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Motivations Numerous CP modeling languages and platforms have been - PowerPoint PPT Presentation

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On T esting C onstraint P rograms Nadjib LAZAAR* , Arnaud GOTLIEB*, Yahia LEBBAH** *INRIA Rennes Bretagne Atlantique ** Universit d'Oran Es-Senia CP2010 St -Andrews, Scotland 08 september 1 /21 Motivations Numerous CP modeling

  1. On T esting C onstraint P rograms Nadjib LAZAAR* , Arnaud GOTLIEB*, Yahia LEBBAH** *INRIA Rennes Bretagne Atlantique ** Université d'Oran Es-Senia CP’2010 St -Andrews, Scotland 08 september 1 /21

  2. Motivations  Numerous CP modeling languages and platforms have been developed (OPL, SICStus Prolog, ZINC, GECODE, CHOCO…) for solving combinatorial problems that arise in optimization, planning, scheduling… 2 /21

  3. Motivations  Numerous CP modeling languages and platforms have been developed (OPL, SICStus Prolog, ZINC, GECODE, CHOCO…) for solving combinatorial problems that arise in optimization, planning, scheduling…  CP programs begin to be used in business-critical systems (e.g., combinatorial auctions) 2 /21

  4. Motivations  Numerous CP modeling languages and platforms have been developed (OPL, SICStus Prolog, ZINC, GECODE, CHOCO…) for solving combinatorial problems that arise in optimization, planning, scheduling…  CP programs begin to be used in business-critical systems (e.g., combinatorial auctions)  Refinement in CP 2 /21

  5. Motivations  Numerous CP modeling languages and platforms have been developed (OPL, SICStus Prolog, ZINC, GECODE, CHOCO…) for solving combinatorial problems that arise in optimization, planning, scheduling…  CP programs begin to be used in business-critical systems (e.g., combinatorial auctions)  Refinement in CP SPEC 2 /21

  6. Motivations  Numerous CP modeling languages and platforms have been developed (OPL, SICStus Prolog, ZINC, GECODE, CHOCO…) for solving combinatorial problems that arise in optimization, planning, scheduling…  CP programs begin to be used in business-critical systems (e.g., combinatorial auctions)  Refinement in CP SPEC 2 /21

  7. Motivations  Numerous CP modeling languages and platforms have been developed (OPL, SICStus Prolog, ZINC, GECODE, CHOCO…) for solving combinatorial problems that arise in optimization, planning, scheduling…  CP programs begin to be used in business-critical systems (e.g., combinatorial auctions)  Refinement in CP SPEC 2 /21

  8. Motivations  Numerous CP modeling languages and platforms have been developed (OPL, SICStus Prolog, ZINC, GECODE, CHOCO…) for solving combinatorial problems that arise in optimization, planning, scheduling…  CP programs begin to be used in business-critical systems (e.g., combinatorial auctions)  Refinement in CP SPEC 2 /21

  9. Golomb Rulers 3 /21

  10. Golomb Rulers 3 /21

  11. Golomb Rulers in O ptimization P rogramming L anguage M using CP; int m=...; dvar int x[1..m] in 0..m*m; minimize x[m]; subject to { (1) forall (i in 1..m-1) x[i] < x[i+1]; (2) forall (i in 1..m, j in 1..m, k in 1..m, l in 1..m: (i < j, k < l)) x[j] - x[i] != x[l] - x[k]; } 4 /21

