minimise the peak value

[April Lee]

Dear Löfberg,

My problem is the mix-integer optimisation, where the simplified version is as follows:

int=0.25; % 24 h is cut into 96, and each is 15 min (0.25h)

start=[5];% start time 

arrival=[8];%arrival time

parking=[1:start,(arrival+1):96];

distance=[5]; %distance 

chargingrate=3.16;%kw

energycon=0.188;%kwh/km

capacity=24;%kwh

chargingeff=0.9;

% define variables and constraints

soc=sdpvar(1,96); Constraints1=[soc>0 & soc<=1];% constraint 1: state of charge(soc) should between 0 and 1 at any time period among [1,96]

u=intvar(1,96);   Constraints2=[];% constraint 2: u is binary,  u = {0 or 1} within parking period parking=[1:start,(arrival+1):96], and u = 0, othervise;

Constraints1=[Constraints1,soc(1,arrival)==1-energycon.*distance./capacity];

Constraints2=[Constraints2,u(1,1:arrival)==0];%1:41

Constraints1=[Constraints1,soc>0 & soc<=1];

for ii=arrival:95

Constraints1=[Constraints1,soc(1,ii+1) == soc(1,ii) + u(ii+1).*chargingrate*int];

end

ops = sdpsettings('verbose',1,'debug',1);

obj=max( sum(u,1).*chargingrate; %objective is to minimise the peak value among time period of [1,96];

optimize(Constraints1,Constraints2,obj),ops)

I got an error as:

Error using solvesdp (line 91)

Second argument (the objective function h) should be an sdpvar or logdet object (or empty).

Error in optimize (line 31)

[varargout{1:nargout}] = solvesdp(varargin{:}); 

Thank you! 

[Johan Löfberg]

Incorrect use of optimizer

https://yalmip.github.io/tutorial/basics/

[April Lee]

Thank you very much for your reply. I have revised it accordingly as:

My current code is :

int=0.25; % 24 h is cut into 96, and each is 15 min (0.25h)

start=[5,10,25];% start time 

arrival=[8,20,45];%arrival time

dis=[10,80,100]; %distance 

chargingrate=3.16;%kw

energycon=0.188;%kwh/km

capacity=24;%kwh

chargingeff=0.9;

u=binvar(1,96);

soc=sdpvar(1,96);

Constraints1=[];

Constraints1=[Constraints1,soc(1,arrival(1,1))==1-energycon.*dis(1,1)./capacity];

Constraints1=[Constraints1,u(1,1:arrival(1,1))==0];

Constraints1=[Constraints1,soc(1,arrival(1,1))>=0.5 &soc(arrival(1,1))<=1];

for jj=2:3

    Constraints1=[Constraints1,soc(1,start(1,jj))==soc(1,arrival(1,jj)-1)+sum(u(1,(arrival(1,jj-1)+1):start(1,jj))).*chargingrate*int];%43=43+

    Constraints1=[Constraints1,u(1,(start(1,jj)+1):arrival(1,jj))==0];

    Constraints1=[Constraints1,soc(1,arrival(1,jj))==soc(1,start(1,jj))-energycon.*dis(1,jj)./capacity];

    Constraints1=[Constraints1,soc(1,arrival(1,jj)) >= 0.5 & soc(1,arrival(1,jj)) <= 1];% constraint: soc should between 0 and 1

    Constraints1=[Constraints1,soc(1,start(1,jj)) >= 0.5 & soc(1,start(1,jj)) <= 1];% constraint: soc should between 0 and 1

end

ops = sdpsettings('solver','cplex','cachesolvers',11);

optimize(Constraints1,max(sum(u,1).*chargingrate),ops)

%u1=value(u)

%soc1=value(soc)

But there is still an error as:

Row 'c127' infeasible, all entries at implied bounds.

Presolve time = 0.00 sec. (0.02 ticks)

ans = 

  struct with fields:

    yalmiptime: 0.1150

    solvertime: 0.0135

          info: 'Infeasible problem (CPLEX-IBM)'

       problem: 1

[Johan Löfberg]

The solver finds your problem trivially infeasible as you have conflicting bounds or something similar to that

https://yalmip.github.io/debugginginfeasible/