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@INPROCEEDINGS{MontanezBarrera:1020504,
      author       = {Montanez-Barrera, Jhon Alejandro and van den Heuvel, Pim
                      and Willsch, Dennis and Michielsen, Kristel},
      title        = {{I}mproving {P}erformance in {C}ombinatorial {O}ptimization
                      {P}roblems with {I}nequality {C}onstraints: {A}n
                      {E}valuation of the {U}nbalanced {P}enalization {M}ethod on
                      {D}-{W}ave {A}dvantage},
      reportid     = {FZJ-2024-00223},
      year         = {2023},
      abstract     = {Combinatorial optimization problems are one ofthe target
                      applications of current quantum technology, mainly because
                      of their industrial relevance, the difficulty of solving
                      large instances of them classically, and their equivalence
                      to Ising Hamiltonians using the quadratic unconstrained
                      binary optimization (QUBO) formulation. Many of these
                      applications have inequality constraints, usually encoded as
                      penalization terms in the QUBO formulation using additional
                      variables known as slack variables. The slack variables have
                      two disadvantages: (i) these variables extend the search
                      space of optimal and suboptimal solutions, and (ii) the
                      variables add extra qubits and connections to the quantum
                      algorithm. Recently, a new method known as unbalanced
                      penalization has been presented to avoid using slack
                      variables. This method offers a trade-off between additional
                      slack variables to ensure that the optimal solution is given
                      by the ground state of the Ising Hamiltonian, and using an
                      unbalanced heuristic function to penalize the region where
                      the inequality constraint is violated with the only
                      certainty that the optimal solution will be in the vicinity
                      of the ground state. This work tests the unbalanced
                      penalization method using real quantum hardware on D-Wave
                      Advantage for the traveling salesman problem (TSP). The
                      results show that the unbalanced penalization method
                      outperforms the solutions found using slack variables and
                      sets a new record for the largest TSP solved with quantum},
      month         = {Sep},
      date          = {2023-09-17},
      organization  = {2023 IEEE International Conference on
                       Quantum Computing and Engineering
                       (QCE), Bellevue, WA (USA), 17 Sep 2023
                       - 22 Sep 2023},
      subtyp        = {After Call},
      cin          = {JSC},
      cid          = {I:(DE-Juel1)JSC-20090406},
      pnm          = {5111 - Domain-Specific Simulation $\&$ Data Life Cycle Labs
                      (SDLs) and Research Groups (POF4-511) / BMBF 13N16149 -
                      QSolid (BMBF-13N16149)},
      pid          = {G:(DE-HGF)POF4-5111 / G:(DE-Juel1)BMBF-13N16149},
      typ          = {PUB:(DE-HGF)6},
      doi          = {10.1109/QCE57702.2023.00067},
      url          = {https://juser.fz-juelich.de/record/1020504},
}