SCIPはバイナリ変数に非バイナリ値を割り当てます

Question

私は1つの整数変数（最小化する目的）と22016バイナリ変数でILP問題を解決しています。トップソリューションでは、バイナリ変数のうち4つに非​​バイナリ値が割り当てられています。値は関連しているようです。

A8350 = 1.1102230246251565E-16 
B1958 = 1.1102230246251565E-16 
B1896 = 1.1102230246251565E-16 
C1404 = 2.220446049250313E-16 

これは、変数C1404は、例えば、JSCIPOptを使用して作成された方法です：問題で

scip.createVar("C1404", 0d, 1d, 0d, SCIP_Vartype.SCIP_VARTYPE_BINARY); 

制約のすべては、整数パラメータを持つ線形です。私はJSCIPOptにそうようにそれらを作成します。

scip.createConsLinear(String name, Variable[] vars, double[] vals, double lhs, double rhs); 

私が表現しようとしている制約は、その後、私は-scip.infinity()にlhsを設定し、それがlhs = rhsであるならば、私はrhsと同じ値にlhsを設定lhs <= rhsある場合。ここでも、rhsは常にdoubleとして表現される整数値です。ここでは例えば

制約の2の引数は、C1404が関与している：期待これらの非ゼロ値は

Constraint 1: 
vars: [ 
    C1404 in [-0.0,1.0] obj = 0.0 type = SCIP_VARTYPE_BINARY, 
    B1569 in [-0.0,1.0] obj = 0.0 type = SCIP_VARTYPE_BINARY, 
    B1625 in [-0.0,1.0] obj = 0.0 type = SCIP_VARTYPE_BINARY, 
    B1896 in [-0.0,1.0] obj = 0.0 type = SCIP_VARTYPE_BINARY, 
    B1958 in [-0.0,1.0] obj = 0.0 type = SCIP_VARTYPE_BINARY, 
    B2455 in [-0.0,1.0] obj = 0.0 type = SCIP_VARTYPE_BINARY 
    ] 
vals: [1.0, -1.0, -1.0, -1.0, -1.0, -1.0] 
lhs: -1.0E20 
rhs: 0.0 

Constraint 2: 
vars: [ 
    C1404 in [-0.0,1.0] obj = 0.0 type = SCIP_VARTYPE_BINARY, 
    D1404 in [-0.0,1.0] obj = 0.0 type = SCIP_VARTYPE_BINARY 
    ] 
vals: [1.0, -1.0] 
lhs: -1.0E20 
rhs: 0.0 

