TY - GEN

T1 - Why adding more constraints makes a problem easier for hill-climbing algorithms

T2 - 3rd International Conference on Principles and Practice of Constraint Programming, CP 1997

AU - Yokoo, Makoto

N1 - Publisher Copyright:
© Springer-Verlag Berlin Heidelberg 1997.

PY - 1997

Y1 - 1997

N2 - It is well known that constraint satisfaction problems (CSPs) in the phase transition region are most difficult for complete search algorithms. On the other hand, for incomplete hill-climbing algorithms, problems in the phase transition region axe more difficult than problems beyond the phase transition region, i.e., more constrained problems. This result seems somewhat unnatural since these more constrained problems have fewer solutions than the phase transition problems. In this paper, we clarify the cause of this paradoxical phenomenon by exhaustively analyzing the state-space landscape of CSPs, which is formed by the evaluation values of states. The analyses show that by adding more constraints, while the number of solutions decreases, the number of local-minima also decreases, thus the number of states that are reachable to solutions increases. Furthermore, the analyses clarify that the decrease in local-minima is caused by a set of interconnected local-minima (basin) being divided into smaller regions by adding more constraints.

AB - It is well known that constraint satisfaction problems (CSPs) in the phase transition region are most difficult for complete search algorithms. On the other hand, for incomplete hill-climbing algorithms, problems in the phase transition region axe more difficult than problems beyond the phase transition region, i.e., more constrained problems. This result seems somewhat unnatural since these more constrained problems have fewer solutions than the phase transition problems. In this paper, we clarify the cause of this paradoxical phenomenon by exhaustively analyzing the state-space landscape of CSPs, which is formed by the evaluation values of states. The analyses show that by adding more constraints, while the number of solutions decreases, the number of local-minima also decreases, thus the number of states that are reachable to solutions increases. Furthermore, the analyses clarify that the decrease in local-minima is caused by a set of interconnected local-minima (basin) being divided into smaller regions by adding more constraints.

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U2 - 10.1007/bfb0017451

DO - 10.1007/bfb0017451

M3 - Conference contribution

AN - SCOPUS:84948981891

SN - 3540637532

SN - 9783540637530

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 356

EP - 370

BT - Principles and Practice of Constraint Programming - CP 1997 - 3rd International Conference, CP 1997, Proceedings

A2 - Smolka, Gert

PB - Springer Verlag

Y2 - 29 October 1997 through 1 November 1997

ER -