  12. Golomb Rulers in O ptimization P rogramming L anguage M P using CP; using CP; int m=...; int m=...; tuple indexerTuple {int i; dvar int x[1..m] in 0..m*m; int j;} {indexerTuple} indexes1 = {<i, j> | ordered i,j in 1..m}; minimize x[m]; {indexerTuple} indexes2 = {<i, j> | ordered i,j in 1..m div 2}; subject to { dvar int x[1..m] in 0..m*m; (1) forall (i in 1..m-1) dvar int d[indexes1]; x[i] < x[i+1]; (2) forall (i in 1..m, j in 1..m, minimize x[m]; k in 1..m, l in 1..m: (i < j, k < l)) subject to { x[j] - x[i] != x[l] - x[k]; (1) x[1]==0; } (2) forall (i in (1)..m-1) x[i] < x[i+1]; (3) forall(ind in indexes1) d[ind] == x[ind.i]-x[ind.j]; (4) x[m] >= (m * (m - 1)) / 2; (5) x[2] <= x[m]-x[m-1]; (6) forall(ind1,ind2,ind3:(ind1.i==ind2.i)&&(ind2.j==ind3.i)&& (ind1.j==ind3.j)&&( ind1.i < ind2.j < ind1.j)) d[ind1]==d[ind2]+d[ind3]; (7) forall(ind1,ind2,ind3,ind4 in indexes2 : (ind1.i==ind2.i)&&(ind1.j==ind3.j)&&(ind2.j==ind4.j) &&(ind3.i==ind4.i)&&(ind1.i<m-1)&&(3<ind1.j<m+1) &&(2<ind2.j<m)&&(1<ind3.i<m-1)&& (ind1.i < ind3.i < ind2.j < ind1.j)) d[ind1]==d[ind2]+d[ind3]-d[ind4]; (8) forall(ind in indexes2, k in 1..m div 2) x[ind.i+1]==x[ind.i]+k => x[ind.j+1] != x[ind.j]+k; } 4 /21

  13. Golomb Rulers in O ptimization P rogramming L anguage M P using CP; using CP; int m=...; int m=...; tuple indexerTuple {int i; dvar int x[1..m] in 0..m*m; int j;} {indexerTuple} indexes1 = {<i, j> | ordered i,j in 1..m}; minimize x[m]; {indexerTuple} indexes2 = {<i, j> | ordered i,j in 1..m div 2}; subject to { dvar int x[1..m] in 0..m*m; (1) forall (i in 1..m-1) dvar int d[indexes1]; x[i] < x[i+1]; (2) forall (i in 1..m, j in 1..m, minimize x[m]; k in 1..m, l in 1..m: (i < j, k < l)) subject to { x[j] - x[i] != x[l] - x[k]; (1) x[1]==0; } (2) forall (i in (1)..m-1) x[i] < x[i+1]; (3) forall(ind in indexes1) d[ind] == x[ind.i]-x[ind.j]; (4) x[m] >= (m * (m - 1)) / 2; (5) x[2] <= x[m]-x[m-1]; Does P conform to M (6) forall(ind1,ind2,ind3:(ind1.i==ind2.i)&&(ind2.j==ind3.i)&& (ind1.j==ind3.j)&&( ind1.i < ind2.j < ind1.j)) d[ind1]==d[ind2]+d[ind3]; (7) forall(ind1,ind2,ind3,ind4 in indexes2 : (ind1.i==ind2.i)&&(ind1.j==ind3.j)&&(ind2.j==ind4.j) &&(ind3.i==ind4.i)&&(ind1.i<m-1)&&(3<ind1.j<m+1) &&(2<ind2.j<m)&&(1<ind3.i<m-1)&& (ind1.i < ind3.i < ind2.j < ind1.j)) d[ind1]==d[ind2]+d[ind3]-d[ind4]; (8) forall(ind in indexes2, k in 1..m div 2) x[ind.i+1]==x[ind.i]+k => x[ind.j+1] != x[ind.j]+k; } 4 /21

  14. Golomb Rulers in O ptimization P rogramming L anguage M P using CP; using CP; int m=...; int m=...; tuple indexerTuple {int i; dvar int x[1..m] in 0..m*m; int j;} {indexerTuple} indexes1 = {<i, j> | ordered i,j in 1..m}; minimize x[m]; {indexerTuple} indexes2 = {<i, j> | ordered i,j in 1..m div 2}; subject to { dvar int x[1..m] in 0..m*m; (1) forall (i in 1..m-1) dvar int d[indexes1]; x[i] < x[i+1]; (2) forall (i in 1..m, j in 1..m, minimize x[m]; k in 1..m, l in 1..m: (i < j, k < l)) subject to { x[j] - x[i] != x[l] - x[k]; (1) x[1]==0; } (2) forall (i in (1)..m-1) x[i] < x[i+1]; (3) forall(ind in indexes1) d[ind] == x[ind.i]-x[ind.j]; (4) x[m] >= (m * (m - 1)) / 2; (5) x[2] <= x[m]-x[m-1]; Does P conform to M (6) forall(ind1,ind2,ind3:(ind1.i==ind2.i)&&(ind2.j==ind3.i)&& (ind1.j==ind3.j)&&( ind1.i < ind2.j < ind1.j)) d[ind1]==d[ind2]+d[ind3]; m=8 (7) forall(ind1,ind2,ind3,ind4 in indexes2 : (ind1.i==ind2.i)&&(ind1.j==ind3.j)&&(ind2.j==ind4.j) &&(ind3.i==ind4.i)&&(ind1.i<m-1)&&(3<ind1.j<m+1) &&(2<ind2.j<m)&&(1<ind3.i<m-1)&& X= [0 1 3 6 10 26 27 28] (ind1.i < ind3.i < ind2.j < ind1.j)) d[ind1]==d[ind2]+d[ind3]-d[ind4]; (8) forall(ind in indexes2, k in 1..m div 2) x[ind.i+1]==x[ind.i]+k => x[ind.j+1] != x[ind.j]+k; } 4 /21

