_ratio.txt');
Upload2 = importdata('12Maj_Fat_transfer.txt');
Damage_vs_Maj_to_Fatality =  [Upload1.data Upload2.data];
% Ref. MCEER report (System performance under multi-hazard environments)
DrR = [0.7  2.5  5]; % Drift Ratio limits based on FEMA 356-2000
% Amplified factor=ratio of area of structure/MCEER demonstration hospital
% structural costs
Str_RC = (138^2)/(275*56.5)*[280000 1512000 67500000  67500000]; % repair cost
Str_IC = (138^2)/(275*56.5)*[0      4380000 203670000 203670000]; % Indirect cost
% HVAC 
HVAC_Chillers = ceil((138^2)/(275*56.5)*2); % rounded up to next integer
AL_HVAC = [2 4]; % acceleration limits
HVAC_RC = [90000    500000]; % HVAC repair cost per chiller
HVAC_IC = [139500   1395000]; % HVAC indirect cost per chiller
% Partition walls
PW_RC = [230  460  690  920]; % partition wall repair cost
PW_IC = [1500 3000 4500 4500]; % partition wall indirect cost 
% Piping
DL_P =  [1.1 2.2]; % drift ratio limits for existing system
P_RC =  (138^2)/(275*56.5)*[5380 12770 14050];     % piping repair cost for all the floors combinedly
P_IC =  (138^2)/(275*56.5)*[0 97650 1046250];      % piping indirect cost all floors
%
Max_CL = 1.85*HB_Initial_Cost;   % Loss of Contents for 100% damage (1.85 factor from ATC-13, Table 4.11)
Max_RC = 276544.5573;   % Relocation Cost per month for 100% damage
Max_MinIL = 854599.5;     % Minor Injury Loss for 100% damage
Max_MajIL = 8545995;    % Major Injury Loss for 100% damage
Max_DL = 4021781613;   % Death Loss for 100% damage
% Drift Prediction
for j = 1:length(PGA)
    NN_Input(j,:) =  [sec_prop(HB_Designs(x(1),1),10) sec_prop(HB_Designs(x(1),2),10) sec_prop(HB_Designs(x(1),3),10) sec_prop(HB_Designs(x(1),4),10) ...
        sec_prop(HB_Designs(x(1),5),10) sec_prop(HB_Designs(x(1),6),10) sec_prop(HB_Designs(x(1),7),10) sec_prop(HB_Designs(x(1),8),10) 50 PGA(j)];
end 
Drift_Output = HB_NNFcn_BR_Drift_Ratio(NN_Input');
Drift_ratio_HB = round(Drift_Output',2);   
Acc_Output = HB_NNFcn_BR_Abs_Acc(NN_Input');
Abs_Acc = round(Acc_Output',2);
for j = 1:length(Drift_ratio_HB)
    if Drift_ratio_HB(j)<0.2
        DmR = 0;
        HB_RT(j) = 0;
        MinIF = 0;
        MajIF = 0;
        DF = 0;
    elseif (Drift_ratio_HB(j)>=0.2) && (Drift_ratio_HB(j)<=5)
        DmR = Drift_vs_Damage(find(Drift_ratio_HB(j)==(Drift_vs_Damage(:,1)),1),2);
        HB_RT(j) = Damage_vs_Recovery(find(DmR==(Damage_vs_Recovery(:,1)),1),2);
          initial_MinIF = Damage_vs_Minor_injury(find(DmR==(Damage_vs_Minor_injury(:,1)),1),2);
          if DmR<0.006
              Min_to_MajIF = 0;
          else
              Min_to_MajIF = Damage_vs_Min_to_Maj_injury(find(DmR==(Damage_vs_Min_to_Maj_injury(:,1)),1),2);
          end
          MinIF = initial_MinIF*(1-Min_to_MajIF/100);
          if DmR<=0.8
          initial_MajIF = Damage_vs_Major_injury(find(DmR==(Damage_vs_Major_injury(:,1)),1),2);
          if DmR<0.005
              Maj_to_FatF = 0;
          else
              Maj_to_FatF = Damage_vs_Maj_to_Fatality(find(DmR==(Damage_vs_Maj_to_Fatality(:,1)),1),2);
          end
          MajIF = initial_MajIF*(1-Maj_to_FatF/100) + initial_MinIF*Min_to_MajIF/100; 