ていますか？もしそうなら、バイナリ変数を量子化する正しいテストは何ですか？それはval >= 0.5 ? 1d : 0dですか？

これは、参考になる場合はSCIPの出力です。

presolving: 
(round 1, fast)  8082 del vars, 10240 del conss, 1 add conss, 1659 chg bounds, 1991 chg sides, 1991 chg coeffs, 0 upgd conss, 0 impls, 32520 clqs 
(round 2, fast)  11936 del vars, 47461 del conss, 1 add conss, 4711 chg bounds, 1991 chg sides, 1991 chg coeffs, 0 upgd conss, 0 impls, 14440 clqs 
(round 3, fast)  13952 del vars, 50946 del conss, 1 add conss, 4713 chg bounds, 2010 chg sides, 2010 chg coeffs, 0 upgd conss, 0 impls, 12425 clqs 
(round 4, fast)  13974 del vars, 50948 del conss, 1 add conss, 4713 chg bounds, 2024 chg sides, 2024 chg coeffs, 0 upgd conss, 0 impls, 12432 clqs 
(round 5, exhaustive) 13974 del vars, 58850 del conss, 1 add conss, 4713 chg bounds, 2051 chg sides, 2024 chg coeffs, 0 upgd conss, 0 impls, 12432 clqs 
(round 6, exhaustive) 13975 del vars, 58851 del conss, 1 add conss, 4713 chg bounds, 2051 chg sides, 2024 chg coeffs, 31716 upgd conss, 0 impls, 12431 clqs 
(round 7, medium)  14110 del vars, 61288 del conss, 5597 add conss, 4713 chg bounds, 2051 chg sides, 2024 chg coeffs, 31716 upgd conss, 0 impls, 17686 clqs 
(round 8, exhaustive) 14110 del vars, 61450 del conss, 5643 add conss, 4713 chg bounds, 2051 chg sides, 2024 chg coeffs, 31716 upgd conss, 0 impls, 17694 clqs 
(round 9, exhaustive) 14111 del vars, 61451 del conss, 5644 add conss, 4713 chg bounds, 2051 chg sides, 2024 chg coeffs, 31855 upgd conss, 0 impls, 17688 clqs 
(round 10, medium)  14213 del vars, 61642 del conss, 5883 add conss, 4713 chg bounds, 2051 chg sides, 2024 chg coeffs, 31855 upgd conss, 0 impls, 17755 clqs 
(round 11, fast)  14213 del vars, 61687 del conss, 5883 add conss, 4713 chg bounds, 2051 chg sides, 2024 chg coeffs, 31855 upgd conss, 0 impls, 17758 clqs 
(round 12, exhaustive) 14213 del vars, 61714 del conss, 5887 add conss, 4713 chg bounds, 2051 chg sides, 2097 chg coeffs, 31863 upgd conss, 0 impls, 17758 clqs 
(round 13, exhaustive) 14219 del vars, 61734 del conss, 5901 add conss, 4713 chg bounds, 2051 chg sides, 2097 chg coeffs, 31863 upgd conss, 0 impls, 17758 clqs 
(round 14, exhaustive) 14263 del vars, 61734 del conss, 5901 add conss, 4713 chg bounds, 2051 chg sides, 2215 chg coeffs, 31863 upgd conss, 0 impls, 17637 clqs 
(round 15, fast)  14265 del vars, 61888 del conss, 5901 add conss, 4713 chg bounds, 2051 chg sides, 2221 chg coeffs, 31866 upgd conss, 0 impls, 17651 clqs 
(round 16, medium)  14277 del vars, 61903 del conss, 5901 add conss, 4713 chg bounds, 2051 chg sides, 2221 chg coeffs, 31866 upgd conss, 0 impls, 17639 clqs 
(round 17, exhaustive) 14277 del vars, 61927 del conss, 5905 add conss, 4713 chg bounds, 2051 chg sides, 2221 chg coeffs, 31866 upgd conss, 0 impls, 17639 clqs 
(round 18, exhaustive) 14312 del vars, 61932 del conss, 5910 add conss, 4713 chg bounds, 2051 chg sides, 2221 chg coeffs, 31866 upgd conss, 0 impls, 17795 clqs 
(round 19, fast)  14312 del vars, 62020 del conss, 5910 add conss, 4713 chg bounds, 2051 chg sides, 2225 chg coeffs, 31868 upgd conss, 0 impls, 17798 clqs 
(round 20, exhaustive) 14314 del vars, 62071 del conss, 5913 add conss, 4713 chg bounds, 2051 chg sides, 2225 chg coeffs, 31868 upgd conss, 0 impls, 17796 clqs 
(round 21, exhaustive) 14352 del vars, 62074 del conss, 5916 add conss, 4713 chg bounds, 2051 chg sides, 2225 chg coeffs, 31868 upgd conss, 0 impls, 18036 clqs 
(round 22, fast)  14352 del vars, 62165 del conss, 5916 add conss, 4713 chg bounds, 2051 chg sides, 2227 chg coeffs, 31871 upgd conss, 0 impls, 18039 clqs 
(round 23, exhaustive) 14393 del vars, 62179 del conss, 5920 add conss, 4713 chg bounds, 2051 chg sides, 2227 chg coeffs, 31871 upgd conss, 0 impls, 17986 clqs 
(round 24, fast)  14393 del vars, 62283 del conss, 5920 add conss, 4713 chg bounds, 2051 chg sides, 2230 chg coeffs, 31875 upgd conss, 0 impls, 17989 clqs 
(round 25, exhaustive) 14394 del vars, 62307 del conss, 5925 add conss, 4713 chg bounds, 2051 chg sides, 2230 chg coeffs, 31875 upgd conss, 0 impls, 17987 clqs 
(round 26, exhaustive) 14433 del vars, 62322 del conss, 5925 add conss, 4713 chg bounds, 2051 chg sides, 2233 chg coeffs, 31875 upgd conss, 0 impls, 17907 clqs 
(round 27, fast)  14434 del vars, 62414 del conss, 5925 add conss, 4713 chg bounds, 2051 chg sides, 2236 chg coeffs, 31878 upgd conss, 0 impls, 17896 clqs 
