Set Based Hierarchical Design: A Constraint Satisfaction Approach

1995 ◽  
Author(s):  
Christian Bliek
Keyword(s):  
Constraint Satisfaction ◽  
Design Automation ◽  
Constraint Satisfaction Problems ◽  
Combinatorial Complexity ◽  
Hierarchical Decomposition ◽  
Hierarchical Design ◽  
Decomposition Techniques ◽  
New Approach ◽  
Candidate Solution ◽  
Literature Reviews

Abstract Many are the literature reviews where constraint satisfaction is rejected as a candidate solution for design automation. Some point to the combinatorial complexity associated with the solution of large constraint satisfaction problems, others claim it is inadequate to handle the uncertainty prominent in engineering design. In this paper we present a new approach in which hierarchical decomposition techniques exploit sensitivity to reduce combinatorial complexity and uncertainty is modeled using conservative enclosures of sets of possible solutions.

scholarly journals Solving Set Constraint Satisfaction Problems using ROBDDs

2005 ◽  
Vol 24 ◽  
pp. 109-156 ◽  
Author(s):  
P. J. Hawkins ◽  
V. Lagoon ◽  
P. J. Stuckey
Keyword(s):  
Constraint Satisfaction ◽  
Constraint Satisfaction Problems ◽  
Set Domain ◽  
Ordered Binary Decision Diagrams ◽  
Binary Decision ◽  
New Approach ◽  
Performance Improvements ◽  
Set Constraints ◽  
Finite Set ◽  
Standard Set

In this paper we present a new approach to modeling finite set domain constraint problems using Reduced Ordered Binary Decision Diagrams (ROBDDs). We show that it is possible to construct an efficient set domain propagator which compactly represents many set domains and set constraints using ROBDDs. We demonstrate that the ROBDD-based approach provides unprecedented flexibility in modeling constraint satisfaction problems, leading to performance improvements. We also show that the ROBDD-based modeling approach can be extended to the modeling of integer and multiset constraint problems in a straightforward manner. Since domain propagation is not always practical, we also show how to incorporate less strict consistency notions into the ROBDD framework, such as set bounds, cardinality bounds and lexicographic bounds consistency. Finally, we present experimental results that demonstrate the ROBDD-based solver performs better than various more conventional constraint solvers on several standard set constraint problems.

Searching Feasible Design Space by Solving Quantified Constraint Satisfaction Problems

2013 ◽  
Vol 136 (3) ◽  
Author(s):  
Jie Hu ◽  
Masoumeh Aminzadeh ◽  
Yan Wang
Keyword(s):  
Monte Carlo ◽  
Constraint Satisfaction ◽  
Design Space ◽  
Constraint Satisfaction Problem ◽  
Constraint Satisfaction Problems ◽  
Design Solution ◽  
New Approach ◽  
Solution Sets ◽  
Branch And Prune Algorithm ◽  
Branch And Prune

In complex systems design, multidisciplinary constraints are imposed by stakeholders. Engineers need to search feasible design space for a given problem before searching for the optimum design solution. Searching feasible design space can be modeled as a constraint satisfaction problem (CSP). By introducing logical quantifiers, CSP is extended to quantified constraint satisfaction problem (QCSP) so that more semantics and design intent can be captured. This paper presents a new approach to formulate searching design problems as QCSPs in a continuous design space based on generalized interval, and to numerically solve them for feasible solution sets, where the lower and upper bounds of design variables are specified. The approach includes two major components. One is a semantic analysis which evaluates the logic relationship of variables in generalized interval constraints based on Kaucher arithmetic, and the other is a branch-and-prune algorithm that takes advantage of the logic interpretation. The new approach is generic and can be applied to the case when variables occur multiple times, which is not available in other QCSP solving methods. A hybrid stratified Monte Carlo method that combines interval arithmetic with Monte Carlo sampling is also developed to verify the correctness of the QCSP solution sets obtained by the branch-and-prune algorithm.

scholarly journals Finding robust solutions for constraint satisfaction problems with discrete and ordered domains by coverings

2013 ◽  
Vol 44 (2) ◽  
pp. 131-156 ◽  
Author(s):  
Laura Climent ◽  
Richard J. Wallace ◽  
Miguel A. Salido ◽  
Federico Barber
Keyword(s):  
Constraint Satisfaction ◽  
Constraint Satisfaction Problems ◽  
Robust Solutions

scholarly journals A fine-grained arc-consistency algorithm for non-normalized constraint satisfaction problems

2011 ◽  
Vol 21 (4) ◽  
pp. 733-744 ◽  
Author(s):  
Marlene Arangú ◽  
Miguel Salido
Keyword(s):  
Constraint Satisfaction ◽  
Constraint Programming ◽  
Real Life ◽  
Search Space ◽  
Constraint Satisfaction Problems ◽  
Fine Grained ◽  
Arc Consistency ◽  
Life Problems ◽  
Programming Techniques ◽  
Np Complete

A fine-grained arc-consistency algorithm for non-normalized constraint satisfaction problems Constraint programming is a powerful software technology for solving numerous real-life problems. Many of these problems can be modeled as Constraint Satisfaction Problems (CSPs) and solved using constraint programming techniques. However, solving a CSP is NP-complete so filtering techniques to reduce the search space are still necessary. Arc-consistency algorithms are widely used to prune the search space. The concept of arc-consistency is bidirectional, i.e., it must be ensured in both directions of the constraint (direct and inverse constraints). Two of the most well-known and frequently used arc-consistency algorithms for filtering CSPs are AC3 and AC4. These algorithms repeatedly carry out revisions and require support checks for identifying and deleting all unsupported values from the domains. Nevertheless, many revisions are ineffective, i.e., they cannot delete any value and consume a lot of checks and time. In this paper, we present AC4-OP, an optimized version of AC4 that manages the binary and non-normalized constraints in only one direction, storing the inverse founded supports for their later evaluation. Thus, it reduces the propagation phase avoiding unnecessary or ineffective checking. The use of AC4-OP reduces the number of constraint checks by 50% while pruning the same search space as AC4. The evaluation section shows the improvement of AC4-OP over AC4, AC6 and AC7 in random and non-normalized instances.

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