How to use SOS2 on IBM ILOG CPLEX Optimization Studio - websphere

Please help me. I am using the IBM ILOG CPLEX Optimization Studio to solve my problem which is some variables in my model are type SOS2. I don't know, how to use SOS2 on IBM ILOG CPLEX.

that depends on the API you use.
With the docplex python API let me share the example from https://github.com/AlexFleischerParis/zoodocplex/blob/master/zoosos2.py
from docplex.mp.model import Model
mdl = Model(name='buses')
nbbus30 = mdl.integer_var(name='nbBus30')
nbbus40 = mdl.integer_var(name='nbBus40')
nbbus50 = mdl.integer_var(name='nbBus50')
cost = mdl.continuous_var(name='cost')
mdl.add_constraint(nbbus50*50+nbbus40*40 + nbbus30*30 >= 300, 'kids')
mdl.add_constraint(cost==nbbus40*500 + nbbus30*400+nbbus50*550)
mdl.add_constraint(nbbus50==1)
mdl.minimize(cost)
mdl.solve()
for v in mdl.iter_integer_vars():
print(v," = ",v.solution_value)
print("The minimum cost is ",cost.solution_value);
print("and then with sos2 nbbus30,nbbus40,nbbus50")
mdl.add_sos2([nbbus30,nbbus40,nbbus50])
mdl.minimize(cost)
mdl.solve( )
for v in mdl.iter_integer_vars():
print(v," = ",v.solution_value)
print("The minimum cost is ",cost.solution_value);
which gives
nbBus30 = 3.0
nbBus40 = 4.0
nbBus50 = 1.0
The minimum cost is 3750.0
and then with sos2 nbbus30,nbbus40,nbbus50
nbBus30 = 0
nbBus40 = 7.0
nbBus50 = 1.0
The minimum cost is 4050.0

Related

OpenMDAO hierarchical solvers recording

In OpenMDAO, is there any recommendation on how to record and read solver cases if the model is composed of multiple groups/cycles, and multiple nonlinear solvers?
I have a model built of 2 cycles (cycle1 and cycle2), one of them containing two subcycles (cycle1_1 and cycle1_2). For now I am attaching a solver to each of my nonlinear solvers:
solver1 = model.cycle1.nonlinear_solver
solver1_1 = model.cycle1.cycle1_1.nonlinear_solver
solver1_2 = model.cycle1.cycle1_2.nonlinear_solver
solver2 = model.cycle2.nonlinear_solver
solver1.add_recorder(recorder)
solver1_1.add_recorder(recorder)
solver1_2.add_recorder(recorder)
solver2.add_recorder(recorder)
When trying to read the results with:
cr = om.CaseReader(results)
I am getting the following error:
RuntimeError: Can't parse solver iteration coordinate:
rank0:root._solve_nonlinear|0|NLRunOnce|0|cycle1._solve_nonlinear|0|NonlinearBlockGS|1|cycle1.cycle1_1._solve_nonlinear|1|NonlinearBlockGS|1
I am looking to get information about the convergence history and some plots on the coupling variables.
EDIT: My code has a structure similar to that in https://openmdao.org/newdocs/versions/latest/basic_user_guide/multidisciplinary_optimization/sellar.html, with the groups defined in setup:
import openmdao.api as om
class MDA(om.Group):
# class ObjCmp(om.ExplicitComponent):
# some objective component
# class ConCmp(om.ExplicitComponent):
# some constraint component
def setup(self):
cycle1 = self.add_subsystem('cycle1', om.Group(), promotes=['*'])
cycle1_1 = cycle1.add_subsystem('cycle1_1', om.Group(), promotes=['*'])
cycle1_1_comp = cycle1_1.add_subsystem('comp', om.ExecComp('x1 = 3 + x2'), promotes=["*"])
cycle1_2 = cycle1.add_subsystem('cycle1_2', om.Group(), promotes=['*'])
cycle1_2_comp = cycle1_2.add_subsystem('comp', om.ExecComp('x2 = 3 + x1 + y'), promotes=["*"])
cycle2 = self.add_subsystem('cycle2', om.Group(), promotes=['*'])
cycle2.add_subsystem('comp', om.ExecComp('y = x1 + 2'), promotes=['*'])
p = om.Problem(model=MDA())
model = p.model
p.setup()
p.run_model()
Unfortunately, as of OpenMDAO V3.16 this looks like a bug. Its been logged as a high priority issue on the OpenMDAO development backlog: Issue #2453
I can replicate it with the following script:
import openmdao.api as om
p = om.Problem()
model = p.model
cycle1 = p.model.add_subsystem('cycle1', om.Group(), promotes=['*'])
cycle1_1 = cycle1.add_subsystem('cycle1_1', om.Group(), promotes=['*'])
cycle1_1_comp = cycle1_1.add_subsystem('comp', om.ExecComp('x1 = 3 + x2'), promotes=["*"])
cycle1_2 = cycle1.add_subsystem('cycle1_2', om.Group(), promotes=['*'])
cycle1_2_comp = cycle1_2.add_subsystem('comp', om.ExecComp('x2 = 3 + x1 + y'), promotes=["*"])
cycle2 = p.model.add_subsystem('cycle2', om.Group(), promotes=['*'])
cycle2.add_subsystem('comp', om.ExecComp('y = x1 + 2'), promotes=['*'])
solver1 = model.cycle1.nonlinear_solver
solver1_1 = model.cycle1.cycle1_1.nonlinear_solver
solver1_2 = model.cycle1.cycle1_2.nonlinear_solver
solver2 = model.cycle2.nonlinear_solver
print(solver1, solver1_1, solver1_2, solver2)
recorder = om.SqliteRecorder('cases.db')
solver1.add_recorder(recorder)
# recorders on nested solvers trigger the bug
# solver1_1.add_recorder(recorder)
# solver1_2.add_recorder(recorder)
# Kind-of workaround, put the recorder on the child component/group instead
cycle1_1_comp.add_recorder(recorder)
cycle1_2_comp.add_recorder(recorder)
solver2.add_recorder(recorder)
p.setup()
p.run_model()
reader = om.CaseReader('cases.db')
print(reader.list_sources())
It seems to be the nested recorders that are triggering the bug. As a kind-of workaround you can stick the recorder on the lower level group/component instead. That will make it a bit harder to know which cases are from which solver iteration, but the naming scheme of the iteration coordinates should at least help a little there. Hopefully that gets you moving in the meantime, while the bug is fixed.

