YALMIP INTEGRATION WITH MOSEK: THE TERMINATION CONDITION FAILS TO STOP THE SOLUTION PROCESS

[YuenLiSze]

Hi Professor，

I'm working on an optimization problem using YALMIP with MOSEK as the solver in MATLAB. Despite setting specific termination conditions in ops, the solver doesn't stop as expected when these conditions are met.

Environment:

• MATLAB: R2023b
• YALMIP: [latest version,20230622]
• MOSEK: [latest version,10.1.28]

The solver continues past the maximum time I've set (MSK_DPAR_OPTIMIZER_MAX_TIME and MSK_DPAR_MIO_MAX_TIME both set to 300). Not only that, but I tried controlling other parameters of the solver to terminate the code run, and it didn't work either.Here's how I'm setting my ops:

ops = sdpsettings('solver','mosek', ...
'mosek.MSK_DPAR_OPTIMIZER_MAX_TIME', 300, ...
'mosek.MSK_DPAR_MIO_MAX_TIME',300, ...
'mosek.MSK_DPAR_MIO_TOL_REL_GAP', 1e-4, ...
'mosek.MSK_IPAR_MIO_MAX_NUM_BRANCHES',500000, ...
'mosek.MSK_IPAR_MIO_MAX_NUM_RELAXS',500000);

Attempted Solutions:

Verified ops settings are correctly applied by inspecting the structure in the workspace.
Checked YALMIP and MOSEK for compatibility issues; both are up to date.
I'm looking for any insights on why these termination conditions might not be respected by the solver, or if there's any known issue with these specific settings in YALMIP's integration with MOSEK.

Thanks in advance for your help!

The entire function code:
function [p_wt,p_pv,p_load,x,UB,p_g,p_ch,p_dis,p_buy,p_sell] = down_layer1_checked(ee_bat_int,p_wt_int,p_pv_int,p_g_int,LB,yita)

optimize_paremeters;
p_bat_int = ee_bat_int0.21;
ee0 = 0.55ee_bat_int;

p_ch = sdpvar(24,4);
p_dis = sdpvar(24,4);
uu_bat = binvar(24,4);

uu_m = binvar(24,4);
p_buy = sdpvar(24,4);
p_sell = sdpvar(24,4);
p_wt = sdpvar(24,4);
p_pv = sdpvar(24,4);
p_load = sdpvar(24,4);

p_g = sdpvar(24,4);

p_l = xlsread('4typicalday.xlsx','0%','B3:E26')*900;
max_p_wt = xlsread('4typicalday.xlsx','0%','H3:K26')*p_wt_int;
max_p_pv = xlsread('4typicalday.xlsx','0%','N3:Q26')*p_pv_int;
price = [0.48;0.48;0.48;0.48;0.48;0.48;0.48;0.9;1.35;1.35;1.35;0.9;0.9;0.9;0.9;0.9;0.9;0.9;1.35;1.35;1.35;1.35;1.35;0.48];

C = [];
load = p_l';

wwt = 0.05;wpv = 0.1;wl = 0.15;
C = [C, (1 - wwt)*max_p_wt <= p_wt,p_wt <= (1 + wwt)*max_p_wt];
C = [C, (1 - wpv)*max_p_pv <= p_pv,p_pv <= (1 + wpv)*max_p_pv];
C = [C, (1 - wl)*load' <= p_load,p_load <= (1 + wl)*load'];

lam1 = sdpvar(96,1);lam11 = sdpvar(96,1);
lam2 = sdpvar(192,1);lam21 = sdpvar(192,1);lam3 = sdpvar(4,1);
lam4 = sdpvar(192,1);lam41 = sdpvar(192,1);lam5 = sdpvar(96,1);
lam51 = sdpvar(96,1);lam6 = sdpvar(96,1);

beta1 = binvar(96,1);beta11 = binvar(96,1);
beta2 = binvar(192,1);beta21 = binvar(192,1);beta3 = binvar(4,1);
beta4 = binvar(192,1);beta41 = binvar(192,1);beta5 = binvar(96,1);
beta51 = binvar(96,1);beta6 = binvar(96,1);beta7 = binvar(480,1);beta8 = binvar(288,1);