  15. Golomb Rulers in O ptimization P rogramming L anguage M P using CP; using CP; int m=...; int m=...; tuple indexerTuple {int i; dvar int x[1..m] in 0..m*m; int j;} {indexerTuple} indexes1 = {<i, j> | ordered i,j in 1..m}; minimize x[m]; {indexerTuple} indexes2 = {<i, j> | ordered i,j in 1..m div 2}; subject to { dvar int x[1..m] in 0..m*m; (1) forall (i in 1..m-1) dvar int d[indexes1]; x[i] < x[i+1]; (2) forall (i in 1..m, j in 1..m, minimize x[m]; k in 1..m, l in 1..m: (i < j, k < l)) subject to { x[j] - x[i] != x[l] - x[k]; (1) x[1]==0; } (2) forall (i in (1)..m-1) x[i] < x[i+1]; (3) forall(ind in indexes1) d[ind] == x[ind.i]-x[ind.j]; (4) x[m] >= (m * (m - 1)) / 2; (5) x[2] <= x[m]-x[m-1]; Does P conform to M (6) forall(ind1,ind2,ind3:(ind1.i==ind2.i)&&(ind2.j==ind3.i)&& (ind1.j==ind3.j)&&( ind1.i < ind2.j < ind1.j)) d[ind1]==d[ind2]+d[ind3]; m=8 (7) forall(ind1,ind2,ind3,ind4 in indexes2 : (ind1.i==ind2.i)&&(ind1.j==ind3.j)&&(ind2.j==ind4.j) &&(ind3.i==ind4.i)&&(ind1.i<m-1)&&(3<ind1.j<m+1) &&(2<ind2.j<m)&&(1<ind3.i<m-1)&& X= [0 1 3 6 10 26 27 28] (ind1.i < ind3.i < ind2.j < ind1.j)) d[ind1]==d[ind2]+d[ind3]-d[ind4]; 1 1 (8) forall(ind in indexes2, k in 1..m div 2) x[ind.i+1]==x[ind.i]+k => x[ind.j+1] != x[ind.j]+k; Fault detected in P ! } 4 /21

  16. Contributions • A first framework for testing constraint programs Definitions of testing notions Conformity relations: • Constraint solving problem • Optimization problem • A method and a tool, called CPTEST to detect non- conformities ( e.g., X= [0 1 3 6 10 26 27 28] ) • An experimental validation on two classical benchmarks (Golomb rulers, car sequencing) 5 /21

  17. Notations Model- Oracle M x (k ) 6 /21

  18. Notations Model- CPUT Oracle P z (k) M x (k ) 6 /21

  19. Notations Model- CPUT Oracle Conformity Relation P z (k) M x (k ) 6 /21

  20. Conformity relation in constraint solving problem  One Solution (conf k one ) 7 /21

  21. Conformity relation in constraint solving problem  One Solution (conf k one ) non-conform M : solutions set of M P : solutions set of P 7 /21

  22. Conformity relation in constraint solving problem  One Solution (conf k one ) non-conform M : solutions set of M P : solutions set of P 7 /21

  23. Conformity relation in constraint solving problem  One Solution (conf k one ) non-conform M : solutions set of M P : solutions set of P 7 /21

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