(round 28, exhaustive) 14464 del vars, 62431 del conss, 5929 add conss, 4713 chg bounds, 2051 chg sides, 2236 chg coeffs, 31878 upgd conss, 0 impls, 18203 clqs 
(round 29, fast)  14465 del vars, 62490 del conss, 5929 add conss, 4713 chg bounds, 2051 chg sides, 2238 chg coeffs, 31881 upgd conss, 0 impls, 18202 clqs 
(round 30, exhaustive) 14527 del vars, 62505 del conss, 5932 add conss, 4713 chg bounds, 2051 chg sides, 2238 chg coeffs, 31881 upgd conss, 0 impls, 17942 clqs 
(round 31, fast)  14527 del vars, 63543 del conss, 5932 add conss, 4713 chg bounds, 2051 chg sides, 2322 chg coeffs, 31881 upgd conss, 0 impls, 17947 clqs 
(round 32, exhaustive) 14562 del vars, 63543 del conss, 5932 add conss, 4713 chg bounds, 2051 chg sides, 2322 chg coeffs, 31881 upgd conss, 0 impls, 17921 clqs 
(round 33, fast)  14563 del vars, 63642 del conss, 5932 add conss, 4713 chg bounds, 2051 chg sides, 2330 chg coeffs, 31884 upgd conss, 0 impls, 17922 clqs 
(round 34, exhaustive) 14565 del vars, 63667 del conss, 5934 add conss, 4713 chg bounds, 2051 chg sides, 2330 chg coeffs, 31884 upgd conss, 0 impls, 17918 clqs 
(round 35, exhaustive) 14619 del vars, 63669 del conss, 5936 add conss, 4713 chg bounds, 2051 chg sides, 2330 chg coeffs, 31884 upgd conss, 0 impls, 17800 clqs 
(round 36, fast)  14621 del vars, 63815 del conss, 5936 add conss, 4713 chg bounds, 2051 chg sides, 2335 chg coeffs, 31884 upgd conss, 0 impls, 17802 clqs 
(round 37, fast)  14632 del vars, 63827 del conss, 5936 add conss, 4713 chg bounds, 2051 chg sides, 2335 chg coeffs, 31884 upgd conss, 0 impls, 17791 clqs 
(round 38, exhaustive) 14685 del vars, 63831 del conss, 5937 add conss, 4713 chg bounds, 2051 chg sides, 2335 chg coeffs, 31884 upgd conss, 0 impls, 17290 clqs 
(round 39, fast)  14687 del vars, 64576 del conss, 5937 add conss, 4713 chg bounds, 2051 chg sides, 2394 chg coeffs, 31884 upgd conss, 0 impls, 17292 clqs 
(round 40, exhaustive) 14716 del vars, 64576 del conss, 5937 add conss, 4713 chg bounds, 2051 chg sides, 2394 chg coeffs, 31884 upgd conss, 0 impls, 17382 clqs 
(round 41, fast)  14716 del vars, 65016 del conss, 5937 add conss, 4713 chg bounds, 2051 chg sides, 2445 chg coeffs, 31884 upgd conss, 0 impls, 17384 clqs 
(round 42, exhaustive) 14749 del vars, 65017 del conss, 5938 add conss, 4713 chg bounds, 2051 chg sides, 2445 chg coeffs, 31884 upgd conss, 0 impls, 17372 clqs 
(round 43, fast)  14749 del vars, 65275 del conss, 5938 add conss, 4713 chg bounds, 2051 chg sides, 2473 chg coeffs, 31886 upgd conss, 0 impls, 17373 clqs 
(round 44, exhaustive) 14753 del vars, 65308 del conss, 5941 add conss, 4713 chg bounds, 2051 chg sides, 2473 chg coeffs, 31886 upgd conss, 0 impls, 17365 clqs 
(round 45, exhaustive) 14789 del vars, 65309 del conss, 5942 add conss, 4713 chg bounds, 2051 chg sides, 2473 chg coeffs, 31886 upgd conss, 0 impls, 17355 clqs 
(round 46, fast)  14800 del vars, 65404 del conss, 5942 add conss, 4713 chg bounds, 2051 chg sides, 2494 chg coeffs, 31889 upgd conss, 0 impls, 17299 clqs 
(round 47, fast)  14802 del vars, 65462 del conss, 5942 add conss, 4713 chg bounds, 2051 chg sides, 2494 chg coeffs, 31889 upgd conss, 0 impls, 17291 clqs 
(round 48, exhaustive) 14883 del vars, 65470 del conss, 5944 add conss, 4713 chg bounds, 2051 chg sides, 2494 chg coeffs, 31889 upgd conss, 0 impls, 17465 clqs 
(round 49, fast)  14884 del vars, 65768 del conss, 5944 add conss, 4713 chg bounds, 2051 chg sides, 2558 chg coeffs, 31890 upgd conss, 0 impls, 17466 clqs 
(round 50, fast)  14896 del vars, 65806 del conss, 5944 add conss, 4713 chg bounds, 2051 chg sides, 2558 chg coeffs, 31890 upgd conss, 0 impls, 17419 clqs 
(round 51, exhaustive) 14900 del vars, 65834 del conss, 5945 add conss, 4713 chg bounds, 2051 chg sides, 2558 chg coeffs, 31890 upgd conss, 0 impls, 17401 clqs 
(round 52, exhaustive) 14964 del vars, 65835 del conss, 5946 add conss, 4713 chg bounds, 2051 chg sides, 2558 chg coeffs, 31890 upgd conss, 0 impls, 17169 clqs 
(round 53, fast)  14966 del vars, 66063 del conss, 5946 add conss, 4713 chg bounds, 2051 chg sides, 2625 chg coeffs, 31890 upgd conss, 0 impls, 17170 clqs 
(round 54, exhaustive) 15004 del vars, 66078 del conss, 5946 add conss, 4713 chg bounds, 2051 chg sides, 2625 chg coeffs, 31890 upgd conss, 0 impls, 17316 clqs 
