Comparing CSP Algorithms Without Considering Variable Ordering Heuristics can be Misleading (original) (raw)

Algorithms for Constraint Satisfaction Problems (CSPs

Many problems in AI can be modeled as constraint satisfaction problems (CSPs). Hence the development of e ective solution techniques for CSPs is an important research problem. Forward checking (FC) with some other heuristics has been traditionally considered to be the best algorithm for solving CSPs while recently there have been a number of claims that maintaining arc consistency (MAC) is more e cient on large and hard CSPs. In this thesis, we p r o vide a systematic comparison empirically of the performances of the MAC a n d F C algorithms on large and hard CSPs. In particular, we compare their performance with regard to the size, constraint density and constraint t i g h tness of the problems. Though there is a trend that MAC e v entually outperforms FC on hard problems as we increase the problem size, we found that the superiority o f M A C o ver FC w ould not be revealed on the hard problems with low constraint t i g h tness and high constraint density u n til the size of these problems is quite large. We also devised a new FC algorithm | FC4, which s h o ws good performance on the hard problems with low constraint tightness and high constraint density. iv I w ould also like to thank Jean-Charles Regin of ILOG for providing his programs, and his assistance in my understanding his algorithms.

A non-binary constraint ordering heuristic for constraint satisfaction problems

Applied Mathematics and Computation, 2008

Nowadays many real problems can be modelled as Constraint Satisfaction Problems (CSPs). A search algorithm for constraint programming requires an order in which variables and values should to be considered. Choosing the right order of variables and values can noticeably improve the efficiency of constraint satisfaction.

Preprocessing versus Search Processing for Constraint Satisfaction Problems

2016

A perennial problem in hybrid backtrack CSP search is how much local consistency processing should be done to achieve the best efficiency. This can be divided into two separate questions: (1) how much work should be done before the actual search begins, i.e. during preprocessing?, and (2) how much of the same processing should be interleaved with search? At present there are two leading approaches to establishing stronger consistencies than the basic arc consistency maintenance that is done in most solvers. On the one hand there are various kinds singleton arc consistency that can be used; on the other there are several variants of restricted path consistency. To date these have not been compared directly. The present work attempts to do this for a variety of problems, and in so doing, it also provides an empirical evaluation of the preprocessing versus search processing issue. Comparisons are made using the domain/degree and domain/weighted degree variable ordering heuristics. In g...

Optimization-based heuristics for maximal constraint satisfaction

1995

We present a new heuristic approach for maximal constraint satisfaction of overconstrained problems (MAX-CSP). This approach is based on a formulation of CSP as an optimization problem presented in a previous paper [Meseguer and Larrosa, 95], which has given good results on some classes of solvable CSP. For MAX-CSP, we have developed two heuristics for dynamic variable and value ordering, called highest weight and lowest support respectively, to be used inside the extended forward checking algorithm (P-EFC3).

Mapping the performance of heuristics for Constraint Satisfaction

2010

Hyper-heuristics are high level search methodologies that operate over a set of heuristics which operate directly on the problem domain. In one of the hyper-heuristic frameworks, the goal is automating the process of selecting a human-designed low level heuristic at each step to construct a solution for a given problem. Constraint Satisfaction Problems (CSP) are well know NP complete problems. In this study, behaviours of two variable ordering heuristics Max-Conflicts (MXC) and Saturation Degree (SD) with respect to various combinations of constraint density and tightness values are investigated in depth over a set of random CSP instances. The empirical results show that the performance of these two heuristics are somewhat complementary and they vary for changing constraint density and tightness value pairs. The outcome is used to design three hyper-heuristics using MXC and SD as low level heuristics to construct a solution for unseen CSP instances. It has been observed that these hyper-heuristics improve the performance of individual low level heuristics even further in terms of mean consistency checks for some CSP instances.

