Routing-solver + use_depth_first_search(true) -> complete/infeasibility-certificate for initial-solution search?

[sschnug]

I'm currently observing the following behaviour:

• routing-solver with (somewhat) default parameters on some instance: ROUTING_FAIL_TIMEOUT => not able to find solution
• routing-solver with same parameters but use_depth_first_search = true with same instance: ROUTING_FAIL => not able to find solution
  • time-limit not fully used (significant gap)!

Furthermore we can use params.mutable_solver_parameters()->set_trace_search(true); to see:

I0109 21:47:39.998561  122017 search.cc:341] ########  EnterSearch(0)
I0109 21:47:39.998590  122017 search.cc:375] ########  BeginInitialPropagation()
I0109 21:47:40.672837  122017 search.cc:378] ########  EndInitialPropagation()
I0109 21:47:40.672924  122017 search.cc:350] ########  BeginNextDecision(AddConstraintDecisionBuilder(TrueConstraint())) 
I0109 21:47:40.672949  122017 search.cc:356] ########  EndNextDecision(AddConstraintDecisionBuilder(TrueConstraint())) 
I0109 21:47:40.672957  122017 search.cc:385] ########  AcceptSolution()
I0109 21:47:40.672962  122017 search.cc:381] ########  AtSolution()
I0109 21:47:40.703000  122017 search.cc:347] ########  ExitSearch(1)
I0109 21:47:40.705700  122017 search.cc:341] ########  EnterSearch(0)
I0109 21:47:40.705760  122017 search.cc:375] ########  BeginInitialPropagation()
I0109 21:47:41.425972  122017 search.cc:378] ########  EndInitialPropagation()
I0109 21:47:41.426060  122017 search.cc:350] ########  BeginNextDecision(ComposeDecisionBuilder(RestoreAssignment, RestoreAssignment, ComposeDecisionBuilder(ChooseFirstUnbound_SelectMinValue(Nexts0(1..3935 4735), Nexts1(2..3935 4735..5534), Nexts2(1 3..3935 4735..5534), Nexts3(1 2 4..3935 4735..5534), Nexts4(1..3 5..3935 4735..5534), Nexts5(1..4 6..3935 4735..5534), Nexts6(1..5 7..3935 4735..5534), Nexts7(1..6 8..3935 4735..5534), Nexts8(1..7 9..3935 4735..5534), Nexts9(1..8 10..3935 4735..5534), Nexts10(1..9 11..3935 4735..5534), Nexts11(1..10 12..3935 4735..5534), Nexts12(1..11 13..3935 4735..5534), Nexts13(1..12 14..3935 4735..5534), Nexts14(1..13 15..3935 4735..5534), Nexts15(1..14 16..3935 4735..5534), Nexts16(1..15 17..3935 4735..5534), Nexts17(1..16 18..3935 4735..5534), Nexts18(1..17 19..3935 4735..5534), Nexts19(1..18 20..3935 4735..5534), Nexts20(1..19 21..3935 4735..5534), Nexts21(1..20 22..3935 4735..5534), Nexts22(1..21 23..3935 4735..5534), Nexts23(1..22 24..3935 4735..5534), Nexts24(1..23 25..3935 4735..5534), Nexts25(1..24 26..3935 4735..5534), Nexts26(1..25 27..3935 4735..5534), Nexts27(1..26 28..3935 4735..5534), Nexts28(1..27 29..3935 4735..5534), Nexts29(1..28 30..3935 4735..5534), Nexts30(1..29 31..3935 4735..5534), Nexts31(1..30 32..3935 4735..5534), Nexts32(1..31 33..3935 4735..5534), Nexts33(1..32 34..3935 4735..5534), Nexts34(1..33 35..3935 4735..5534), Nexts35(1..34 36..3935 4735..5534), Nexts36(1..35 37..3935 4735..5534), Nexts37(1..36 38..3935 4735..5534), Nexts38(1..37 39..3935 4735..5534), Nexts39(1..38 40..3935 4735..5534), Nexts40(1..39 41..3935 4735..5534), Nexts41(1..40 42..3935 4735..5534), Nexts42(1..41 43..3935 4735..5534), Nexts43(1..42 44..3935 4735..5534), Nexts44(1..43 45..3935 4735..5534), Nexts45(1..44 46..3935 4735..5534), Nexts46(1..45 47..3935 4735..5534), Nexts47(1..46 48..3935 4735..5534), Nexts48(1..47 49..3935 4735..5534), Nexts49(1..48 50..3935 4735..5534), Nexts50(1..49 51..3935 4735..5534), Nexts51(1..50 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I0109 21:47:41.478277  122017 search.cc:369] ########  BeginFail(0)
