Dear all,

I am experimenting with CPLEX and multi-objective problems, and I found out a bug in the Python interface. Namely, for some reason, when you use the model.set_multi_objective() method the expression you pass for the multi-objective function are "transformed" to discrete ones (even though they're naturally continuous, like dot products with real coefficients) and, consequently, the solution.get_objective_value() returns their value rounded to integers of the real ones.

The original expressions are unaffected, this means that you can still retrieve the actual real values, however I think that this behaviour deserves investigation (in principle I cannot tell where the rounding takes place and whether it affects the results).

I attach a MWE to this (which is related to the problem I try to solve):

import docplex.mp.model as cpx
from itertools import product
from collections import defaultdict


def create_model(papers, authors):
 """
 Create the cplex model for a given optimization problem.


 Parameters
 ----------
 papers : dict
 a dictionary with one entry for each paper. 
 The keys are the paper handles and the values are the scores of the paper, one for each author.
 Format example: { '11390/1234567': {'1234': 1.0, '1235': 0.7}, ... }


 authors : dict
 a dictionary with one entry for each author.
 The author id is the key, while his/her status according to
 the different optimization criteria are the values (TODO: still to be considered)
 Format example: { '1234': { 'young': True }, '1235': {'young': False } }


 """
 with cpx.Model(name='VQR Optimization') as model:
 x = defaultdict(lambda: dict()) # x variables are the decision variables from the viewpoint of papers (i.e., they are indexed [paper, author])
 y = defaultdict(lambda: dict()) # y variables are the decision variables from the viewpoint of authors (i.e., they are indexed [author, paper])
 c = defaultdict(lambda: defaultdict(lambda: 0.0)) # c are the coefficients of the paper, indexed as [paper, author]
 d = defaultdict(lambda: defaultdict(lambda: 0.0)) # d are the coefficients of the author, indexed as [author, paper]


 overall_sum_variables = []
 overall_sum_coefficients = []
 young_sum_variables = []
 young_sum_coefficients = []
 for paper, paper_authors in papers.items():
 for author, score in paper_authors.items():
# score = score * 10
 variable = model.binary_var(f'select[{paper}, {author}]')
 x[paper][author] = variable
 y[author][paper] = variable
 c[paper][author] = score
 d[author][paper] = score
 overall_sum_variables.append(variable)
 overall_sum_coefficients.append(score)
 if authors[author].get('young', False):
 young_sum_variables.append(variable)
 young_sum_coefficients.append(score)


 # each paper selected only once FIXME: just for testing
 model.add_constraint(sum(x[paper].values()) <= 1)


 # each author just one paper FIXME: just for testing
 
 for author, variables in y.items():
 model.add_constraint(sum(variables.values()) == 1)
 
 overall = model.dot(overall_sum_variables, overall_sum_coefficients)
 young = model.dot(young_sum_variables, young_sum_coefficients)
 # optimization criterion
 model.set_multi_objective('max', [overall, young], priorities=[2, 1], reltols=[0.1, 0.1], names=['overall', 'young']) 


 sol = model.solve(log_output=True)
 if sol is None:
 print('model is infeasible')
 else: 
 print(sol)
 print(sol.solve_status)
 print(sol.get_value(overall), sol.get_value(young))
 print(sol.get_objective_value())
 
 print(model._objective_expr.is_discrete())


if __name__ == '__main__': 
 test_papers = { '11390/1234567': {'1234': 0.7, '1235': 0.7}, '11390/1234568': {'1234': 0.8, '1236': 0.9}, '11390/1234569': {'1235': 0.7, '1236': 0.7},}
 test_authors = { '1234': { 'young': True }, '1235': {}, '1236': { 'young': False } }


 create_model(test_papers, test_authors)

The output is:

Version identifier: 12.10.0.0 | 2019-11-26 | 843d4de
CPXPARAM_Read_DataCheck 1
CPXPARAM_RandomSeed 201903125

Multi-objective solve log . . .

Index Priority Blend Objective Nodes Time (sec.) DetTime (ticks)
 1 2 1 2.3000000000e+00 0 0.00 0.01
 2 1 1 8.0000000000e-01 0 0.00 0.02
solution for: VQR Optimization
select[11390/1234567, 1235]=1
select[11390/1234568, 1234]=1
select[11390/1234569, 1236]=1

JobSolveStatus.OPTIMAL_SOLUTION
2.2 0.8
[2, 1]
True

------------------------------
Luca Di Gaspero
------------------------------

#DecisionOptimization

Thanks a lot for reporting this. I have reproduced the problem here and filed and appropriate bug report.
The problem is indeed that all expressions used in the multi-objective are considered discrete. The workaround is what you did in your code: keep a reference to the expressions that make up the individual objectives and then call `get_value()` on them.