Evaluating Constraint Processing Algorithms

1998

Since for most arti cial intelligence problems worstcase analysis does not necessarily re ect actual performance and since informative performance guarantees are not always available, empirical evaluation of algorithms is necessary. T o do that we need to address the question of distributions, and benchmarks. Based on our study of CSP algorithms we propose the use of multiple types of benchmarks and multiple forms of presenting the results. The benchmarks should include: 1. Individual problem instances representing domains of interest, 2. Parameterized random problems, 3. Application-based parameterized random problems. Results should be presented using 1. Average and variances of the data, 2. frequency and distribution graphs, 3. scatter diagrams The target is to identify a small number of algorithms not one that are dominating, namely proved superior on some class of problems. For dominating algorithms we wish to identify problem characteristics on which they are likely to be good.

Complexity Analysis vs. Engineering Design in CSP Algorithms: Contravening Conventional Wisdom Again

2016

In this work we compare simple and ‘advanced’ algorithms that have been used to perform various functions in connection with constraint satisfaction problems (CSPs). These include algorithms for arc consistency, singleton arc consistency, arc consistency used with MAC, maxRPC algorithms, and algorithms for simple table reduction with non-binary constraints. In each case tested so far, we find tradeoffs between efficient implementations of basic operations like constraint checking and elaborations that allow a reduction in the number of these basic operations but add bookkeeping expenses. It is argued that such tradeoffs must be given more thorough consideration. This also suggests that there are interesting theoretical problems in this connection that have not yet received the attention they merit. Finally, the possibility that certain psychological biases have affected the analysis of algorithms in this area is considered.

Heuristic techniques for variable and value ordering in CSPs

A Constraint Satisfaction Problem (CSP) is a powerful framework for representing and solving constraint problems. When solving a CSP using a backtrack search method, one important factor that reduces the size of the search space drastically is the order in which variables and values are examined. Many heuristics for static and dynamic variable ordering have been proposed and the most popular and powerful are those that gather information about the failures during the constraint propagation phase, in the form of constraint weights. These later heuristics are called conflict driven heuristics. In this paper, we propose two of these heuristics respectively based on Hill Climbing (HC) and Ant Colony Optimization (ACO) for weighing constraints. In addition, we propose two new value ordering techniques, respectively based on HC and ACO, that rank the values based on their ability to satisfy the constraints attached to their corresponding variables. Several experiments were conducted on various types of problems including random, quasi random and patterned problems. The results show that the proposed variable ordering heuristics, are successful especially in the case of hard random problems. Also, when using the proposed value and variable ordering together, we can improve the performance particularly in the case of random problems.

A Normative-Prescriptive-Descriptive Approach to Analyzing CSP Heuristics

2017

This paper presents a general framework for analyzing heuristics for constraint solving, including backtracking and arc consistency algorithms. It will emphasize heuristics for variable selection during search, since this is where major differences are found. In earlier work two basic approaches to this problem were developed. The first was a general theoretical framework for different types of heuristics, which characterized ideal performance so that the actual performance of heuristics could be compared to this standard. The second involved the discovery that, while there are a large number of features that can be used for heuristic decisions in variable ordering, differences in effectiveness boil down to only two basic “heuristic actions”. The present paper applies basic ideas from decision analysis to characterize these two approaches to better understand their status and interrelations. It shows that the first is essentially a normative decision analysis, and that models of thi...

Solution Techniques for Constraint Satisfaction Problems: Foundations

Artificial Intelligence Review, 2001

Conventional techniques for the constraint satisfaction problem (CSP) have had considerable success in their applications. However, there are many areas in which the performance of the basic approaches may be improved. These include heuristic ordering of certain tasks performed by the CSP solver, hybrids which combine compatible solution techniques and graph based methods which exploit the structure of the constraint graph representation of a CSP. Also, conventional constraint satisfaction techniques only address problems with hard constraints (i.e. each of which are completely satisfied or completely violated, and all of which must be satisfied by a valid solution). Many real applications require a more flexible approach which relaxes somewhat these rigid requirements. To address these issues various approaches have been developed. This paper attempts a systematic review of them.