Given any feasible upper level solution the lower level problem is feasible, however MibS found no solution?

[tomaslg]

Hi,

I wonder if I'm using the solver the wrong way... My problem has four upper level feasible solutions. If necessary I can generate and share the bilevel feasible solutions for this problem (I mean leader-feasible and follower optimal response).

My problem uses some input data and an underlying network G(V,E), where V is a set of components and E is a set of undirected edges. The horizon has two time periods, the leader defends at time t=1, and the follower can attack at times t=1 and/or t=2.

I use the following input files for MibS: model.zip

Here is the output I received: mibs_output.txt

Here is a bilevel optimal solution for the problem:

upper level: (minimizes the number of damaged components over horizon) z[i, t] (indicates defend/protection of i at time t) [(1,1) 0.0; (2,1) 1.0; (3,1) 0.0; (4,1) 0.0]

lower level: (maximizes the number of damaged components over horizon) y[i,t,0] (indicates attack of i at time t) [(1,1,0) 0.0; (2,1,0) 0.0; (3,1,0) 0.0; (4,1,0) 0.0; (1,2,0) 0.0; (2,2,0) 0.0; (3,2,0) 0.0; (4,2,0) 1.0]

w[i,t,0] (indicates spread damage in i at time t) [(3, 2, 0) 1.0; (1, 2, 0) 0.0; (3, 1, 0) 0.0; (1, 1, 0) 0.0; (4, 2, 0) 1.0; (4, 1, 0) 0.0; (2, 2, 0) 0.0; (2, 1, 0) 0.0]

x[i,t,0] (measures the vulnerability of the component at time t) (z[i,t-1]=1 or w[i,t-1,0]=1 makes this measure decrease) [(3, 2, 0) 14.267529141593812; (1, 2, 0) 6.551886343581829; (3, 1, 0) 13.872371946231844; (1, 1, 0) 4.726983106693199; (4, 2, 0) 16.33995846253321; (4, 1, 0) 16.32883247435988; (2, 2, 0) 8.165345055858875; (2, 1, 0) 16.010449108646597]

θ[i,t,0] (indicates the component i is vulnerable at time t, i.e. x[i,t,0] is over a threshold = 13.4) [(3, 2, 0) 1.0; (1, 2, 0) 0.0; (3, 1, 0) 1.0; (1, 1, 0) 0.0; (4, 2, 0) 1.0; (4, 1, 0) 1.0; (2, 2, 0) 0.0; (2, 1, 0) 0.0]

ε[(i,j),t,0] (indicates the (i, j) ∈ E connection can spread the attack because both end-points are vulnerable at time t) [((1, 2), 1, 0) 0.0; ((1, 3), 1, 0) 0.0; ((1, 2), 2, 0) 0.0; ((2, 4), 2, 0) 0.0; ((3, 4), 1, 0) 1.0; ((1, 3), 2, 0) 0.0; ((3, 4), 2, 0) 1.0; ((2, 4), 1, 0) 0.0]

ϕ[i,j,t,0] (indicates that (i,j) ∈ V×V are connected through active edges in E at time t, i.e., those having ε[(i,j),t,0]=1) [(1, 1, 1, 0) 0.0; (2, 2, 2, 0) 0.0; (1, 2, 1, 0) 0.0; (2, 3, 2, 0) 0.0; (4, 4, 2, 0) 1.0; (1, 3, 1, 0) 0.0; (2, 4, 2, 0) 0.0; (1, 1, 2, 0) 0.0; (1, 4, 1, 0) 0.0; (3, 3, 1, 0) 1.0; (1, 2, 2, 0) 0.0; (3, 4, 1, 0) 1.0; (1, 3, 2, 0) 0.0; (1, 4, 2, 0) 0.0; (2, 2, 1, 0) 0.0; (3, 3, 2, 0) 1.0; (2, 3, 1, 0) 0.0; (4, 4, 1, 0) 1.0; (3, 4, 2, 0) 1.0; (2, 4, 1, 0) 0.0]

μ[(k,k'), i, j, t, 0] (flow through arc (k,k') where (k,k') ∈ E or (k',k) ∈ E of a commodity sourced at component i directed towards component j at time t) [((2, 1), 1, 4, 2, 0) 0.0; ((3, 4), 1, 4, 2, 0) 0.0; ((4, 3), 2, 3, 2, 0) 0.0; ((2, 4), 2, 3, 1, 0) 0.0; ((4, 2), 1, 4, 1, 0) 0.0; ((2, 4), 2, 3, 2, 0) 0.0; ((4, 3), 1, 4, 1, 0) 0.0; ((4, 2), 1, 4, 2, 0) 0.0; ((4, 3), 1, 4, 2, 0) 0.0; ((2, 4), 1, 4, 1, 0) 0.0; ((1, 2), 2, 3, 1, 0) 0.0; ((3, 1), 2, 3, 1, 0) 0.0; ((2, 4), 1, 4, 2, 0) 0.0; ((1, 3), 2, 3, 1, 0) 0.0; ((1, 2), 2, 3, 2, 0) 0.0; ((3, 1), 2, 3, 2, 0) 0.0; ((1, 3), 2, 3, 2, 0) 0.0; ((1, 2), 1, 4, 1, 0) 0.0; ((3, 1), 1, 4, 1, 0) 0.0; ((1, 3), 1, 4, 1, 0) 0.0; ((1, 2), 1, 4, 2, 0) 0.0; ((3, 1), 1, 4, 2, 0) 0.0; ((2, 1), 2, 3, 1, 0) 0.0; ((1, 3), 1, 4, 2, 0) 0.0; ((3, 4), 2, 3, 1, 0) 0.0; ((2, 1), 2, 3, 2, 0) 0.0; ((3, 4), 2, 3, 2, 0) 0.0; ((4, 2), 2, 3, 1, 0) 0.0; ((2, 1), 1, 4, 1, 0) 0.0; ((3, 4), 1, 4, 1, 0) 0.0; ((4, 3), 2, 3, 1, 0) 0.0; ((4, 2), 2, 3, 2, 0) 0.0]

ϕy[i,j,t,0] (product between variables ϕ[i,j,t,0] and y[j,t,0]) [(1, 1, 1, 0) 0.0; (2, 2, 2, 0) 0.0; (1, 2, 1, 0) 0.0; (2, 3, 2, 0) 0.0; (4, 4, 2, 0) 1.0; (1, 3, 1, 0) 0.0; (2, 4, 2, 0) 0.0; (1, 1, 2, 0) 0.0; (1, 4, 1, 0) 0.0; (3, 3, 1, 0) 0.0; (1, 2, 2, 0) 0.0; (3, 4, 1, 0) 0.0; (1, 3, 2, 0) 0.0; (1, 4, 2, 0) 0.0; (2, 2, 1, 0) 0.0; (3, 3, 2, 0) 0.0; (2, 3, 1, 0) 0.0; (4, 4, 1, 0) 0.0; (3, 4, 2, 0) 1.0; (2, 4, 1, 0) 0.0]

Thanks!