(round 55, fast)  15004 del vars, 66225 del conss, 5946 add conss, 4713 chg bounds, 2051 chg sides, 2660 chg coeffs, 31890 upgd conss, 0 impls, 17319 clqs 
(round 56, exhaustive) 15035 del vars, 66237 del conss, 5946 add conss, 4713 chg bounds, 2051 chg sides, 2660 chg coeffs, 31890 upgd conss, 0 impls, 19526 clqs 
(round 57, fast)  15035 del vars, 66659 del conss, 5946 add conss, 4713 chg bounds, 2051 chg sides, 2712 chg coeffs, 31890 upgd conss, 0 impls, 19526 clqs 
(round 58, exhaustive) 15086 del vars, 66660 del conss, 5947 add conss, 4713 chg bounds, 2051 chg sides, 2714 chg coeffs, 31890 upgd conss, 0 impls, 19393 clqs 
(round 59, fast)  15092 del vars, 66859 del conss, 5947 add conss, 4713 chg bounds, 2051 chg sides, 2767 chg coeffs, 31890 upgd conss, 0 impls, 19372 clqs 
(round 60, fast)  15104 del vars, 66892 del conss, 5947 add conss, 4713 chg bounds, 2051 chg sides, 2767 chg coeffs, 31890 upgd conss, 0 impls, 19350 clqs 
(round 61, exhaustive) 15142 del vars, 66892 del conss, 5947 add conss, 4713 chg bounds, 2051 chg sides, 2767 chg coeffs, 31890 upgd conss, 0 impls, 19053 clqs 
(round 62, fast)  15146 del vars, 67040 del conss, 5947 add conss, 4713 chg bounds, 2051 chg sides, 2804 chg coeffs, 31890 upgd conss, 0 impls, 18863 clqs 
(round 63, fast)  15151 del vars, 67074 del conss, 5947 add conss, 4713 chg bounds, 2051 chg sides, 2804 chg coeffs, 31890 upgd conss, 0 impls, 18851 clqs 
(round 64, exhaustive) 15181 del vars, 67074 del conss, 5947 add conss, 4713 chg bounds, 2051 chg sides, 2804 chg coeffs, 31890 upgd conss, 0 impls, 19819 clqs 
(round 65, fast)  15181 del vars, 67166 del conss, 5947 add conss, 4713 chg bounds, 2051 chg sides, 2830 chg coeffs, 31890 upgd conss, 0 impls, 19821 clqs 
(round 66, fast)  15198 del vars, 67249 del conss, 5947 add conss, 4713 chg bounds, 2051 chg sides, 2830 chg coeffs, 31890 upgd conss, 0 impls, 19558 clqs 
(round 67, fast)  15198 del vars, 67307 del conss, 5947 add conss, 4713 chg bounds, 2051 chg sides, 2830 chg coeffs, 31890 upgd conss, 0 impls, 19558 clqs 
(round 68, exhaustive) 15226 del vars, 67309 del conss, 5948 add conss, 4713 chg bounds, 2051 chg sides, 2830 chg coeffs, 31890 upgd conss, 0 impls, 25712 clqs 
(round 69, fast)  15226 del vars, 67368 del conss, 5948 add conss, 4713 chg bounds, 2051 chg sides, 2843 chg coeffs, 31890 upgd conss, 0 impls, 25715 clqs 
(round 70, exhaustive) 15229 del vars, 67404 del conss, 5952 add conss, 4713 chg bounds, 2051 chg sides, 2843 chg coeffs, 31890 upgd conss, 0 impls, 25683 clqs 
(round 71, exhaustive) 15297 del vars, 67409 del conss, 5953 add conss, 4713 chg bounds, 2051 chg sides, 2850 chg coeffs, 31890 upgd conss, 0 impls, 22704 clqs 
(round 72, fast)  15297 del vars, 67743 del conss, 5953 add conss, 4713 chg bounds, 2051 chg sides, 2952 chg coeffs, 31890 upgd conss, 0 impls, 22705 clqs 
(round 73, exhaustive) 15330 del vars, 67743 del conss, 5953 add conss, 4713 chg bounds, 2051 chg sides, 2952 chg coeffs, 31890 upgd conss, 0 impls, 22670 clqs 
(round 74, fast)  15330 del vars, 67826 del conss, 5953 add conss, 4713 chg bounds, 2051 chg sides, 2968 chg coeffs, 31890 upgd conss, 0 impls, 22672 clqs 
(round 75, fast)  15338 del vars, 67877 del conss, 5953 add conss, 4713 chg bounds, 2051 chg sides, 2968 chg coeffs, 31890 upgd conss, 0 impls, 22608 clqs 
(round 76, exhaustive) 15392 del vars, 67882 del conss, 5953 add conss, 4713 chg bounds, 2051 chg sides, 2968 chg coeffs, 31890 upgd conss, 0 impls, 22644 clqs 
(round 77, fast)  15393 del vars, 68093 del conss, 5953 add conss, 4713 chg bounds, 2051 chg sides, 3034 chg coeffs, 31890 upgd conss, 0 impls, 22631 clqs 
(round 78, fast)  15406 del vars, 68165 del conss, 5953 add conss, 4713 chg bounds, 2051 chg sides, 3034 chg coeffs, 31890 upgd conss, 0 impls, 22547 clqs 
(round 79, exhaustive) 15436 del vars, 68169 del conss, 5953 add conss, 4713 chg bounds, 2051 chg sides, 3035 chg coeffs, 31890 upgd conss, 0 impls, 23722 clqs 
(round 80, fast)  15439 del vars, 68247 del conss, 5953 add conss, 4713 chg bounds, 2051 chg sides, 3060 chg coeffs, 31890 upgd conss, 0 impls, 23723 clqs 
(round 81, medium)  15445 del vars, 68266 del conss, 5953 add conss, 4713 chg bounds, 2051 chg sides, 3060 chg coeffs, 31890 upgd conss, 0 impls, 23682 clqs 
(round 82, exhaustive) 15555 del vars, 68274 del conss, 5955 add conss, 4713 chg bounds, 2051 chg sides, 3060 chg coeffs, 31890 upgd conss, 0 impls, 25208 clqs 