          DF = Damage_vs_Fatality(find(DmR==(Damage_vs_Fatality(:,1)),1),2);
          DF = DF + initial_MajIF*Maj_to_FatF/100;
          else
              % linear interpolation
              initial_MajIF = 0.04+((DmR-0.8)/0.2)*(0.4-0.04);
              Maj_to_FatF = 100;
              MajIF = initial_MajIF*(1-Maj_to_FatF/100) + initial_MinIF*Min_to_MajIF/100; 
              DF = 0.01+((DmR-0.8)/0.2)*(0.2-0.01);
              DF = DF + initial_MajIF*Maj_to_FatF/100;
          end
      else
          DmR = 1;
          HB_RT(j) = 723.4;
  %       Minor injury completely transferred into major injury and major injury into death        
  %       MinIF = 0.4; 
          MinIF = 0;
          MajIF = 0.4;
          DF = 0.2+0.4;           
      end
          CL(j) = Max_CL*DmR;
          RC(j) = Max_RC*HB_RT(j)/30; 
          MinIL(j) = Max_MinIL*MinIF;
          MajIL(j) = Max_MajIL*MajIF;
          DL(j) = Max_DL*DF;
      % Structural cost evaluation
      % Performance level identification
      c = find(Drift_ratio_HB(j)<DrR,1); % to find the index of the matrix DrR
      if isempty(c)==0          
          PL = c;   % Performance Level
      else PL = 4;  % Drift > 5
      end
      Src(j) = Str_RC(PL); % repair cost
      Sic(j) = Str_IC(PL); % indirect cost  
      % HVAC cost evaluation
      % Performance level identification
      c = find(Abs_Acc(j)<AL_HVAC,1);
      if isempty(c)==0          
          PL = c;   % Performance Level
      else PL = 3;  % Acc > 4
      end
      if PL==1
          HVACrc(j) = 0;
          HVACic(j) = 0;
      else
          HVACrc(j) = HVAC_Chillers*HVAC_RC(PL-1);
          HVACic(j) = HVAC_Chillers*HVAC_IC(PL-1);
      end
      % Partition wall cost evaluation
      PWrc(j) = 0;
      PWic(j) = 0;
      beds = ceil(138^2/(275*57.5)*93);
      levels = {'Minor' 'Moderate' 'Extensive' 'Complete'};
      for l=1:length(levels)
          upload1 = importdata(char(strcat('HB_PW',levels(l),'_drift.txt')));
          upload2 = importdata(char(strcat('HB_PW',levels(l),'_prob.txt'))); 
          e = upload1.data;
          f = upload2.data; 
          g = Drift_ratio_HB(j);
          % probability of exceedance damage state
          if g<=min(e)
              pds(l) = 0;
          elseif g>max(e)
              pds(l) = 1;
          else pds(l) = f(find(g==e,1));
          end   
      end
      % probability of each damage state
      pd = pds;
      for m=1:(length(levels)-1)
          pd(m) = pds(m) - pds(m+1);
      end
      PWrc(j) = pd*PW_RC';            
      PWic(j) = beds*pd*PW_IC';
      % Piping cost evaluation
      % Performance level identification
      Prc(j)=0;
      Pic(j)=0;
      c=find(Drift_ratio_HB(j)<DL_P,1);
      if isempty(c)==0          
          PL = c;   % Performance Level
      else PL = 3;  % Drift ratio > 2.2
      end
      Prc(j) = P_RC(PL);
      Pic(j) = P_IC(PL);                   
  end
HB_Annual_DD_Cost =  (Src+HVACrc+PWrc+Prc+CL+Sic+HVACic+PWic+Pic+RC+MinIL+MajIL+DL)*PPGA; % Direct+Indirect+Social including death loss damage cost
HB_Exp_DD_Cost = HB_Annual_DD_Cost/r*(1-(1/(1+r)^N));
% HB_Rest_Time = RT*PPGA;
y(1) = HB_Initial_Cost;
y(2) = HB_Exp_DD_Cost;