how to solve ini equation problem using gekko?

If I want use V1_0 represent the initiate value of V1 and V2_0 represent the initiate value of V2,and has the initiate equation V2_0-V1_0=5,how should I to use gekko to express this relation?
For that level of control, I recommend writing out the dynamic problem as arrays. You'll need to include your own collocation equations if you have differential equations.
from gekko import GEKKO
m = GEKKO()
n = 5
V1 = m.Array(m.Var,n)
V2 = m.Array(m.Var,n)
# rename initial conditions
V1_0 = V1[0]; V2_0 = V2[0]
m.Equation(V1_0==3)
m.Equation(V2_0-V1_0==5)
for i in range(1,n):
m.Equation(V1[i]==V1[i-1]+1)
m.Equation(V2[i]==V2[i-1]+0.5)
m.solve(disp=False)
print(V1)
print(V2)
This produces the solution for V1 and V2:
[[3.0] [4.0] [5.0] [6.0] [7.0]]
[[8.0] [8.5] [9.0] [9.5] [10.0]]
If you are using a dynamic mode (IMODE=5 or IMODE=6), you can also try the m.Connection() function to connect the initial conditions with V1_0=m.FV() and V2_0=m.FV() with V2_0.STATUS=1. Then you can write the Equation m.Equation(V2_0-V1_0==5).

is SOP(sentence order prediction) implemented?

I am reviewing huggingface's version of Albert.
However, I cannot find any code or comment about SOP.
I can find NSP(Next Sentence Prediction) implementation from modeling_from src/transformers/modeling_bert.py.
if masked_lm_labels is not None and next_sentence_label is not None:
loss_fct = CrossEntropyLoss()
masked_lm_loss = loss_fct(prediction_scores.view(-1, self.config.vocab_size), masked_lm_labels.view(-1))
next_sentence_loss = loss_fct(seq_relationship_score.view(-1, 2), next_sentence_label.view(-1))
total_loss = masked_lm_loss + next_sentence_loss
outputs = (total_loss,) + outputs
Is SOP inherited from here with SOP-style labeling? or Is there anything I am missing?
The sentence order loss is here:
sentence_order_loss = loss_fn(y_true=sentence_order_label, y_pred=sentence_order_reduced_logits)
It's just a cross entropy loss.

How to speed up MATLAB integration?