------------------------------
Daniel Junglas
------------------------------

Original Message:
Sent: Tue May 05, 2020 02:40 AM
From: Luca Di Gaspero
Subject: Python: Multi-Objective cplex MILP objectives are rounded

Dear all,

I am experimenting with CPLEX and multi-objective problems, and I found out a bug in the Python interface. Namely, for some reason, when you use the model.set_multi_objective() method the expression you pass for the multi-objective function are "transformed" to discrete ones (even though they're naturally continuous, like dot products with real coefficients) and, consequently, the solution.get_objective_value() returns their value rounded to integers of the real ones.

The original expressions are unaffected, this means that you can still retrieve the actual real values, however I think that this behaviour deserves investigation (in principle I cannot tell where the rounding takes place and whether it affects the results).

I attach a MWE to this (which is related to the problem I try to solve):

import docplex.mp.model as cpx
from itertools import product
from collections import defaultdict

def create_model(papers, authors):
 """
 Create the cplex model for a given optimization problem.

 Parameters
 ----------
 papers : dict
 a dictionary with one entry for each paper. 
 The keys are the paper handles and the values are the scores of the paper, one for each author.
 Format example: { '11390/1234567': {'1234': 1.0, '1235': 0.7}, ... }

 authors : dict
 a dictionary with one entry for each author.
 The author id is the key, while his/her status according to
 the different optimization criteria are the values (TODO: still to be considered)
 Format example: { '1234': { 'young': True }, '1235': {'young': False } }

 """
 with cpx.Model(name='VQR Optimization') as model:
 x = defaultdict(lambda: dict()) # x variables are the decision variables from the viewpoint of papers (i.e., they are indexed [paper, author])
 y = defaultdict(lambda: dict()) # y variables are the decision variables from the viewpoint of authors (i.e., they are indexed [author, paper])
 c = defaultdict(lambda: defaultdict(lambda: 0.0)) # c are the coefficients of the paper, indexed as [paper, author]
 d = defaultdict(lambda: defaultdict(lambda: 0.0)) # d are the coefficients of the author, indexed as [author, paper]

 overall_sum_variables = []
 overall_sum_coefficients = []
 young_sum_variables = []
 young_sum_coefficients = []
 for paper, paper_authors in papers.items():
 for author, score in paper_authors.items():
# score = score * 10
 variable = model.binary_var(f'select[{paper}, {author}]')
 x[paper][author] = variable
 y[author][paper] = variable
 c[paper][author] = score
 d[author][paper] = score
 overall_sum_variables.append(variable)
 overall_sum_coefficients.append(score)
 if authors[author].get('young', False):
 young_sum_variables.append(variable)
 young_sum_coefficients.append(score)

 # each paper selected only once FIXME: just for testing
 model.add_constraint(sum(x[paper].values()) <= 1)

 # each author just one paper FIXME: just for testing
 
 for author, variables in y.items():
 model.add_constraint(sum(variables.values()) == 1)
 
 overall = model.dot(overall_sum_variables, overall_sum_coefficients)
 young = model.dot(young_sum_variables, young_sum_coefficients)
 # optimization criterion
 model.set_multi_objective('max', [overall, young], priorities=[2, 1], reltols=[0.1, 0.1], names=['overall', 'young']) 

 sol = model.solve(log_output=True)
 if sol is None:
 print('model is infeasible')
 else: 
 print(sol)
 print(sol.solve_status)
 print(sol.get_value(overall), sol.get_value(young))
 print(sol.get_objective_value())
 
 print(model._objective_expr.is_discrete())

if __name__ == '__main__': 
 test_papers = { '11390/1234567': {'1234': 0.7, '1235': 0.7}, '11390/1234568': {'1234': 0.8, '1236': 0.9}, '11390/1234569': {'1235': 0.7, '1236': 0.7},}
 test_authors = { '1234': { 'young': True }, '1235': {}, '1236': { 'young': False } }

 create_model(test_papers, test_authors)

The output is:

Version identifier: 12.10.0.0 | 2019-11-26 | 843d4de
CPXPARAM_Read_DataCheck 1
CPXPARAM_RandomSeed 201903125

Multi-objective solve log . . .

Index Priority Blend Objective Nodes Time (sec.) DetTime (ticks)
 1 2 1 2.3000000000e+00 0 0.00 0.01
 2 1 1 8.0000000000e-01 0 0.00 0.02
solution for: VQR Optimization
select[11390/1234567, 1235]=1
select[11390/1234568, 1234]=1
select[11390/1234569, 1236]=1

JobSolveStatus.OPTIMAL_SOLUTION
2.2 0.8
[2, 1]
True

------------------------------
Luca Di Gaspero
------------------------------

#DecisionOptimization