Hi,

let's go on with the example from https://www.linkedin.com/pulse/what-optimization-how-can-help-you-do-more-less-zoo-buses-fleischer/

and let's see how easy moving to multiobjective is with docplex.

from docplex.mp.model import Model

mdl = Model(name='buses')

nbbus50 = mdl.integer_var(name='nbBus50')
nbbus40 = mdl.integer_var(name='nbBus40')
nbbus30 = mdl.integer_var(name='nbBus30')

cost = mdl.continuous_var(name='cost')
co2emission = mdl.continuous_var(name='co2emission')

mdl.add_constraint(nbbus50*50+nbbus40*40 + nbbus30*30 >= 200, 'kids')
mdl.add_constraint(co2emission==nbbus50+nbbus40*1.1+nbbus30*1.2)
mdl.add_constraint(cost==nbbus40*500 + nbbus30*400+nbbus50*625)
            
mdl.minimize_static_lex([cost,co2emission])

mdl.solve()

for v in mdl.iter_integer_vars():
   print(v," = ",v.solution_value)

print("The minimum cost is ",cost.solution_value);
print("CO2 emission is ",co2emission.solution_value);

gives

nbBus50  =  4.0
nbBus40  =  0
nbBus30  =  0
The minimum cost is  2500.0
CO2 emission is  4.0

If we had used 5 buses 40 seats, the cost would have been 2500 also but the CO2 emission would have been bigger.

regards

NB: Til CPLEX 12.8 that was possible only with CP models, and since 12.9 this works also for mathematical models.

regards

PS: Many other very simple docplex examples at https://www.linkedin.com/pulse/making-optimization-simple-python-alex-fleischer/

And now with set_multi_objective

from docplex.mp.model import Model

mdl = Model(name='buses')

nbbus50 = mdl.integer_var(name='nbBus50')
nbbus40 = mdl.integer_var(name='nbBus40')
nbbus30 = mdl.integer_var(name='nbBus30')

cost = mdl.continuous_var(name='cost')
co2emission = mdl.continuous_var(name='co2emission')

mdl.add_constraint(nbbus50*50+nbbus40*40 + nbbus30*30 >= 200, 'kids')
mdl.add_constraint(co2emission==nbbus50+nbbus40*1.1+nbbus30*1.2)
mdl.add_constraint(cost==nbbus40*500 + nbbus30*400+nbbus50*625)
                
sense="min"
exprs=[cost,co2emission]
priorities=[1,2]
weights=[1,1]
mdl.set_multi_objective(sense, exprs, priorities, weights, abstols=None, reltols=None, names=None)

mdl.solve(lex_mipgaps = [0.001, 0.05], log_output=True)

for v in mdl.iter_integer_vars():
    print(v," = ",v.solution_value)

print("The minimum cost is ",cost.solution_value);
print("CO2 emission is ",co2emission.solution_value);

which gives

nbBus50  =  4.0
nbBus40  =  0
nbBus30  =  0
The minimum cost is  2500.0
CO2 emission is  4.0

We were able to set gaps per iterations through lex_mipgaps

PS: Many other very simple docplex examples at https://www.linkedin.com/pulse/making-optimization-simple-python-alex-fleischer/