(round 83, fast)  15555 del vars, 69541 del conss, 5955 add conss, 4713 chg bounds, 2051 chg sides, 3196 chg coeffs, 31890 upgd conss, 0 impls, 25215 clqs 
(round 84, exhaustive) 15559 del vars, 69585 del conss, 5964 add conss, 4713 chg bounds, 2051 chg sides, 3196 chg coeffs, 31890 upgd conss, 0 impls, 25087 clqs 
(round 85, exhaustive) 15589 del vars, 69585 del conss, 5964 add conss, 4713 chg bounds, 2051 chg sides, 3196 chg coeffs, 31890 upgd conss, 0 impls, 27603 clqs 
(round 86, fast)  15608 del vars, 69695 del conss, 5964 add conss, 4713 chg bounds, 2051 chg sides, 3222 chg coeffs, 31890 upgd conss, 0 impls, 27527 clqs 
(round 87, fast)  15612 del vars, 69731 del conss, 5964 add conss, 4713 chg bounds, 2051 chg sides, 3222 chg coeffs, 31890 upgd conss, 0 impls, 27527 clqs 
(round 88, exhaustive) 15612 del vars, 69749 del conss, 5970 add conss, 4713 chg bounds, 2051 chg sides, 3222 chg coeffs, 31890 upgd conss, 0 impls, 27531 clqs 
(round 89, exhaustive) 15642 del vars, 69749 del conss, 5970 add conss, 4713 chg bounds, 2051 chg sides, 3222 chg coeffs, 31890 upgd conss, 0 impls, 29574 clqs 
(round 90, fast)  15653 del vars, 69866 del conss, 5970 add conss, 4713 chg bounds, 2051 chg sides, 3249 chg coeffs, 31890 upgd conss, 0 impls, 29520 clqs 
(round 91, fast)  15680 del vars, 69967 del conss, 5970 add conss, 4713 chg bounds, 2051 chg sides, 3249 chg coeffs, 31890 upgd conss, 0 impls, 29331 clqs 
(round 92, fast)  15681 del vars, 70001 del conss, 5970 add conss, 4713 chg bounds, 2051 chg sides, 3249 chg coeffs, 31890 upgd conss, 0 impls, 29303 clqs 
(round 93, exhaustive) 15730 del vars, 70009 del conss, 5972 add conss, 4713 chg bounds, 2051 chg sides, 3250 chg coeffs, 31890 upgd conss, 0 impls, 26873 clqs 
(round 94, fast)  15730 del vars, 70580 del conss, 5972 add conss, 4713 chg bounds, 2051 chg sides, 3318 chg coeffs, 31890 upgd conss, 0 impls, 26875 clqs 
(round 95, exhaustive) 15756 del vars, 70584 del conss, 5973 add conss, 4713 chg bounds, 2051 chg sides, 3318 chg coeffs, 31890 upgd conss, 0 impls, 33781 clqs 
(round 96, fast)  15761 del vars, 70651 del conss, 5973 add conss, 4713 chg bounds, 2051 chg sides, 3332 chg coeffs, 31890 upgd conss, 0 impls, 33755 clqs 
(round 97, fast)  15772 del vars, 70702 del conss, 5973 add conss, 4713 chg bounds, 2051 chg sides, 3332 chg coeffs, 31890 upgd conss, 0 impls, 33300 clqs 
(round 98, fast)  15787 del vars, 70756 del conss, 5973 add conss, 4713 chg bounds, 2051 chg sides, 3332 chg coeffs, 31890 upgd conss, 0 impls, 33188 clqs 
(round 99, exhaustive) 15788 del vars, 70779 del conss, 5978 add conss, 4713 chg bounds, 2051 chg sides, 3332 chg coeffs, 31890 upgd conss, 0 impls, 33184 clqs 
    (9.2s) probing: 1000/8583 (11.7%) - 976 fixings, 324 aggregations, 57830 implications, 0 bound changes 
    (9.7s) probing: 1330/8583 (15.5%) - 978 fixings, 324 aggregations, 58396 implications, 0 bound changes 
    (9.7s) probing aborted: 50/50 successive totally useless probings 
(round 100, exhaustive) 15812 del vars, 70780 del conss, 5979 add conss, 4713 chg bounds, 2051 chg sides, 3332 chg coeffs, 31890 upgd conss, 0 impls, 53331 clqs 
(round 101, fast)  15827 del vars, 70875 del conss, 5979 add conss, 4713 chg bounds, 2051 chg sides, 3361 chg coeffs, 31890 upgd conss, 0 impls, 52989 clqs 
(round 102, fast)  15849 del vars, 71105 del conss, 5979 add conss, 4713 chg bounds, 2051 chg sides, 3361 chg coeffs, 31890 upgd conss, 0 impls, 51380 clqs 
(round 103, exhaustive) 15850 del vars, 71125 del conss, 5982 add conss, 4713 chg bounds, 2051 chg sides, 3361 chg coeffs, 31890 upgd conss, 0 impls, 51237 clqs 
    (9.9s) probing: 1453/8583 (16.9%) - 979 fixings, 324 aggregations, 59796 implications, 0 bound changes 
    (9.9s) probing aborted: 50/50 successive totally useless probings 
presolving (104 rounds: 104 fast, 53 medium, 49 exhaustive): 
18836 deleted vars, 81732 deleted constraints, 5983 added constraints, 4713 tightened bounds, 0 added holes, 2051 changed sides, 3361 changed coefficients 
0 implications, 51981 cliques 
presolved problem has 3979 variables (3979 bin, 0 int, 0 impl, 0 cont) and 14978 constraints 
    8241 constraints of type <setppc> 
     3 constraints of type <and> 
    6734 constraints of type <logicor> 
transformed objective value is always integral (scale: 1) 
Presolving Time: 9.95 

