Nogood backmarking with min-conflict repair in constraint satisfaction and optimization

  • Yuejun Jiang
  • Thomas Richards
  • Barry Richards
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 874)


There are generally three approaches to constraint satisfaction and optimization: domain-filtering, tree-search labelling and solution repair. The main attractions of repair-based algorithms over domain-filtering and/or tree-search algorithms seem to be their scalability, reactivity and applicability to optimization problems. The main detraction of the repair-based algorithms appear to be their failure to guarantee optimality. In this paper, a repair-based algorithm, that guarantees to find an optimal solution if one exists, is presented. The search space of the algorithm is controlled by no-good backmarking, a learning process of polynomial complexity that records generic patterns of no-good partial labels. These no-goods serve to avoid the repeated traversing of those failed paths of a search graph and to force the search process to jump out of a local optimum. Unlike some similar repair-based methods which usually work on complete (but possibly inconsistent) labels, the proposed algorithm works on partial (possibly inconsistent) labels by repairing those variables that contribute to the violation of constraints in the spirit of dependency-directed backjumping. In addition, the algorithm will accept a repair if it can minimise the conflicts of a label even if it does not eliminate them. To control the space of no-good patterns, we propose to generate the most generic no-good pattern as early as possible. To support dynamic constraint satisfaction, we introduce several strategies to maintain no-good patterns on the tradeoffs between space, efficiency and overheads. In particular, through the comparisons with other works such as Dynamic Backtracking, weighted GSAT and Breakout, we suggest possible strategies to improve the proposed method.


Constraint Satisfaction and Optimization Backmarking Learning Backjumping Repair-based Methods Simulated Annealing Tabu Search No-good recording and No-good Justification Dynamic Backtracking GSAT and Breakout 


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Copyright information

© Springer-Verlag Berlin Heidelberg 1994

Authors and Affiliations

  • Yuejun Jiang
    • 1
  • Thomas Richards
    • 1
  • Barry Richards
    • 1
  1. 1.IC-ParcImperial CollegeLondonEngland

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