LP SCIP NEOS URL. example1.lp 2.1 LP 1. minimize. subject to, bounds, free, general, binary, end. .lp 1 2.2

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1 c LP SCIP LP SCIP NEOS 1. URL LP 1 LP LP.lp minimize 3x +4.5y 2z 1 + f subject to g 1,1 + g 1,2 5, 3g 1,1 7g 1,2 + z 2 10, 2f g 1,1 =6, x +0.5y = 4.6, f 0, y 0, g 1,2 0, g 1,1 Z, g 1,2 Z, z 1 {0, 1}, z 2 {0, 1}. LP example1.lp minimize - 3 x y - 2 z(1) + f subject to c1: - g(1,1) + g(1,2) <= 5 c2: 3 g(1,1) - 7 g(1,2) + z(2) >= - 10 c3: 2 f - g(1,1) = 6 c4: x y = bounds x free g(1,1) free general g(1,1) g(1,2) binary z(1) z(2) end example1.lp LP example1.lp minimize, subject to, bounds, free, general, binary, end LP Copyright c by ORSJ. Unauthorized reproduction of this article is prohibited

2 SCIP [11] SCIP 4.1 Windows SCIP web [11] download SCIP SCIP version Binaries Windows/PC, 32bit, cl15 64bit SCIP 2.4 NEOS zip SCIP SCIP 2.3 SCIP 2.1 LP example1.lp SCIP SCIP SCIP> example1.lp SCIP> read example1.lp SCIP> optimize SCIP> write solution example1.sol 1 example1.sol example1.sol solution status: optimal solution found objective value: 13.3 z(1) 1 (obj:-2) z(2) 1 (obj:0) g(1,1) -3 (obj:0) x -4.6 (obj:-3) f 1.5 (obj:1) 1 display display (obj: ) display solution example1.lp SCIP Ctrl-C write optimize quit SCIP help SCIP SCIP LP 2.4 NEOS SCIP SCIP GLPK [3] lp solve [6] NEOS [9] SCIP NEOS NEOS web [9] NEOS Solvers Mixed Integer Linear Programming scip CPLEX Input 2 example1.sol z(2)0 example1.sol z(2) Copyright c by ORSJ. Unauthorized reproduction of this article is prohibited.

3 SCIP data (CPLEX-LP format file) LP example1.lp example1.sol 3 3. LP LP LP LP LP 2 Special Ordered Set (SOS), (semicontinuous variable) LP end example1.lp maximize, minimize subject to 3 =, >=, >, <, <= > >= < <= : c1:, c2:,... bounds 4 free 5 free x x <= - 7 free free x x <= - 7 general binary 0-1 free general free general end LP end LP LP maximize, minimize, subject to, bounds, free, general, binary, end free 4 free Copyright c by ORSJ. Unauthorized reproduction of this article is prohibited

4 Y= LP +, -, =, <, > *, /, [, ], ^ LP x(1) x)(1))) x 1,2 x(1,2), x 1 2 LP x - 1 y = + 1 x - y = 1 LP 1 f y x g 1,2 g 1,1 z 1 z example1.lp 4. SCIP SCIP 4.1 SCIP SCIP [11] Zuse Institute Berlin SCIP LP NEOS lp solve [6], GLPK [3] 2012 SCIP 4.2 SCIP OS SCIP example2.lp example3.lp script.txt read example2.lp optimize write solution example2.sol read example3.lp optimize write solution example3.sol quit script.txt, SCIP scip.exe LP OS Windows scip.exe < script.txt script.txt SCIP example2.sol example3.sol script.txt SCIP = LP SCIP read count example1.lp 13.3 c5: - 3 x y - 2 z(1) + f = 13.3 count Feasible Solutions: 2 (0 non-trivial Copyright c by ORSJ. Unauthorized reproduction of this article is prohibited.

5 [2] 40 LP LP LP SCIP LP CLI, GUI, API, LP MPS LP,IP,QP,QCP,QCQIP, LP, SCIP> read example4.lp SCIP> write problem example5.lp LP MPS 7 MPS SCIP LP MPS SCIP> read example6.mps SCIP> write problem example6.lp Mittelmann SCIP> read example7.lp web [7] 2012 SCIP> write problem example7.mps CPLEX [5] Gurobi [4] XPRESS [1] LP CPLEX LP 8 LP LP SCIP MPS GLPK [3] lp solve [6] CPLEX 7.1/8.1/9.1/10.1/11.1 [8] CPU MPS URL[6] 9 GLPK[3] glpk.exe --check --lp example8.lp 8 URL[6] --wfreemps example8.mps LP MPS Copyright c by ORSJ. Unauthorized reproduction of this article is prohibited

6 [10] 0-1 neos rail n3seq netdiversion LP LP 100 xi 3 i=1 x(1) + x(2) + x(3) + + x(100) <= LP API LP LP xi 3 i=1 sum(i in )(x[i]) <= [10] 0-1 sts sts queens neos API 1 MIPLIB 2010 [10] [10] Copyright c by ORSJ. Unauthorized reproduction of this article is prohibited.

7 [1] FICO, FICO Xpress, 20 [2] R. Fourer, Software Survey: Linear Programming, 5 SCIP 2012 OR/MS Today, 38 (2011). Public-Articles/June-Volume-38-Number-3/ Software-Survey-Linear-Programming LP-survey.html [3] GNU Project, GLPK (GNU linear programming kit), [4] Gurobi Optimization, Gurobi Optimizer, gurobi.html [5] IBM, IBM ILOG CPLEX, ilog/optimization/core-products-technologies/cplex/ [6] lp solve, NEOS [7] H. Mittelmann, Benchmarks for Optimization Software, [8] RAMP 2008, [9] NEOS Server for Optimization, [10] Zuse Institute Berlin, MIPLIB 2010, [11] Zuse Institute Berlin, SCIP (Solving Constraint Integer Programs), 10 MPS NEOS Gurobi [4] 11 MIPLIB 2010 [10] go Copyright c by ORSJ. Unauthorized reproduction of this article is prohibited