I have the following code:
function [] = Solver( t )
%pre-declaration
foo=[1,1,1];
fooCell = num2cell(foo);
[q, val(q), star]=fooCell{:};
%functions used in prosomoiwsh
syms q val(q) star;
qd1=symfun(90*pi/180+30*pi/180*cos(q),q);
qd2=symfun(90*pi/180+30*pi/180*sin(q),q);
p1=symfun(79*pi/180*exp(-1.25*q)+pi/180,q);
p2=symfun(79*pi/180*exp(-1.25*q)+pi/180,q);
e1=symfun(val-qd1,q);
e2=symfun(val-qd2,q);
T1=symfun(log(-(1+star)/star),star);
T2=symfun(log(star/(1-star)),star);
%anonymous function handles
lambda=[0.75;10.494441313222076];
calcEVR_handles={#(t,x)[double(subs(diff(subs(T1,star,e1/p1),q)+subs(lambda(1)*T1,star,e1/p1),{diff(val,q);val;q},{x(2);x(1);t})),double(subs(diff(subs(T1,star,e1/p1),q)+subs(lambda(1)*T1,star,e1/p1),{diff(val,q);val;q},{0;x(1);t})),double(subs(double(subs(subs(diff(T1,star),star,e1/p1),{val;q},{x(1);t}))/p1,q,t))];#(t,x)[double(subs(diff(subs(T2,star,e2/p2),q)+subs(lambda(2)*T2,star,e2/p2),{diff(val,q);val;q},{x(4);x(3);t})),double(subs(diff(subs(T2,star,e2/p2),q)+subs(lambda(2)*T2,star,e2/p2),{diff(val,q);val;q},{0;x(3);t})),double(subs(double(subs(subs(diff(T2,star),star,e2/p2),{val;q},{x(3);t}))/p2,q,t))]};
options = odeset('AbsTol',1e-1,'RelTol',1e-1);
[T,x_r] = ode23(#prosomoiwsh,[0 t],[80*pi/180;0;130*pi/180;0;2.4943180186983711;11.216948999754299],options);
save newresult T x_r
function dx_th = prosomoiwsh(t,x_th)
%declarations
k=0.80773938740480955;
nf=6.2860930902603602;
hGa=0.16727117784664769;
hGb=0.010886618389781832;
dD=0.14062935253218495;
s=0.64963817519705203;
IwF={[4.5453398382686956 5.2541234145178066 -6.5853972592002235 7.695225990702979];[-4.4358339284697337 -8.1138542053372298 -8.2698210582548395 3.9739729629084071]};
IwG={[5.7098975358444752 4.2470526600975802 -0.83412489434697168 0.53829395964565041] [1.8689492167233894 -0.0015017513794517434 8.8666804106266461 -1.0775021663921467];[6.9513235639494155 -0.8133752392893685 7.4032432556804162 3.1496138243338709] [5.8037182454981568 2.0933267947187457 4.852362963697928 -0.10745559204132382]};
IbF={-1.2165533594615545;7.9215291787744917};
IbG={2.8425752327892844 2.5931576770598168;9.4789237295474873 7.9378928037841252};
p=2;
m=2;
signG=1;
n_vals=[2;2];
nFixedStates=4;
gamma_nn=[0.31559428834175318;9.2037894041383641];
th_star_guess=[2.4943180186983711;11.216948999754299];
%solution
x = x_th(1:nFixedStates);
th = x_th(nFixedStates+1:nFixedStates+p);
f = zeros(m,1);
G = zeros(m,m);
ZF = zeros(p,m);
ZG = zeros(p,m,m);
for i=1:m
[f(i), ZF(:,i)] = calculate_neural_output(x, IwF{i}, IbF{i}, th);
for j=1:m
[G(i,j), ZG(:,i,j)] = calculate_neural_output(x, IwG{i,j}, IbG{i,j}, th);
end
end
detG = det(G);
if m == 1
adjG = 1;
else
adjG = detG*G^-1;
end
E = zeros(m,1);
V = zeros(m,1);
R = zeros(m,m);
for i=1:m
EVR=calcEVR_handles{i}(t,x);
E(i)=EVR(1);
V(i)=EVR(2);
R(i,i)=EVR(3);
end
Rinv = R^-1;
prod_R_E = R*E;
ub = f + Rinv * (V + k*E) + nf*prod_R_E;
ua = - detG / (detG^2+dD) * (adjG * ub) ;
u = ua - signG * (hGa*(ua'*ua) + hGb*(ub'*ub)) * prod_R_E;
dx_th = zeros(nFixedStates+p, 1); %preallocation
%System in form (1) of the IEEE paper
[vec_sys_f, vec_sys_G] = sys_f_G(x);
dx_nm = vec_sys_f + vec_sys_G*u;
%Calculation of dx
index_start = 1;
index_end = -1;
for i=1:m
index_end = index_end + n_vals(i);
for j=index_start:index_end
dx_th(j) = x(j+1);
end
dx_th(index_end+1) = dx_nm(i);
index_start = index_end + 2;
end
%Calculation of dth
AFvalueT = zeros(p,m);
for i=1:m
AFvalueT(:,i) = 0;
for j=1:m
AFvalueT(:,i) = AFvalueT(:,i)+ZG(:,i,j)*ua(j);
end
end
dx_th(nFixedStates+1:nFixedStates+p) = diag(gamma_nn)*( (ZF+AFvalueT)*prod_R_E -s*(th-th_star_guess) );
display(t)
end
function [y, Z] = calculate_neural_output(input, Iw, Ib, state)