x = [p_buy(:,1)' p_sell(:,1)' p_g(:,1)' p_ch(:,1)' p_dis(:,1)' p_buy(:,2)' p_sell(:,2)' p_g(:,2)' p_ch(:,2)' p_dis(:,2)' p_buy(:,3)' p_sell(:,3)' p_g(:,3)' p_ch(:,3)' p_dis(:,3)' p_buy(:,4)' p_sell(:,4)' p_g(:,4)' p_ch(:,4)' p_dis(:,4)']';
u = [p_wt(:,1)' p_pv(:,1)' p_load(:,1)' p_wt(:,2)' p_pv(:,2)' p_load(:,2)' p_wt(:,3)' p_pv(:,3)' p_load(:,3)' p_wt(:,4)' p_pv(:,4)' p_load(:,4)']';

P = [price' -price' (c_g_om+c_fuel).*ones(1,24) c_bat_om.*ones(1,48)...
price' -price' (c_g_om+c_fuel).*ones(1,24) c_bat_om.*ones(1,48)...
price' -price' (c_g_om+c_fuel).*ones(1,24) c_bat_om.*ones(1,48)...
price' -price' (c_g_om+c_fuel).*ones(1,24) c_bat_om.*ones(1,48)]';

Q1 = [ zeros(24,48) eye(24) zeros(24,48) zeros(24,360);
zeros(24,120) zeros(24,48) eye(24) zeros(24,48) zeros(24,240);
zeros(24,240) zeros(24,48) eye(24) zeros(24,48) zeros(24,120);
zeros(24,360) zeros(24,48) eye(24) zeros(24,48)];
Q2 = [zeros(48,72) eye(48) zeros(48,360);
zeros(48,120) zeros(48,72) eye(48) zeros(48,240);
zeros(48,240) zeros(48,72) eye(48) zeros(48,120);
zeros(48,360) zeros(48,72) eye(48)];
Q3 = [zeros(1,72) eta.*ones(1,24) -1/eta.*ones(1,24) zeros(1,360);
zeros(1,120) zeros(1,72) eta.*ones(1,24) -1/eta.*ones(1,24) zeros(1,240);
zeros(1,240) zeros(1,72) eta.*ones(1,24) -1/eta.*ones(1,24) zeros(1,120);
zeros(1,360) zeros(1,72) eta.*ones(1,24) -1/eta.*ones(1,24)];
Q4 = [eye(48) zeros(48,72) zeros(48,360);
zeros(48,120) eye(48) zeros(48,72) zeros(48,240);
zeros(48,240) eye(48) zeros(48,72) zeros(48,120);
zeros(48,360) eye(48) zeros(48,72)];
Q5 = [zeros(24,72) eta.*tril(ones(24,24),0) -1/eta.*tril(ones(24,24),0) zeros(24,360);
zeros(24,120) zeros(24,72) eta.*tril(ones(24,24),0) -1/eta.*tril(ones(24,24),0) zeros(24,240);
zeros(24,240) zeros(24,72) eta.*tril(ones(24,24),0) -1/eta.*tril(ones(24,24),0) zeros(24,120);
zeros(24,360) zeros(24,72) eta.*tril(ones(24,24),0) -1/eta.*tril(ones(24,24),0)];
Q6 = [eye(24) -eye(24) eye(24) -eye(24) eye(24) zeros(24,360);
zeros(24,120) eye(24) -eye(24) eye(24) -eye(24) eye(24) zeros(24,240);
zeros(24,240) eye(24) -eye(24) eye(24) -eye(24) eye(24) zeros(24,120);
zeros(24,360) eye(24) -eye(24) eye(24) -eye(24) eye(24)];
Q10=[eye(48) zeros(48,72) zeros(48,360);
zeros(48,120) eye(48) zeros(48,72) zeros(48,240);
zeros(48,240) eye(48) zeros(48,72) zeros(48,120);
zeros(48,360) eye(48) zeros(48,72)];