I0109 21:47:41.478308  122017 search.cc:372] ########  EndFail(0)
I0109 21:47:41.478315  122017 search.cc:389] ########  NoMoreSolutions()
I0109 21:47:41.510844  122017 search.cc:347] ########  ExitSearch(1)
I0109 21:47:41.511089  122017 search.cc:341] ########  EnterSearch(0)
I0109 21:47:41.511115  122017 search.cc:375] ########  BeginInitialPropagation()
I0109 21:47:42.188307  122017 search.cc:378] ########  EndInitialPropagation()
I0109 21:47:42.188389  122017 search.cc:350] ########  BeginNextDecision(ComposeDecisionBuilder(RestoreAssignment, ComposeDecisionBuilder(TryDecisionBuilder(IntVarFilteredDecisionBuilder(EvaluatorCheapestAdditionFilteredHeuristic), PathSelector_SelectCheapestValue(Nexts0(1..3935 4735), Nexts1(2..3935 4735..5534), Nexts2(1 3..3935 4735..5534), Nexts3(1 2 4..3935 4735..5534), Nexts4(1..3 5..3935 4735..5534), Nexts5(1..4 6..3935 4735..5534), Nexts6(1..5 7..3935 4735..5534), Nexts7(1..6 8..3935 4735..5534), Nexts8(1..7 9..3935 4735..5534), Nexts9(1..8 10..3935 4735..5534), Nexts10(1..9 11..3935 4735..5534), Nexts11(1..10 12..3935 4735..5534), Nexts12(1..11 13..3935 4735..5534), Nexts13(1..12 14..3935 4735..5534), Nexts14(1..13 15..3935 4735..5534), Nexts15(1..14 16..3935 4735..5534), Nexts16(1..15 17..3935 4735..5534), Nexts17(1..16 18..3935 4735..5534), Nexts18(1..17 19..3935 4735..5534), Nexts19(1..18 20..3935 4735..5534), Nexts20(1..19 21..3935 4735..5534), Nexts21(1..20 22..3935 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I0109 21:47:42.292262  122017 search.cc:354] ########  EndNextDecision(ComposeDecisionBuilder(RestoreAssignment, ComposeDecisionBuilder(TryDecisionBuilder(IntVarFilteredDecisionBuilder(EvaluatorCheapestAdditionFilteredHeuristic), PathSelector_SelectCheapestValue(Nexts0(1..3935 4735), Nexts1(2..3935 4735..5534), Nexts2(1 3..3935 4735..5534), Nexts3(1 2 4..3935 4735..5534), Nexts4(1..3 5..3935 4735..5534), Nexts5(1..4 6..3935 4735..5534), Nexts6(1..5 7..3935 4735..5534), Nexts7(1..6 8..3935 4735..5534), Nexts8(1..7 9..3935 4735..5534), Nexts9(1..8 10..3935 4735..5534), Nexts10(1..9 11..3935 4735..5534), Nexts11(1..10 12..3935 4735..5534), Nexts12(1..11 13..3935 4735..5534), Nexts13(1..12 14..3935 4735..5534), Nexts14(1..13 15..3935 4735..5534), Nexts15(1..14 16..3935 4735..5534), Nexts16(1..15 17..3935 4735..5534), Nexts17(1..16 18..3935 4735..5534), Nexts18(1..17 19..3935 4735..5534), Nexts19(1..18 20..3935 4735..5534), Nexts20(1..19 21..3935 4735..5534), Nexts21(1..20 22..3935 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Nexts385(1..384 386..3935 4735..5534), Nexts386(1..385 387..3935 4735.
I0109 21:47:42.392749  122017 search.cc:360] ########  ApplyDecision(TryDecision) 
I0109 21:47:42.392771  122017 search.cc:366] ########  AfterDecision(TryDecision, true) 