Z = [tanh(Iw*input+Ib);1];
y = state' * Z;
end
function [ f,g ] = sys_f_G( x )
Iz1=0.96;
Iz2=0.81;
m1=3.2;
m2=2.0;
l1=0.5;
l2=0.4;
g=9.81;
q1=x(1);
q2=x(3);
q1dot=x(2);
q2dot=x(4);
M=[Iz1+Iz2+m1*l1^2/4+m2*(l1^2+l2^2/4+l1*l2*cos(q2)),Iz2+m2*(l2^2/4+l1*l2*cos(q2)/2);Iz2+m2*(l2^2/4+l1*l2*cos(q2)/2),Iz2+m2*l2^2/4];
c=0.5*m2*l1*l2*sin(q2);
C=[-c*q2dot,-c*(q1dot+q2dot);c*q1dot,0];
G=[0.5*m1*g*l1*cos(q1)+m2*g*(l1*cos(q1)+0.5*l2*cos(q1+q2));0.5*m2*g*l2*cos(q1+q2)];
f=-M\(C*[q1dot;q2dot]+G);
g=inv(M);
end
end
Its target is to simulate the control of a 2-DOF robotic arm using a certain control law. The results I get after running the simulation are correct(I have a graph of the output I should expect), but it takes ages to finish!
Is there anything I could do to speed up the process?
In order to improve the computational speed of any integration in Matlab, a few options are available to you:
Reduce the required accuracy (which you already have done)
Use an adapted integrator. As mentioned by #sanchises, sometimes ode23 can be longer than another ode solver in Matlab (if your equation is stiff for instance). You could try to determine which solver is most adapted from the documentation... Or simply try them all!
The best solution, but by far the most time consuming, would be to use a compiled language, such as C or Fortran. If the integration is but a part of your Matlab program, you could use Mex files, and translate only the integration to a compiled language. You could also create dynamic libraries in your compiled language and load them in Matlab using loadlibrary. I use loadlibrary and an integration routine written in Fortran for the integration of orbits and trajectories, and I get over 100 times speedup with Fortran vs. Matlab! Of course, technically, the integration is not in Matlab anymore... But the library or Mex files trick allows you to only convert the integration part of your program to a different language! A number of open source integrators are available, such as ODEPACK or RKSUITE in Fortran. Then, you only need to create a wrapper and your dynamics function in the correct language.
So to put it in a nutshell, if you're going to use this integration a lot, I would advise using a compiled language. If not, you should make do with Matlab, and be patient!

Porting algorithm from Python to Go

I am trying to port this python code to Go but there is no beta() in math package. Where can i find beta and other functions required for this?
from numpy import *
from scipy.stats import beta
class BetaBandit(object):
def __init__(self, num_options=2, prior=(1.0,1.0)):
self.trials = zeros(shape=(num_options,), dtype=int)
self.successes = zeros(shape=(num_options,), dtype=int)
self.num_options = num_options
self.prior = prior
def add_result(self, trial_id, success):
self.trials[trial_id] = self.trials[trial_id] + 1
if (success):
self.successes[trial_id] = self.successes[trial_id] + 1
def get_recommendation(self):
sampled_theta = []
for i in range(self.num_options):
#Construct beta distribution for posterior
dist = beta(self.prior[0]+self.successes[i],
self.prior[1]+self.trials[i]-self.successes[i])
#Draw sample from beta distribution
sampled_theta += [ dist.rvs() ]
# Return the index of the sample with the largest value
return sampled_theta.index( max(sampled_theta) )
If you are talking about numpy.random.beta, the Beta distribution which is a special case of the Dirichlet distribution, and is related to the Gamma distribution, you can check the project gostat.
It has a beta.go source code which implements that function.

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