G = [eye(24) eye(24) -eye(24) zeros(24,216);
zeros(24,72) eye(24) eye(24) -eye(24) zeros(24,144);
zeros(24,144) eye(24) eye(24) -eye(24) zeros(24,72);
zeros(24,216) eye(24) eye(24) -eye(24)];
T2 = [uu_bat(:,1);(1-uu_bat(:,1));uu_bat(:,2);(1-uu_bat(:,2));uu_bat(:,3);(1-uu_bat(:,3));uu_bat(:,4);(1-uu_bat(:,4))].p_bat_int;
T4 = [uu_m(:,1);1-uu_m(:,1);uu_m(:,2);1-uu_m(:,2);uu_m(:,3);1-uu_m(:,3);uu_m(:,4);1-uu_m(:,4)].pm_max;
T5 = repmat(0.9ee_bat_int-ee0,96,1);
T51 = repmat(0.1ee_bat_int-ee0,96,1);

C = [C, Q1x <= p_g_int];
C = [C, Q1x >= 0];
C = [C, Q2x <= T2];
C = [C, Q2x >= 0];

C = [C, Q3*x == 0];

C = [C, Q4x <= T4];
C = [C, Q4x >= 0];

C = [C, Q5x <= T5];
C = [C, Q5x >= T51];

C = [C, Q6x + Gu == 0];

C = [C, Q1'*lam1-Q1'*lam11+Q2'*lam2-Q2'*lam21+Q3'*lam3+Q4'*lam4-Q4'*lam41+Q5'*lam5-Q5'*lam51+Q6'*lam6>=-P];

C = [C, Q1*x-p_g_int>=-(1-beta1).*M,lam1<=beta1.M];
C = [C, Q1x<=beta11.*M,lam11>=-(1-beta11).*M];

C = [C, Q2*x-T2>=-(1-beta2).*M,lam2<=beta2.M];
C = [C, Q2x<=beta21.*M,lam21>=-(1-beta21).*M];

C = [C, Q4*x-T4>=-(1-beta4).*M,lam4<=beta4.M];
C = [C, Q4x<=beta41.*M,lam41>=-(1-beta41).*M];

C = [C, Q5*x-T5>=-(1-beta5).*M,lam5<=beta5.M];
C = [C, Q5x-T51<=beta51.*M,lam51>=-(1-beta51).*M];

C = [C, lam1>=0,lam11<=0,lam2>=0,lam21<=0,lam4>=0,lam41<=0,lam5>=0,lam51<=0];
C = [C, P+Q1'*lam1-Q1'*lam11+Q2'*lam2-Q2'*lam21+Q3'*lam3+Q4'*lam4-Q4'*lam41+Q5'*lam5-Q5'*lam51+Q6'*lam6<=M.beta7,x<=M.(1-beta7)];

obj_o = sum(sum(repmat(price,1,4).(p_buy(:,:)-p_sell(:,:)))+c_fuelsum(p_g(:,1))+...
sum(c_wt_omp_wt(:,:))+sum(c_pv_omp_pv(:,:))+sum(c_g_omp_g(:,:))+sum(c_bat_omp_dis(:,:))+sum(c_bat_omp_ch(:,:)));
%c_bat(1,1)/3ee_bat_int*k_suo;
Cj = -obj_o;
%ops = sdpsettings('solver','MOSEK','MSK_IPAR_OPTIMIZER',MSK_OPTIMIZER_FREE_SIMPLEX,'mosek.MSK_DPAR_MIO_TOL_REL_GAP', 1.0e-3);
ops=sdpsettings('solver','mosek',...
'mosek.MSK_DPAR_OPTIMIZER_MAX_TIME', 300, ...
'mosek.MSK_DPAR_MIO_MAX_TIME',300,...
'mosek.MSK_DPAR_MIO_TOL_REL_GAP', 1e-4,...
'mosek.MSK_IPAR_MIO_MAX_NUM_BRANCHES',500000,...
'mosek.MSK_IPAR_MIO_MAX_NUM_RELAXS',700000);

%%
reuslt = optimize(C,Cj,ops);

Q=value(Cj);
UB=LB-yita-Q;
p_wt=value(p_wt);
p_pv=value(p_pv);
p_load=value(p_load);
p_g=value(p_g);
p_ch=value(p_ch);
p_dis=value(p_dis);
p_buy=value(p_buy);
p_sell=value(p_sell);