time | node | left |LP iter|LP it/n| mem |mdpt |frac |vars |cons |cols |rows |cuts |confs|strbr| dualbound | primalbound | gap 
T10.2s|  1 |  0 |  0 |  - | 196M| 0 | - |3979 | 14k|3979 | 14k| 0 | 3 | 0 |-4.634700e+05 | 5.942710e+05 | Inf 
b10.2s|  1 |  0 |  0 |  - | 196M| 0 | - |3979 | 14k|3979 | 14k| 0 | 3 | 0 |-4.634700e+05 | 4.910190e+05 | Inf 
10.3s|  1 |  0 | 2350 |  - | 196M| 0 | 573 |3979 | 14k|3979 | 14k| 0 | 3 | 0 | 1.093312e+05 | 4.910190e+05 | 349.11% 
s10.3s|  1 |  0 | 2350 |  - | 197M| 0 | 573 |3979 | 14k|3979 | 14k| 0 | 4 | 0 | 1.093312e+05 | 2.975580e+05 | 172.16% 
b10.3s|  1 |  0 | 2350 |  - | 198M| 0 | 573 |3979 | 14k|3979 | 14k| 0 | 4 | 0 | 1.093312e+05 | 2.800590e+05 | 156.16% 
10.7s|  1 |  0 | 2553 |  - | 199M| 0 | 634 |3979 | 14k|3979 | 15k| 30 | 4 | 0 | 1.113979e+05 | 2.800590e+05 | 151.40% 
11.1s|  1 |  0 | 2869 |  - | 199M| 0 | 652 |3979 | 14k|3979 | 15k| 49 | 6 | 0 | 1.115939e+05 | 2.800590e+05 | 150.96% 
s11.1s|  1 |  0 | 2869 |  - | 199M| 0 | 652 |3979 | 14k|3979 | 15k| 49 | 7 | 0 | 1.115939e+05 | 2.795390e+05 | 150.50% 
11.4s|  1 |  0 | 2998 |  - | 201M| 0 | 472 |3979 | 14k|3979 | 15k| 70 | 7 | 0 | 1.116789e+05 | 2.795390e+05 | 150.31% 
b11.4s|  1 |  0 | 2998 |  - | 201M| 0 | 472 |3979 | 14k|3979 | 15k| 70 | 7 | 0 | 1.116789e+05 | 2.608210e+05 | 133.55% 
R11.4s|  1 |  0 | 2998 |  - | 202M| 0 | 472 |3979 | 14k|3979 | 15k| 70 | 8 | 0 | 1.116789e+05 | 2.454230e+05 | 119.76% 
s11.4s|  1 |  0 | 2998 |  - | 202M| 0 | 472 |3979 | 14k|3979 | 15k| 70 | 8 | 0 | 1.116789e+05 | 2.444030e+05 | 118.84% 
11.8s|  1 |  0 | 3078 |  - | 203M| 0 | 410 |3979 | 14k|3979 | 15k| 85 | 8 | 0 | 1.117042e+05 | 2.444030e+05 | 118.79% 
R11.8s|  1 |  0 | 3078 |  - | 203M| 0 | 410 |3979 | 14k|3979 | 15k| 85 | 8 | 0 | 1.117042e+05 | 2.432350e+05 | 117.75% 
s11.8s|  1 |  0 | 3078 |  - | 203M| 0 | 410 |3979 | 14k|3979 | 15k| 85 | 8 | 0 | 1.117042e+05 | 2.422220e+05 | 116.84% 
time | node | left |LP iter|LP it/n| mem |mdpt |frac |vars |cons |cols |rows |cuts |confs|strbr| dualbound | primalbound | gap 
b11.8s|  1 |  0 | 3078 |  - | 203M| 0 | 410 |3979 | 14k|3979 | 15k| 85 | 8 | 0 | 1.117042e+05 | 2.325800e+05 | 108.21% 
12.2s|  1 |  0 | 3170 |  - | 203M| 0 | 486 |3979 | 14k|3979 | 15k| 101 | 8 | 0 | 1.117185e+05 | 2.325800e+05 | 108.18% 
12.5s|  1 |  0 | 3270 |  - | 205M| 0 | 306 |3979 | 14k|3979 | 15k| 115 | 9 | 0 | 1.117272e+05 | 2.325800e+05 | 108.17% 
R12.5s|  1 |  0 | 3270 |  - | 205M| 0 | 306 |3979 | 14k|3979 | 15k| 115 | 10 | 0 | 1.117272e+05 | 1.692700e+05 | 51.50% 
s12.5s|  1 |  0 | 3270 |  - | 206M| 0 | 306 |3979 | 14k|3979 | 15k| 115 | 10 | 0 | 1.117272e+05 | 1.682570e+05 | 50.60% 
12.9s|  1 |  0 | 3415 |  - | 207M| 0 | 548 |3979 | 14k|3979 | 15k| 127 | 10 | 0 | 1.117284e+05 | 1.682570e+05 | 50.59% 
b12.9s|  1 |  0 | 3415 |  - | 208M| 0 | 548 |3979 | 14k|3979 | 15k| 127 | 10 | 0 | 1.117284e+05 | 1.616510e+05 | 44.68% 
