scholarly journals A Novel Strategy of Combining Variable Ordering Heuristics for Constraint Satisfaction Problems

IEEE Access ◽  
2018 ◽  
Vol 6 ◽  
pp. 42750-42756 ◽  
Author(s):  
Hongbo Li ◽  
Zhanshan Li
Keyword(s):  
Constraint Satisfaction ◽  
Constraint Satisfaction Problems ◽  
Variable Ordering ◽  
Novel Strategy ◽  
Variable Ordering Heuristics

scholarly journals Exploring the Impact of Early Decisions in Variable Ordering for Constraint Satisfaction Problems

2018 ◽  
Vol 2018 ◽  
pp. 1-14
Author(s):  
José Carlos Ortiz-Bayliss ◽  
Ivan Amaya ◽  
Santiago Enrique Conant-Pablos ◽  
Hugo Terashima-Marín
Keyword(s):  
Constraint Satisfaction ◽  
Constraint Satisfaction Problems ◽  
Search Cost ◽  
High Quality ◽  
Simple Method ◽  
Variable Ordering ◽  
It Performance ◽  
The Cost ◽  
The Impact ◽  
Variable Ordering Heuristics

When solving constraint satisfaction problems (CSPs), it is a common practice to rely on heuristics to decide which variable should be instantiated at each stage of the search. But, this ordering influences the search cost. Even so, and to the best of our knowledge, no earlier work has dealt with how first variable orderings affect the overall cost. In this paper, we explore the cost of finding high-quality orderings of variables within constraint satisfaction problems. We also study differences among the orderings produced by some commonly used heuristics and the way bad first decisions affect the search cost. One of the most important findings of this work confirms the paramount importance of first decisions. Another one is the evidence that many of the existing variable ordering heuristics fail to appropriately select the first variable to instantiate. Another one is the evidence that many of the existing variable ordering heuristics fail to appropriately select the first variable to instantiate. We propose a simple method to improve early decisions of heuristics. By using it, performance of heuristics increases.

Improving degree-based variable ordering heuristics for solving constraint satisfaction problems

2015 ◽  
Vol 22 (2) ◽  
pp. 125-145 ◽  
Author(s):  
Hongbo Li ◽  
Yanchun Liang ◽  
Ning Zhang ◽  
Jinsong Guo ◽  
Dong Xu ◽  
...  
Keyword(s):  
Constraint Satisfaction ◽  
Constraint Satisfaction Problems ◽  
Variable Ordering ◽  
Variable Ordering Heuristics

scholarly journals Experimental Matching of Instances to Heuristics for Constraint Satisfaction Problems

2016 ◽  
Vol 2016 ◽  
pp. 1-15 ◽  
Author(s):  
Jorge Humberto Moreno-Scott ◽  
José Carlos Ortiz-Bayliss ◽  
Hugo Terashima-Marín ◽  
Santiago Enrique Conant-Pablos
Keyword(s):  
Artificial Intelligence ◽  
Constraint Satisfaction ◽  
Operations Research ◽  
Special Interest ◽  
Research Community ◽  
Constraint Satisfaction Problems ◽  
The Past ◽  
Variable Ordering ◽  
Instance Space ◽  
Variable Ordering Heuristics

Constraint satisfaction problems are of special interest for the artificial intelligence and operations research community due to their many applications. Although heuristics involved in solving these problems have largely been studied in the past, little is known about the relation between instances and the respective performance of the heuristics used to solve them. This paper focuses on both the exploration of the instance space to identify relations between instances and good performing heuristics and how to use such relations to improve the search. Firstly, the document describes a methodology to explore the instance space of constraint satisfaction problems and evaluate the corresponding performance of six variable ordering heuristics for such instances in order to find regions on the instance space where some heuristics outperform the others. Analyzing such regions favors the understanding of how these heuristics work and contribute to their improvement. Secondly, we use the information gathered from the first stage to predict the most suitable heuristic to use according to the features of the instance currently being solved. This approach proved to be competitive when compared against the heuristics applied in isolation on both randomly generated and structured instances of constraint satisfaction problems.

scholarly journals Effects of Dynamic Variable - Value Ordering Heuristics on the Search Space of Sudoku Modeled as a Constraint Satisfaction Problem

2019 ◽  
Vol 22 (63) ◽  
pp. 1-15
Author(s):  
James L. Cox ◽  
Stephen Lucci ◽  
Tayfun Pay
Keyword(s):  
Constraint Satisfaction ◽  
Constraint Satisfaction Problem ◽  
Search Space ◽  
Constraint Satisfaction Problems ◽  
Decision Making Process ◽  
Dynamic Variable ◽  
Filtering Algorithm ◽  
Variable Ordering ◽  
Encoding Method ◽  
Variable Ordering Heuristics

We carry out a detailed analysis of the effects of different dynamic variable and value ordering heuristics on the search space of Sudoku when the encoding method and the filtering algorithm are fixed. Our study starts by examining lexicographical variable and value ordering and evaluates different combinations of dynamic variable and value ordering heuristics. We eventually build up to a dynamic variable ordering heuristic that has two rounds of tie-breakers, where the second tie-breaker is a dynamic value ordering heuristic. We show that our method that uses this interlinked heuristic outperforms the previously studied ones with the same experimental setup. Overall, we conclude that constructing insightful dynamic variable ordering heuristics that also utilize a dynamic value ordering heuristic in their decision making process could drastically improve the search effort for some constraint satisfaction problems.

Modular lazy search for Constraint Satisfaction Problems

2001 ◽  
Vol 11 (5) ◽  
pp. 557-587 ◽  
Author(s):  
THOMAS NORDIN ◽  
ANDREW TOLMACH
Keyword(s):  
Constraint Satisfaction ◽  
Search Algorithms ◽  
General Purpose ◽  
Constant Factor ◽  
Constraint Satisfaction Problems ◽  
Combinatorial Search ◽  
Intermediate Data ◽  
Variable Ordering ◽  
New Algorithms ◽  
Simple Search

We describe a unified, lazy, declarative framework for solving constraint satisfaction problems, an important subclass of combinatorial search problems. These problems are both practically significant and computationally hard. Finding solutions involves combining good general-purpose search algorithms with problem-specific heuristics. Conventional imperative algorithms are usually implemented and presented monolithically, which makes them hard to understand and reuse, even though new algorithms often are combinations of simpler ones. Lazy functional languages, such as Haskell, encourage modular structuring of search algorithms by separating the generation and testing of potential solutions into distinct functions communicating through an explicit, lazy intermediate data structure. But only relatively simple search algorithms have been treated this way in the past. Our framework uses a generic generation and pruning algorithm parameterized by a labeling function that annotates search trees with conflict sets. We show that many advanced imperative search algorithms, including conflict-directed backjumping, backmarking, minimal forward checking, and fail-first dynamic variable ordering, can be obtained by suitable instantiation of the labeling function. More importantly, arbitrary combinations of these algorithms can be built by simply composing their labeling functions. Our modular algorithms are as efficient as the monolithic imperative algorithms in the sense that they make the same number of consistency checks, and most of our algorithms are within a constant factor of their imperative counterparts in runtime and space usage. We believe our framework is especially well-suited for experimenting to find good combinations of algorithms for specific problems.

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