# JuMP function result_count returns 1 when infinite solutions possible, which solver to use?

Consider the following model of a simple LP problem:

``````using JuMP, HiGHS

m = Model(HiGHS.Optimizer)

@variable(m, x1 >= 0)
@variable(m, x2 <= 0)
@objective(m, Max, 2x1-x2)
@constraint(m, c1, 8x1-4x2<=16)
@constraint(m, c2, 3x1-4x2<=12)

print(m)
#Max 2 x1 - x2
#Subject to
# c1 : 8 x1 - 4 x2 <= 16.0
# c2 : 3 x1 - 4 x2 <= 12.0
# x1 >= 0.0
# x2 <= 0.0

JuMP.optimize!(m)
#Running HiGHS 1.4.2 [date: 1970-01-01, git hash: f797c1ab6]
#Copyright (c) 2022 ERGO-Code under MIT licence terms
#Presolving model
#2 rows, 2 cols, 4 nonzeros
#2 rows, 2 cols, 4 nonzeros
#Presolve : Reductions: rows 2(-0); columns 2(-0); elements 4(-0) - Not reduced
#Problem not reduced by presolve: solving the LP
#Using EKK dual simplex solver - serial
# Iteration        Objective     Infeasibilities num(sum)
#          0    -7.4999893425e-01 Ph1: 2(4.75); Du: 2(0.749999) 0s
#          1     4.0000000000e+00 Pr: 0(0) 0s
#Model   status      : Optimal
#Simplex   iterations: 1
#Objective value     :  4.0000000000e+00
#HiGHS run time      :          0.02

result_count(m)
# 1

println("Objective value: ", JuMP.objective_value(m))
# Objective value: 4.0

solution_summary(m)
#* Solver : HiGHS
#
#* Status
# Result count       : 1
# Termination status : OPTIMAL
# Message from the solver:
#  "kHighsModelStatusOptimal"
#
#* Candidate solution (result #1)
# Primal status      : FEASIBLE_POINT
# Dual status        : FEASIBLE_POINT
#  Objective value    : 4.00000e+00
#  Objective bound    : 4.00000e+00
# Relative gap       : Inf
#  Dual objective value : 4.00000e+00
#
#* Work counters
#  Solve time (sec)   : 1.56868e-02
#  Simplex iterations : 1
#  Barrier iterations : 0
#  Node count         : -1

println("x1 = ", JuMP.value(x1))
# x1 = 2.0

println("x2 = ", JuMP.value(x2))
# x2 = 0.0
``````

The JuMP solution shows there was a optimal (understanding global) solution found however if you consider the solution `(x1,x2)=(1, -2)` then it satisfies as well the constraints and produces the same objective value of 4, clearly multiple slutions are possible

The JuMP result count is 1 and termination status reports optimality. Is it because I defined the problem as LP and not as MILP, and some computational inacuracies show, that it does not report the multiple solutions?

Since the objective gradient and the gradient of c1 are parallel, a whole face of the polytope is composed of minima. So there’s infinitely many of them An LP solver can return any of them (if you tried an interior-point method, you could get a non-corner solution). It’s up to you to analyze the results and perhaps modify your model if you’re not happy with the solution.

1 Like

I understand.

How would i go About extracting the info about the gradients of objective and constraint parallelism from the JuMP Interface explicitly?

I thought this kind of solution will be given by infinite number of solutions as output of the model.