13.3s|  1 |  0 | 3560 |  - | 209M| 0 | 450 |3979 | 14k|3979 | 15k| 143 | 14 | 0 | 1.117513e+05 | 1.616510e+05 | 44.65% 
13.7s|  1 |  0 | 3874 |  - | 210M| 0 | 361 |3979 | 14k|3979 | 15k| 152 | 15 | 0 | 1.117521e+05 | 1.616510e+05 | 44.65% 
R13.7s|  1 |  0 | 3874 |  - | 210M| 0 | 361 |3979 | 14k|3979 | 15k| 152 | 15 | 0 | 1.117521e+05 | 1.187560e+05 | 6.27% 
s13.7s|  1 |  0 | 3874 |  - | 210M| 0 | 361 |3979 | 14k|3979 | 15k| 152 | 15 | 0 | 1.117521e+05 | 1.177290e+05 | 5.35% 
14.2s|  1 |  0 | 3971 |  - | 211M| 0 | 298 |3979 | 14k|3979 | 15k| 162 | 15 | 0 | 1.117532e+05 | 1.177290e+05 | 5.35% 
b14.2s|  1 |  0 | 3971 |  - | 211M| 0 | 298 |3979 | 14k|3979 | 15k| 162 | 15 | 0 | 1.117532e+05 | 1.126550e+05 | 0.81% 
14.2s|  1 |  0 | 3971 |  - | 211M| 0 | 298 |3979 | 14k|3979 | 15k| 162 | 15 | 0 | 1.117532e+05 | 1.126550e+05 | 0.81% 
14.4s|  1 |  0 | 4117 |  - | 211M| 0 | 314 |3979 | 14k|3979 | 15k| 173 | 15 | 0 | 1.117690e+05 | 1.126550e+05 | 0.79% 
time | node | left |LP iter|LP it/n| mem |mdpt |frac |vars |cons |cols |rows |cuts |confs|strbr| dualbound | primalbound | gap 
E14.6s|  1 |  0 | 4117 |  - | 211M| 0 | 314 |3979 | 14k|3979 | 15k| 173 | 15 | 0 | 1.117690e+05 | 1.118470e+05 | 0.07% 
14.6s|  1 |  0 | 4117 |  - | 211M| 0 | 314 |3979 | 14k|3979 | 15k| 173 | 15 | 0 | 1.117690e+05 | 1.118470e+05 | 0.07% 
14.7s|  1 |  0 | 4117 |  - | 212M| 0 | 314 |3979 | 14k|3979 | 14k| 173 | 15 | 0 | 1.117690e+05 | 1.118470e+05 | 0.07% 
14.8s|  1 |  0 | 4181 |  - | 213M| 0 | 311 |3979 | 14k|3979 | 14k| 182 | 15 | 0 | 1.117690e+05 | 1.118470e+05 | 0.07% 
14.8s|  1 |  0 | 4189 |  - | 213M| 0 | 316 |3979 | 14k|3979 | 14k| 183 | 15 | 0 | 1.117694e+05 | 1.118470e+05 | 0.07% 
14.9s|  1 |  0 | 4189 |  - | 213M| 0 | 316 |3979 | 14k|3979 | 14k| 183 | 15 | 0 | 1.117694e+05 | 1.118470e+05 | 0.07% 
14.9s|  1 |  0 | 4189 |  - | 213M| 0 | 316 |3979 | 14k|3979 | 14k| 183 | 15 | 0 | 1.117694e+05 | 1.118470e+05 | 0.07% 
15.1s|  1 |  0 | 4349 |  - | 213M| 0 | 461 |3979 | 14k|3979 | 14k| 194 | 15 | 0 | 1.117720e+05 | 1.118470e+05 | 0.07% 
15.1s|  1 |  0 | 4349 |  - | 213M| 0 | 461 |3979 | 14k|3979 | 14k| 194 | 16 | 0 | 1.117720e+05 | 1.118470e+05 | 0.07% 
15.1s|  1 |  0 | 4376 |  - | 213M| 0 | 407 |3979 | 14k|3979 | 14k| 195 | 16 | 0 | 1.117723e+05 | 1.118470e+05 | 0.07% 
15.1s|  1 |  0 | 4376 |  - | 213M| 0 | 407 |3979 | 14k|3979 | 14k| 195 | 16 | 0 | 1.117723e+05 | 1.118470e+05 | 0.07% 
15.3s|  1 |  0 | 4429 |  - | 213M| 0 | 375 |3979 | 14k|3979 | 14k| 201 | 16 | 0 | 1.117723e+05 | 1.118470e+05 | 0.07% 
15.3s|  1 |  0 | 4436 |  - | 213M| 0 | 381 |3979 | 14k|3979 | 14k| 202 | 17 | 0 | 1.117723e+05 | 1.118470e+05 | 0.07% 
15.6s|  1 |  2 | 4436 |  - | 213M| 0 | 381 |3979 | 14k|3979 | 14k| 202 | 20 | 21 | 1.117727e+05 | 1.118470e+05 | 0.07% 
(run 1, node 1) restarting after 228 global fixings of integer variables 