I0109 21:47:42.392787  122017 search.cc:350] ########  BeginNextDecision(ComposeDecisionBuilder(RestoreAssignment, ComposeDecisionBuilder(TryDecisionBuilder(IntVarFilteredDecisionBuilder(EvaluatorCheapestAdditionFilteredHeuristic), PathSelector_SelectCheapestValue(Nexts0(1..3935 4735), Nexts1(2..3935 4735..5534), Nexts2(1 3..3935 4735..5534), Nexts3(1 2 4..3935 4735..5534), Nexts4(1..3 5..3935 4735..5534), Nexts5(1..4 6..3935 4735..5534), Nexts6(1..5 7..3935 4735..5534), Nexts7(1..6 8..3935 4735..5534), Nexts8(1..7 9..3935 4735..5534), Nexts9(1..8 10..3935 4735..5534), Nexts10(1..9 11..3935 4735..5534), Nexts11(1..10 12..3935 4735..5534), Nexts12(1..11 13..3935 4735..5534), Nexts13(1..12 14..3935 4735..5534), Nexts14(1..13 15..3935 4735..5534), Nexts15(1..14 16..3935 4735..5534), Nexts16(1..15 17..3935 4735..5534), Nexts17(1..16 18..3935 4735..5534), Nexts18(1..17 19..3935 4735..5534), Nexts19(1..18 20..3935 4735..5534), Nexts20(1..19 21..3935 4735..5534), Nexts21(1..20 22..3935 4735..5534), Nexts22(1..21 23..3935 4735..5534), Nexts23(1..22 24..3935 4735..5534), Nexts24(1..23 25..3935 4735..5534), Nexts25(1..24 26..3935 4735..5534), Nexts26(1..25 27..3935 4735..5534), Nexts27(1..26 28..3935 4735..5534), Nexts28(1..27 29..3935 4735..5534), Nexts29(1..28 30..3935 4735..5534), Nexts30(1..29 31..3935 4735..5534), Nexts31(1..30 32..3935 4735..5534), Nexts32(1..31 33..3935 4735..5534), Nexts33(1..32 34..3935 4735..5534), Nexts34(1..33 35..3935 4735..5534), Nexts35(1..34 36..3935 4735..5534), Nexts36(1..35 37..3935 4735..5534), Nexts37(1..36 38..3935 4735..5534), Nexts38(1..37 39..3935 4735..5534), Nexts39(1..38 40..3935 4735..5534), Nexts40(1..39 41..3935 4735..5534), Nexts41(1..40 42..3935 4735..5534), Nexts42(1..41 43..3935 4735..5534), Nexts43(1..42 44..3935 4735..5534), Nexts44(1..43 45..3935 4735..5534), Nexts45(1..44 46..3935 4735..5534), Nexts46(1..45 47..3935 4735..5534), Nexts47(1..46 48..3935 4735..5534), Nexts48(1..47 49..3935 4735..5534), Nexts49(1..48 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Nexts385(1..384 386..3935 4735..5534), Nexts386(1..385 387..3935 473
I0109 21:47:45.437656  122017 routing_search.cc:244] Number of decisions: 629929
I0109 21:47:45.437763  122017 routing_search.cc:245] Number of rejected decisions: 625192
I0109 21:47:45.586358  122017 search.cc:369] ########  BeginFail(1)
I0109 21:47:45.596963  122017 search.cc:372] ########  EndFail(0)
I0109 21:47:45.597057  122017 search.cc:369] ########  BeginFail(0)
I0109 21:47:45.597081  122017 search.cc:372] ########  EndFail(0)
I0109 21:47:45.597104  122017 search.cc:389] ########  NoMoreSolutions()
I0109 21:47:45.628225  122017 search.cc:347] ########  ExitSearch(1)
I0109 21:47:45.628317  122017 routing.cc:3512] Objective lower bound: 0
I0109 21:47:45.628340  122017 oracle_rich_vrp.cc:569] Solve status: 3

I'm not sure how to interpret this.

I'm inclined to think that CP + DFS without any conflict- or backtracking-limits is always complete as it's full enumeration (supported by propagation).

But in this case, i would expect the return-status to be ROUTING_INFEASIBLE. It isn't howewer.

(it seems this status is only used in a very limited way:

or-tools/ortools/constraint_solver/routing.cc

Line 2556 in 8768ed7

// Detect infeasibilities at the root of the search tree.

sounds like root-propagation only to me)

Does above tell me it's proven to be infeasible and the status is not expressing this or does above not mean, that it's proven to be infeasible?

(as indicated in the verbose-output, we cannot easily use cp-sat or other complete-solvers without being careful about scaling: e.g. not using the assignment-polytope lp-relaxation!)