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[TambyVanderpooten] relax the tolerances used to compare objectives #196

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odow merged 2 commits into from
Apr 7, 2026
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[TambyVanderpooten] relax the tolerances used to compare objectives #196

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[TambyVanderpooten] relax the tolerances used to compare objectives
odow Apr 7, 2026
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odow Apr 7, 2026
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26 changes: 22 additions & 4 deletions src/algorithms/TambyVanderpooten.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -32,6 +32,24 @@ This algorithm is restricted to problems with:
"""
struct TambyVanderpooten <: AbstractAlgorithm end

"""
const _TAMBY_VANDERPOOTEN_ATOL = 1e-3

This constant is important.

When we have a solution, we need to decide if the `Y` vector is at the edge of
one of the bounds. The paper assumes exact arithmetic. Solvers have tolerances.

In theory the algorithm works only for problems with integer-valued objectives.
So we could make this as big as `0.5` or something. We previously used `1e-6`,
but this caused problems when the solver's feasibility tolerance meant that the
objective value was something like `1234.00005`.

In future, we could consider how to rewrite the algorithm to make it more robust
to numerical issues like this.
"""
const _TAMBY_VANDERPOOTEN_ATOL = 1e-3

# This is Algorithm 1 from the paper.
function _update_search_region(
U_N::Dict{Vector{Float64},Vector{Vector{Vector{Float64}}}},
Expand Down Expand Up @@ -110,7 +128,7 @@ function _select_search_zone(
)
k_star, u_star, v_star = 1, yN, -Inf
for k in 1:length(yI), u in keys(U_N)
if !isapprox(u[k], yN[k]; atol = 1e-6)
if !isapprox(u[k], yN[k]; atol = _TAMBY_VANDERPOOTEN_ATOL)
v = _h(k, u, yI)
if v > v_star
k_star, u_star, v_star = k, u, v
Expand Down Expand Up @@ -240,7 +258,7 @@ function _minimize_multiobjective!(
push!(V[k], (u, Y))
# We want `if !(Y in U_N[u][k])` but this tests exact equality. We
# want an approximate comparison.
if all(!isapprox(Y; atol = 1e-6), U_N[u][k])
if all(!isapprox(Y; atol = _TAMBY_VANDERPOOTEN_ATOL), U_N[u][k])
_update_search_region(U_N, Y, yN)
solutions[Y] = X
end
Expand Down Expand Up @@ -270,7 +288,7 @@ end

function _clean_search_region_inner(u′, U_N, yI, V, k)
for (u′_k, yI_k) in zip(u′, yI)
if isapprox(u′_k, yI_k; atol = 1e-6)
if isapprox(u′_k, yI_k; atol = _TAMBY_VANDERPOOTEN_ATOL)
return true
end
end
Expand All @@ -285,7 +303,7 @@ function _clean_search_region_inner(u′, U_N, yI, V, k)
end

function _comparison_line_16(u′, u, y_k, k)
if !≈(y_k[k], u′[k]; atol = 1e-6)
if !≈(y_k[k], u′[k]; atol = _TAMBY_VANDERPOOTEN_ATOL)
return false
end
for (i, (u′_i, u_i)) in enumerate(zip(u′, u))
Expand Down
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