(restart) converted 131 cuts from the global cut pool into linear constraints 

presolving: 
(round 1, fast)  235 del vars, 60 del conss, 0 add conss, 0 chg bounds, 0 chg sides, 124 chg coeffs, 0 upgd conss, 0 impls, 36478 clqs 
(round 2, fast)  243 del vars, 61 del conss, 0 add conss, 0 chg bounds, 0 chg sides, 124 chg coeffs, 0 upgd conss, 0 impls, 36478 clqs 
(round 3, medium)  267 del vars, 86 del conss, 0 add conss, 0 chg bounds, 0 chg sides, 124 chg coeffs, 0 upgd conss, 0 impls, 36175 clqs 
(round 4, exhaustive) 271 del vars, 96 del conss, 3 add conss, 0 chg bounds, 0 chg sides, 124 chg coeffs, 0 upgd conss, 0 impls, 36108 clqs 
(round 5, medium)  274 del vars, 106 del conss, 3 add conss, 0 chg bounds, 0 chg sides, 124 chg coeffs, 0 upgd conss, 0 impls, 35920 clqs 
(round 6, medium)  277 del vars, 115 del conss, 3 add conss, 0 chg bounds, 0 chg sides, 124 chg coeffs, 0 upgd conss, 0 impls, 35910 clqs 
(round 7, exhaustive) 277 del vars, 115 del conss, 3 add conss, 0 chg bounds, 0 chg sides, 124 chg coeffs, 131 upgd conss, 0 impls, 35910 clqs 
(round 8, exhaustive) 277 del vars, 127 del conss, 4 add conss, 0 chg bounds, 2 chg sides, 141 chg coeffs, 131 upgd conss, 0 impls, 35912 clqs 
presolving (9 rounds: 9 fast, 7 medium, 4 exhaustive): 
277 deleted vars, 132 deleted constraints, 4 added constraints, 0 tightened bounds, 0 added holes, 2 changed sides, 155 changed coefficients 
0 implications, 35912 cliques 
presolved problem has 3702 variables (3702 bin, 0 int, 0 impl, 0 cont) and 14190 constraints 
    58 constraints of type <knapsack> 
    7458 constraints of type <setppc> 
     1 constraints of type <and> 
    6673 constraints of type <logicor> 
transformed objective value is always integral (scale: 1) 
Presolving Time: 10.28 
transformed 8/18 original solutions to the transformed problem space 

(Some lines removed to stay within StackOverflow limits.) 

time | node | left |LP iter|LP it/n| mem |mdpt |frac |vars |cons |cols |rows |cuts |confs|strbr| dualbound | primalbound | gap 
16.1s|  1 |  0 | 6297 |  - | 218M| 0 | 373 |3702 | 14k|3702 | 14k| 0 | 20 | 21 | 1.117727e+05 | 1.118470e+05 | 0.07% 
16.2s|  1 |  0 | 6297 |  - | 218M| 0 | 373 |3702 | 14k|3702 | 14k| 0 | 23 | 21 | 1.117727e+05 | 1.118470e+05 | 0.07% 
16.6s|  1 |  0 | 6348 |  - | 218M| 0 | 354 |3702 | 14k|3702 | 13k| 37 | 23 | 21 | 1.117727e+05 | 1.118470e+05 | 0.07% 
16.7s|  1 |  0 | 6673 |  - | 218M| 0 | 526 |3702 | 13k|3702 | 13k| 38 | 24 | 21 | 1.117826e+05 | 1.118470e+05 | 0.06% 
17.0s|  1 |  0 | 6771 |  - | 218M| 0 | 298 |3702 | 12k|3702 | 12k| 38 | 25 | 23 | 1.117845e+05 | 1.118470e+05 | 0.06% 
17.3s|  1 |  0 | 6781 |  - | 218M| 0 | 269 |3702 | 11k|3702 | 12k| 38 | 25 | 45 | 1.117914e+05 | 1.118470e+05 | 0.05% 
17.6s|  1 |  2 | 6781 |  - | 218M| 0 | 269 |3702 | 11k|3702 | 12k| 38 | 25 | 73 | 1.117914e+05 | 1.118470e+05 | 0.05% 
*26.3s| 27 |  1 | 8030 | 46.3 | 219M| 17 | - |3702 | 11k|3702 | 12k| 38 | 26 | 887 | 1.117967e+05 | 1.118380e+05 | 0.04% 
*29.0s| 47 |  1 | 8473 | 36.0 | 219M| 17 | - |3702 | 11k|3702 | 12k| 38 | 27 |1122 | 1.117992e+05 | 1.118050e+05 | 0.01% 

SCIP Status  : problem is solved [optimal solution found] 
Solving Time (sec) : 29.38 
Solving Nodes  : 54 (total of 55 nodes in 2 runs) 
Primal Bound  : +1.11805000000000e+05 (21 solutions) 
Dual Bound   : +1.11805000000000e+05 
Gap    : 0.00 % 

Answer 1

1e-16の範囲の値を安全に典型的な倍精度浮動小数点環境においてゼロとみなさができます。私はすべての変数を1e-12の絶対値で扱い、0とすることをお勧めします。